Review Article A Tutorial on Optical Feeding of Millimeter...

Review ArticleA Tutorial on Optical Feeding of Millimeter-Wave Phased ArrayAntennas for Communication Applications

Ivan Aldaya1 Gabriel Campuzano1 Gerardo Castantildeoacuten1 and Alejandro Aragoacuten-Zavala2

1Department of Electrical and Computer Engineering Tecnologico de Monterrey Avenida Eugenio Garza Sada 250164849 Monterrey NL Mexico2Department of Electronics and Mechatronics Tecnologico de Monterrey Campus Queretaro Epigmenio Gonzalez 50076130 Queretaro QRO Mexico

Correspondence should be addressed to Ivan Aldaya ivanaaldayaieeeorg

Received 14 January 2015 Revised 9 April 2015 Accepted 16 April 2015

Academic Editor Felipe Catedra

Copyright copy 2015 Ivan Aldaya et al This is an open access article distributed under the Creative Commons Attribution Licensewhich permits unrestricted use distribution and reproduction in any medium provided the original work is properly cited

Given the interference avoidance capacity high gain and dynamical reconfigurability phased array antennas (PAAs) have emergedas a key enabling technology for future broadbandmobile applicationsThis is especially important at millimeter-wave (mm-wave)frequencies where the high power consumption and significant path loss impose serious range constraints However at mm-wavefrequencies the phase and amplitude control of the feeding currents of the PAA elements is not a trivial issue because electricalbeamforming requires bulky devices and exhibits relatively narrow bandwidth In order to overcome these limitations differentoptical beamforming architectures have been presented In this paper we review the basic principles of phased arrays and identifythe main challenges that is integration of high-speed photodetectors with antenna elements and the efficient optical control ofboth amplitude and phase of the feeding current After presenting the most important solutions found in the literature we analyzethe impact of the different noise sources on the PAA performance giving some guidelines for the design of optically fed PAAs

1 Introduction

Frequency saturation is the sword of Damocles hanging overhigh-capacity wireless systems [1 2] With an outstandingincrease of bandwidth demand the provisioning of futurewireless broadband multimedia applications is uncertainIn this context the use of millimeter-wave (mm-wave)frequencies has been long recognized as a solution to thisspectrum scarcity issue [3] Different unlicensed mm-wavebands have been proposed for wireless local area networks(WLANs) for exampleWiGig that operates at 60GHz [4] aswell as for wireless personal area networks (WPANs) such asIEEE 80215c [5] and ECMA387 [6] and multi-Gbps wirelessbackup [7 8] In addition it is widely accepted that upcoming5G mobile systems will operate at frequencies far above theUHF band [9 10] It goes without saying that migrationto higher frequencies opens a new world of opportunitiesHowever this awesome capacity increase is achieved at theexpense of more complex and power hungry electronicsand more significant wireless path loss [11] In this sense

the limited radiation power alongside higher path losses[12] makes necessary the use of highly directional antennasAlthough in back-haul mm-wave links antennas can bemechanically oriented in mobile systems the transmittermust dynamically control the radiation pattern in order topoint to the desired receiver Phased array antennas (PAAs)have the capacity of varying their radiation pattern a featureknown as beamforming which makes them a key enablingtechnology for either mm-wave access networks [13] or 5Gmobile systems [14] In addition for handling path loss whilekeeping low radiation power dynamically controlled PAAsprovide a higher degree of security [15] improve robustnessto multipath [16] and reduce cochannel interference [17]which further enhances the aggregated capacity

At frequencies below 5GHz great advances have beenmade in compact and low consumption integrated PAAsmaking them an everyday reality that is in 3G and 4Gsystems However at higher frequencies the fabrication ofbroadband low-loss phase delays required to perform beam-forming poses a serious challenge First implementations

Hindawi Publishing CorporationInternational Journal of Antennas and PropagationVolume 2015 Article ID 264812 22 pageshttpdxdoiorg1011552015264812

2 International Journal of Antennas and Propagation

relied on ferrite nucleus that resulted in bulky and heavyarrays [18] As higher degree of integration was requiredarray weight and size decreased progressively [19] After-wards microelectromechanical systems (MEMSs) emergedenabling the implementation of true time delay (TDD)lines which presented significantly broader bandwidth thanferrite-based phase shifters [20] In parallel since the earlydays of microwave photonics different optical techniquesfor controlling the phase of an RF signal were proposed[21 22] Optical techniques have the advantages of being ableto deal with higher RF frequencies as well as to present asignificantly broader bandwidth and lower losses comparedto their electrical counterpart [23] making optical control anattractive approach for mm-wave smart antennas Howeveroptical feeding still presents two significant challenges on theone hand the integration of a fast photodiode (PD) with anantenna requires a thorough design that should pay specialattention to power budget analysis On the other hand phaseand amplitude control of the antenna elements must be donein an efficient way

Several previous books and tutorials have analyzed PAAs[24] ormicrowave photonics [21 22] systems including someaspects of optical feeding of phased arrays Reference [25] isdevoted completely to the application of photonics inmodernradar applications It includes an extensive review of photonictechniques as well as a detailed background but it does notconsider the particularities of mm-wave systemsThe presentpaper constitutes to the best of our knowledge the firstwork fully devoted to covering the particular problems andchallenges of the optical feeding of PAAs operating at mm-wave frequencies Furthermore the literature review allowedus to classify the different beamforming architectures whichwere compared in terms of their performance We had twoaudiences in mind when we wrote this tutorial it is orientedto antenna engineers that want to get some knowledge onthe work done in the optical domain as well as to opticalengineers that require knowing the characteristics of thesignals that must be generated Therefore this work pretendsto be to some extent self-contained which requires somebasic concepts that are included in the paper

The paper is organized as follows Section 2 introducesthe fundamental concepts required for the rest of the paperas well as the nomenclature that we will use Section 3is dedicated to the integration of fast PDs with antennaelements whereas Section 4 presents the different opticalarchitectures as well as particular techniques to control theamplitude and phases of the elementsThese architectures arecompared in terms of the PAA performance in Section 5 InSection 6 some research opportunities are listed and finallySection 7 concludes the paper

2 Fundamental Concepts

In this section we describe in more detail the PAA and itsdifferent types as well as the expression for its radiationpattern Later on beam steering beam shaping and beam-forming concepts are explained On the other hand theoptical generation of RF signals is presented paying specialattention to the phase noise of the generated RF signal

(r Θ Φ)

rarrr minus

rarrr 1

rarrr minus

rarrr minus

rarrr 2 rarr

r minusrarrr 3

rarrr

rarrr 1

rarrr 2

rarrr 3

rarrr i

(x1 y1 z1)

(x2 y2 z2)(x3 y3 z3)

(xi yi zi)

A1

A2

A3

Ai = Aiej120595119894

Φ

Θ

z

y

x

rarrr i

Figure 1 Sketch of a PAA for the calculation of its radiation patternΘ azimuthal angle Φ elevation angle 119903 = (119903 ΘΦ) position ofthe point of interest in spherical coordinates vec119903

119894= (119909119894 119910119894 119911119894)

position of the 119894th antenna element 119860119894complex amplitude of the

feeding currents which can be expressed in terms of the real-valuedamplitude 119860

119894 and phase 120595

119894

21 Phased Array Antennas The scheme of a PAA is acollection of coherently radiating elements that can be inde-pendently fed [26]The elements which are usually identicalare therefore fed with signals at the same frequency butwith possibly different phases and amplitudes PAAs can beclassified according to different features if each element hasa dedicated oscillator then the PAA is said to be active [27]in contrast to passive phased arrays where all the feedingcurrents derive from the same oscillator Depending on thegeometrical configuration a PAA can be linear if the antennaelements are arranged in a line planar if they are in a planeor conformal when the elements are placed on a 3D surfaceUniformPAAs are thosewhere the element positions conformto a regular grid whereas nonuniformPAAs are arrayswith anirregular grid [17] When the amplitudes relation and relativephases of the feeding currents do not vary on time the PAAis static whereas when phases and amplitudes of the elementsare varied it is denominated dynamic PAA By a properdesign PAAs present high gain and dynamic flexibility thatjustify them as a key element in modern communicationsystems

A general PAA is sketched in Figure 1 where the positionof the 119894th antenna element is denoted by 119903

119894= (119909119894 119910119894 119911119894) and

the complex amplitude of the feeding current by119860119894= 119860119894119890119895120595119894

The radiation pattern of the 119873-element PAA can be foundapplying the superposition principle at an arbitrary position

International Journal of Antennas and Propagation 3

119903 = (119903 ΘΦ) The total electrical field strength at 119903 can beexpressed as

119864 ( 119903) =

119873

sum

119894=1119864119894 ( 119903)

=

119873

sum

119894=1

radic21205780119866 (ΘΦ)

4120587119860119894119890119895120595119894

1198901198952120587| 119903minus 119903119894|119891RF119888

1003816100381610038161003816 119903 minus 119903119894

1003816100381610038161003816

(1)

where 119864119894( 119903) is the contribution of the 119894th element 1205780 is the

intrinsic impedance of the vacuum 119866(ΘΦ) is the gain ofeach element as a function of the elevation angle Θ andazimuthal angleΦ 119891RF denotes the operation frequency and119888 denotes the speed of light in the vacuum The previousexpression can be rearranged grouping the terms related tothe amplitude and phase

119864 ( 119903) =

119873

sum

119894=1radic21205780119866 (ΘΦ)

4120587 1003816100381610038161003816 119903 minus 119903119894

1003816100381610038161003816

2 119860119894

⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟

Amplitude term

119890119895(120595119894+2120587| 119903minus 119903119894|119891RF119888)⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟

Phase term (2)

In the far-field region also known as Fraunhofer region | 119903| ≫

| 119903119894| and therefore | 119903 minus 119903

119894| asymp | 119903| = 119903 that is the fields radiated

by the different elements are attenuated in the same wayThisis not the case of the phase where the phase differences leadto an interference pattern The phase of each contribution iscomposed of the phase of the feeding amplitude 120595

119894 and a

space-dependent term 2120587| 119903 minus 119903119894|119891RF119888 that can be written in

terms of the element coordinates according to

1205951015840

119894( 119903) =

2120587119891RF119888

(sinΘ sdot (119909119894cosΦ+119910

119894sinΦ)+ 119911

119894cosΘ) (3)

If the PAA is correctly designed to avoidmismatching amongits elements [28] after far-field approximation and takingthe common factor out of the summation the electric fieldstrength acquires the following form

119864 ( 119903) = radic21205780119866 (ΘΦ)

41205871199032sdot

119873

sum

119894=1119860119894119890119895(120595119894+120595

1015840

119894) (4)

The first factor in (4) depends only on the antenna elementand the spatial coordinates through the element radiationpattern On the contrary the second term does not dependon the characteristics of the antenna element but on theirarrangement and feeding that is 119860

119894and 120595

119894 It is denoted

as array factor (AF) and represents the spatial interferenceamong the different elements of the array

AF (ΘΦ) =

119873

sum

119894=1119860119894119890119895(120595119894+120595

1015840

119894) (5)

In PAAs the position and shape of the elements are typicallyfixed and therefore the radiation pattern is controlledthrough the feeding of the elements varying either their

0 05 1 15

0

5

10

minus15 minus1 minus05minus5

Θ (rad)

|AF(Θ)|

(dB)

RectangularTriangular

Cosine

(a)

0

1

2

1 2 3 4 5 6 7 8Antenna element i

|Ai|

(b)

1 2 3 4 5 6 7 8

02

minus2

Antenna element i

Ang

leA

i

(c)

Figure 2 Beam steering through phase control of an 8-elementlinear array (a) Resulting AF for Φ = 0 (b) amplitudes of theweights and (c) the phase of the elements

amplitudes phases or both of themThe radiation pattern ofthe PAA can be expressed in terms of the AF as

119866PAA (ΘΦ) = 119866 (ΘΦ)|AF (ΘΦ)|

2

sum119873

119894=11003816100381610038161003816119860 119894

1003816100381610038161003816

2 (6)

Usually in PAA systems the antenna elements are notvery directional since otherwise the PAA could be onlydirected within a narrow range [29] Under this assumptionthe radiation pattern of the elements can be consideredisotropic and the gain of the PAA is then given mainly by theAF term Therefore it can be approximated by

119866PAA (ΘΦ) asymp|AF (ΘΦ)|

2

sum119873

119894=11003816100381610038161003816119860 119894

1003816100381610038161003816

2 (7)

By controlling the amplitude and phase of each elementfeeding current both beam steering (controlling the directionof maximum radiation) and beam shaping as well as themore general beamforming can be implemented Both beamsteering Figure 2 and beam shaping Figure 3 using a 1 times 8linear PAA are shown Beam steering is usually accomplishedby applying the same amplitudes to the different antennaelements and setting linearly increasingdecreasing phases ascan be seen in Figures 2(b) and 2(c) In linear PAAs thesephases can be achieved applying a differential time delay 120591



Cosine

0 05 1 15

0

5

10


Θ (rad)

|AF(Θ)|

(dB)

(a)

0

1

2


|Ai|

(b)

1 2 3 4 5 6 7 8

02

minus2

Antenna element i

Ang

leA

i

(c)

Figure 3 Beam shaping through amplitude control of an 8-elementlinear array (a) Resulting AF for Φ = 0 (b) amplitudes of theweights and (c) the phase of the elements

which is related to the desired angle of maximum radiation[30]

ΘMAX = sin (2120591119891RF) (8)

On the other hand beam shaping is typically performedby applying different current amplitudes to antenna elementsFigures 3(b) and 3(c) show the amplitudes and phases of thefeeding currents of the PAA elements Uniform amplitudesresult in the highest gain that is the narrowest main lobeWhen the amplitudes of the elements aremodulated the lobeiswider and the gain reducedHowever it is important to notethat the amplitude of the sidelobes is significantly reducedwhich can be important for some applications In additionthe nulls of the radiation pattern can be set at desired positionavoiding interference

From an implementation point of view the phase andamplitude of the currents can be calculated employing adigital signal processor or can be selected from a preconfig-ured table [17] The former denominated adaptive antennaspresents better performance since it can adapt more preciselyto the channel being able to carry out interference avoidancebut may require complex algorithmsThe latter named beamswitching is less complex but the degree of precision to pointthe main lobe is not so good

22 Photonic Generation of mm-Wave Signals In recentyears a plethora of photonicmm-wave generation techniques

have been proposed [31 32] A literature review reveals thesignificant effort of different research groups to reduce thesize and complexity while increasing the power efficiency ofphotonic mm-wave generators First generation techniquesbased on modulating a free-running laser [33] soon becameobsolete due to their narrow bandwidthThey were overcomeby optical sideband injection locking [34 35] andmodulationof lasers subject to strong optical injection [36] Howeveralthough these techniques present exceptional performancein terms of spectral purity they are difficult to configureand require relatively precise temperature control [21] Withthe advances in broadband modulators techniques basedon external modulation gained popularity especially thoseemploying frequencymultiplication which relaxed the band-width requirements of both themodulator and the associatedelectronics [37] Furthermore external modulation showedits full potential with the advection of photonic chips thatintegrated the laser source together with an electroabsorp-tion modulator [38] Simultaneously mm-wave generatorsbased on alternative approaches have been investigated forinstance in [39] where a passive mode-locked laser is used toavoid the high-frequence electrical oscillator In this case allthe modes of the laser are modulated with the same infor-mation but different modes can be used to simultaneouslygeneratemultiple RF signals [40] If a high number of antennaelements are to be fed the number of high power modesof a semiconductor mode-locked laser would be insufficientIn such cases optical comb generators based on highlynonlinear devices may be employed [41] This techniquerequires an optical amplifier and is difficult to integrate butit is capable of generating more than 1000 highly correlatedtones with 50GHz frequency separation In conclusion thebroad variety of photonic mm-wave generation techniquescan be exploited to meet the required specifications eitherlow cost or high number of channels

Figure 4 shows a simplified photonic mm-wave genera-tion anddistribution system alongside the spectra at differentstages of the system The mm-wave signal is generated bybeating at PD spectral components separated by the desiredRF frequency Even if some previous papers propose thegeneration of mm-wave signals using several modulatedfields [39 42] optical single sideband (OSSB) modulationcomposed of two optical fields one unmodulated and theother modulated with the information signal is preferablesince it ismore robust to fiber dispersion [43] AnOSSB signalcan be expressed mathematically as

119864 (119905) = 11986401 (119905) sdot exp 119895 [21205871198911119905 + 1206011 (119905)] +119898 (119905)

sdot 11986402 (119905) sdot exp 119895 [21205871198912119905 + 1206012 (119905)] (9)

where1198911 and1198912 are the optical frequency of the unmodulatedand modulated fields respectively being related through|1198912 minus 1198911| = 119891RF 11986401(119905) and 11986402(119905) are the real-valuedamplitudes accounting for the intensity fluctuation whereas119898(119905) is a complex modulating signal that allows modelingboth amplitude and in-phasequadrature modulations 1206011(119905)and1206012(119905) are the phase noise of both fields which are typicallymodeled as Wiener processes [44]


fRF fRF fRF

fRFfRFf1 f2

E(t) iPD(t) iRF(t)BPFPDmm-wavegenerator

m(t)

Figure 4 Photonic mm-wave generation and distribution systemand spectra at different stages of the system

TheOSSB signal is detected by a photodetector (PD) witha bandwidth exceeding 119891RF Given the quadratic responseof the PD to the incident optical field the photogeneratedcurrent 119894PD(119905) is proportional to the square of the fieldmodulus

119894PD (119905) = 119877 |119864 (119905)|2+ 119899 (119905) = 119877 [119864 (119905) sdot 119864 (119905)

lowast] + 119899 (119905) (10)

where the responsivity 119877 and the noise of the PD 119899(119905) thatis considered as an additive white Gaussian noise (AWGN)accounting for both the thermal and shot noise The photo-generated current consists of low-frequency components thatare filtered out by a band-pass filter (BPF) and a signal around119891RF which acquires the following expression

119894RF (119905) = 119877 sdot 11986401 (119905) 11986402 (119905)

sdot (Re 119898 (119905) cos [2120587119891RF119905 + Δ120601 (119905)]

sdot Im 119898 (119905) sin [2120587119891RF119905 + Δ120601 (119905)]) + 1198991015840(119905)

(11)

or in a more compact form

119894RF (119905) = 119877 sdot 11986401 (119905) 11986402 (119905) sdot |119898 (119905)|

sdot cos [2120587119891RF119905 + 120601119898 (119905) + Δ120601 (119905)] + 119899

1015840(119905)

(12)

In (12) |119898(119905)| and 120601119898(119905) represent the amplitude and phase of

the modulating signal 119898(119905) respectively Therefore the gen-erated signal is corrupted by amplitude fluctuations whichis mainly caused by the lasersrsquo relative intensity noise (RIN)the filtered AWGN 1198991015840(119905) and the phase noise Δ120601(119905) givenby 1206012(119905) minus 1206011(119905) Hence Δ120601(119905) depends on both individualstatistical properties of 1206011(119905) and 1206012(119905) and their correlationpropertiesThe spectral properties of the photogenerated cur-rent have been studied in detail in [44 45] from which twoparticular cases can be distinguished when 1206011(119905) and 1206012(119905)are completely decorrelated the generated signal presents asignificant phase noise If distributed feedback (DFB) laserswith linewidth in the order of MHz are used the phase noisewill be the limiting impairment degrading the signal qualityWhen the fields have correlated phase noises they compen-sate each other and RF carriers with high spectral purity aregenerated Highly correlated tones can be achieved by usingexternalmodulation [46] by using fields generatedwithin thesame laser cavity [40] or bymeans of optical injection locking

of two lasers to a common master laser [47] In particulardepending on the PAA feeding architecture the system maybe very sensitive to the phase noise of the RF signal sinceas already discussed the shape of the radiation pattern varieswith the phase difference among antenna elements

3 Antenna Integration with High-Speed PDs

Antenna integration is a key factor in building compactand low-cost PAAs We first present the different antennaintegration techniques and then the state-of-the-art highoutput power and broad-bandwidth PDs Afterwards someissues related to the PD-antenna integration are discussed

31 Integrated Phased Arrays The significant research efforthas made integrated antennas a reality in everyday life Thereis no need to be very old to remember mobile terminalswith extensible antennas It is not only a matter of aestheticsbut mainly an issue of cost and reliability Design maturityallows antennas to operate at difference bands with highefficiency at frequency below 10GHz We can distinguishtwomain types of integrated antennas (i) coplanar antennaswhere the antenna and the ground plane are at the samelevel [48] Figure 5(a) and (ii) multilayer antennas where thefeeding networks (including the phase shifters and amplitudecontrollers) are at different planes [49] which are shownin Figure 5(b) Typically coplanar antennas are cheaper andeasier to manufacture since a single metal layer is requiredhowever as operation frequency increases the isolator-induced losses result in a poor efficiency At mm-wavefrequencies where power efficiency is critical the multilayerapproach is preferable In this sense the feeding network isbuilt on a highly conductive semiconductor substrate whileantenna elements can be built using a lower conductivitysemiconductor layer [50] Between the feeding networklayer and the antenna layer a low density isolator (oftendenominated foam) is placed in order to further reduce thelosses The connection between both semiconductor layersis typically accomplished using wire-like structures howeverat high frequencies coupling structures have been shown toimprove the array performance [51]

32 High-Speed PDs Given the band structure of the siliconwith a band gap of 111 120583m it is transparent in both 2ndand 3rd optical communication windows (ie at 1300 and1550 nm) However in recent years impressive advances in Si-based PDs have beenmade in [52] a SiGe PDwith a 628GHzbandwidth is presented andmore recently a Selenium dopedPD exhibiting 20GHz bandwidth was reported [53] Never-theless despite such breakthroughs bandwidth in the orderof mm-wave has only been achieved using IIIndashV elementsInP GaAs and other ternary or quaternary combinations[54]

Typically PDs are composed of three semiconductorlayers a 119875-doped layer an intrinsic layer and an 119873-dopedlayer as shown in Figure 6(a) When the PD is illuminatedby a light beam some of the incident photons interact withthe semiconductor (mainly within the intrinsic layer) and are


Groundplane

GroundplaneAntenna

Substrate

(a)

Groundplane

Groundplane

Antenna

Substrate

Foam

(b) (c)

Figure 5 Antenna integration techniques (a) coplanar antenna and (b) multilayer antenna (c) Deconstruction of a multilayer antenna

h

Conduction band

Absor

ption

Valence

N

P

band

(a)

h

Conduction band

Valence band

Bloc

king

laye

r

Abso

rptio

n

N

P

(b)

Figure 6 Different PD structures (a) PIN-PD and (b) UTC-PD

annihilated generating a hole-electron pair through the so-called photoelectric phenomenon The holes and electronsare drifted by an applied electric field which generates acurrent proportional to the incident optical power [55] Thefundamental bandwidth of the PD is limited by the diffusiontime which is the time required by the generated holes andelectrons to reach the electrodes This time can be reducedby shortening the intrinsic layer of the PD but this resultsin a significant efficiency reduction and consequently thedynamic range also decreases Alternatively diffusion timecan be reduced if only high-mobility carriers are used Uni-travelling carrier (UTC) PD which is shown in Figure 6(b)blocks the diffusion of holes and uses only electrons as activecarriers for photogeneration [56 57] UTC-PD has provedexceptional performance in terms of output power andbandwidth in [58] 20mWis achievedwith a 3-dB bandwidthof 100GHz Recently a more refined scheme is reported withenhanced power and bandwidth 25120583W and 09 THz [59]

33 Issues with the PD-Antenna Integration Antenna inte-gration with high-speed PDs poses two main issues onthe one hand the impedance matching must be ensuredThis can be achieved by well-known microstrip impedancematching networks [60] In [61] the integration of a UTC-PD with a CPA antenna is reported whereas in [56 57]integrationwithmultilayer antenna is presented in [56] a log-periodic antenna is used whereas in [57] a path antenna isused On the other hand integration of antennas with PDsmakes the inclusion of power amplifier between the PD andthe antenna extremely difficult Consequently the radiatedpower is limited by the PD power performance However theuse of PAA helps in overcoming this power limitation

As stated the power radiated by each element is limitedby the output power of the PD and is given by

119875element = 1198900 sdot 119875output (13)

where 1198900 is the antenna efficiency accounting for theimpedance mismatch as well as the ohmic loss and 119875output


is the power delivered by the PD in linear units However themaximum radiated power radiated by an 119873-element PAA ishigher

119875total = 119873 sdot 119875element (14)

And the equivalent isotropic radiated power (EIRP) in linearunits results to be

EIRP = 119875total sdot 119866PAA1003816100381610038161003816max (15)

Therefore increasing the number of antenna elements has atwofold effect first the total radiated power grows linearlywith the number of elements and second since the maxi-mum gain of the PAA increases as the number of elementsdoes the EIRP is further enhanced A higher number ofelements however typically results in significant splitting lossin the optical distribution network whichmay require opticalamplification that is relatively easy to integrate with the PDarray

4 Optical Beamforming

Given the necessity for configurable radiation patternsbeamforming has attracted an increasing attention Particu-larly a lot of effort has been dedicated to the design of broad-bandwidth optical beamforming circuits which typically relyon true time delays (TTDs) [62] In systems operating atfew GHz digital implementation of TTDs has emerged asa flexible solution that outperforms analog implementationboth in steering speed and flexibility with similar powerconsumption [63] In systems operating at mm-wave fre-quencies analog-to-digital and digital-to-analog conversionsare prohibitively expensive and power consuming and con-sequently digital TTDs are not feasible and analog TTDs arechallenging Since in the optical domain broadbandTTDs arerelatively easy to implement optical beamforming appears asan attractive approach [64] In this section we review some ofthemost promising approaches both for amplitude and phasecontrol

41 Optical Architecture for Feeding Antenna Elements Anoptical feeding architecture is typically composed of severalsubsystems single or multiple photonic mm-wave genera-tors an optical beamforming network (OBFN) an opticaldistribution network (ODN) and the antenna unit thatincludes the phased array alongside the broad-bandwidthPDs The photonic mm-wave generator is responsible forgenerating the optical signal that when detected at the PDresults in the desired mm-wave signal In the OBFN thephases and amplitudes of the optical tones are modifiedin order to control the AF of the PAA whereas the ODNis used to communicate signals either from the mm-wavegenerator to the OBFN in the case of on-site beamformingor from the OBFN to the antenna unit if centralized controlis used Typically the ODN accounts for passive elementssuch as splitters and fiber as well as amplifiers that enablelonger distance or higher radiated power Photonic feedingarchitectures can be divided between those with on-site

OBFN and those with centralized OBFN On the other handsome architectures use the same wavelength to feed thedifferent antenna elements while some other architectureshave a dedicated wavelength for each antenna element Thelatter can be further classified according to the mm-wavegeneration type that is if the different optical signals aregenerated using multiple mm-wave generators or a singlegenerator based on a multiwavelength source

411 Optical Feeding Architectures Using a Single WavelengthFigure 7 shows architectures (a) with centralized OBFN and(b) with on-site OBFNThemost striking advantages of thesearchitectures are the lack of demultiplexingmultiplexingdevices and a relaxed frequency stability requirement Incomparison centralized beamforming is preferable since theoptical amplifier is shared by the different antenna elementswhile on-site beamforming requires multiple parallel ODNswhich increases the system cost However the splitting loss inthe case of on-site OBFN may limit the number of elementsto be fed

412 Optical Feeding Architectures Using Multiple Wave-lengths The use of multiple wavelengths typically one perantenna element offers the possibility to multiplex the differ-ent signals into a single fiber Unfortunately the advantagesderived from multiplexing are achieved at the expense of ahuge occupied spectrum which hinders the feeding of mul-tiple base stations using a single fiber In Figure 8 differentschemes are presented single mm-wave generator with on-site OBFN Figure 8(a) and centralized OBFN Figure 8(b)as well as architectures using multiple mm-wave generatorswith on-site OBFN Figure 8(c) and centralized OBFNFigure 8(d) The higher complexity of multiwavelength mm-wave generators is countervailed by the reduction of thenumber of required temperature control modules

42 Photonic Control of Feeding Amplitudes Most of thereported works in the literature focus on optical phasecontrol obviating amplitude control This can be attributedto the a priori simple implementation but it still deservessome attention The amplitude can be controlled in twodifferent ways by directly controlling the emission power ofthe mm-wave generator(s) or by means of variable opticalattenuators The power control can operate on one of the twobeating tones or in both of them depending on themm-wavegeneration technique

421 Amplitude Control through the Emission Power of themm-Wave Generators This approach is cost efficient since itdoes not require additional optical devices but it is limitedto feeding architectures where each antenna element is fed byan independent mm-wave generatorThat is it is not suitableif a single source is used Additionally in many cases thevariation of the bias of the optical sources within the mm-wave generator leads to a frequency deviation because ofthe coupling between the real and imaginary parts of therefractive index in the semiconductor [65 66] If the twobeating fields are shifted by a different amount the resulting


Single-wavelengthmmW generator

mmW generation

Amplitude andphase control



Antenna unitOBFNODN

Element 1

Element 2

Element N1205820

1205820

1205820

(a)

mmW generator 1

mmW generator 2

mmW generator N

mmW generation




Antenna unitOBFN ODN

Element 1

Element 2

Element N1205820

1205820

1205820

(b)

Figure 7 Optical feeding architectures using a single wavelength (a) on-site beamforming and (b) centralized beamforming ODN opticaldistribution network OBFN optical beamforming network

RF frequency differs from the nominal frequency degradingthe system performance

422 Amplitude Control through Variable Optical AttenuatorIt is obvious that amplitude control based upon opticalattenuators is more expensive than the control based ondriving current In addition it is a priori more complicatedto integrate and adds some insertion losses but it presentssome advantages that justify its adoption it does not affectthe frequency of the optical signals and it can be employedeven if a multiwavelength mm-wave generator is used Thistechnique can be implemented using different types of vari-able optical attenuators such as LiNb

3-basedmodulators [67]

or more integrable semiconductor based modulators [68]

43 Photonic Control of Feeding Phases Thephotonic controlof the phases of PAA elements has attracted more attentionthan amplitude control because of the bandwidth limit of theelectrical phase shifters Consequently many different opticaltechniques can be found in the literature In some cases thephase is controlled directly in the optical generation process[69 70] which results in nonlinear phase control but inmostcases an optical true time delay (TTD) is applied after theoptical signal is generated Phase control using TTD is linearin the sense that it does not exploit any nonlinear mechanismthat depends on the power of the incident light Thereforeit is more flexible and simple being more suitable for realapplications When employing TTDs the phase control ofthe antenna element is achieved delaying the optical beating

components Neglecting the phase noise the electrical fieldbefore photo detection can be expressed as

119864 (119905) = 1198641 (119905 minusΔ1198791) + 1198642 (119905 minusΔ1198792)

= 11986401 exp [11989521205871198911 (119905 minusΔ1198791)]

+ 11986402 exp [11989521205871198912 (119905 minusΔ1198792)]

(16)

whereΔ1198791 andΔ1198792 are the delays applied to each componentThe RF photogenerated current then acquires the form of

119894RF (119905) = 2119877 sdot 1198640111986402

sdot cos [21205871198911 (119905 minusΔ1198791) minus 21205871198912 (119905 minusΔ1198792)] (17)

We can define two delay timesΔ119879 = (Δ1198792+Δ1198791)2 and 120575119879 =

Δ1198791minusΔ1198792 corresponding to the common-mode delay and thedifferential delay respectively In thisway the common-modedelay accounts for the average delay induced in both fieldswhereas the differential delay represents the delay differencebetween components Rearranging the previous expression interms of the common-mode and differential delay we get

119894RF (119905) = 2119877 sdot 1198640111986402

sdot cos [2120587119891RF (119905 minus Δ119879) minus 21205871198911 + 1198912

2120575119879]

= 2119877 sdot 1198640111986402 sdot cos [2120587119891RF119905 minus Δ120601CM minusΔ120601diff ]

(18)

In this expression two phase shifts can be identifiedone associated with the common-mode delay Δ120601CM and


MultiwavelengthmmW generator

mmW generation




Antenna unitOBFNODN

Element 1

Element 2

Element N120582N

1205822

1205821

(a)

OBFN ODN

Antenna unit

Element 1

Element 2

Element N120582N

1205822

1205821Amplitude andphase control




mmW generation

(b)

mmW generator 1

mmW generator 2

mmW generator N

mmW generation




Antenna unitOBFNODN

Element 1

Element 2

Element N120582N

1205822

1205821

(c)

mmW generator 1

mmW generator 2

mmW generator N

mmW generation





Element 1

Element 2

Element N120582N

1205822

1205821

120582N

1205822

1205821

(d)

Figure 8 Optical feeding architectures using multiple wavelengths (a) on-site beamforming with a multiwavelength source (b) centralizedbeamforming with a multiwavelength source (c) multiple mm-wave generators with on-site beamforming and (d) multiple mm-wavegenerators with centralized beamforming ODN optical distribution network OBFN optical beamforming network

the other related to the differential delay Δ120601diff which canbe written as

Δ120601CM = 2120587119891RFΔ119879 (19)

Δ120601diff = 21205871198911 + 1198912

2120575119879 (20)

There are two important points to note here first thephase of the generated RF signals can be controlled eitherdelaying single or both beating components Second whenusing one or the other approach we need to consider theother contributionThat is when controlling the phase usingcommon-mode delay the differential delay induced by adispersive medium will add a differential delay and when


controlling the phase through differential delay the commonmode delay induced by the system must be consideredThis becomes especially important as the RF frequencyincreases since the effect of the dispersion is more notoriousFurthermore in schemes using optical double sidebandmodulation the differential delay induced by chromaticdispersion causes frequency selectivity that may significantlyreduce the generated RF power [71 72]

431 Phase Control Based on Common-Mode Delay Phasecontrol using common-mode delay has been extensivelyapplied to PAAs operating at frequencies ranging from fewGHz up to mm-wave frequencies The delay can be inducedchanging the physical length of the path or keeping thephysical length constant but changing the optical length

TTDs using paths with different physical lengths have theadvantage of operating using a constant wavelength sourcewhich reduces the cost of the system However the resultingdelay cannot be continuously tuned but only a set of delayscan be generated This delay discretization does not allowthe implementation of adaptive antennas but it is limitedto beam-switching antennas Configurable TTDs in guidedmeans shown in Figure 9 require different segments of fiberor waveguides and a set of switches that select a path withthe desired length They can be implemented using serialFigure 9(a) or parallel Figure 9(b) architectures as well asswitching matrix which is shown in Figure 9(c) a serialconfigurable TTD with 2 times 2 microelectromechanical system(MEMS) switches is proposed in [73] In [74] switches basedon InP are employed but the delay elements are still fibers Astep ahead in TTD integration is presented in [75] where a3-bit TDD using silicon-on-insulator technology is reportedPools of configurable serial TTDs have been employed tochange the phase of each element independently [30] or ina two-stage architecture that simplifies the 2D operation ofthe PAA [76] In addition it can be used either in single-wavelength systems [73] or in multiwavelength systems [77]Serial configurable TDDs are an inexpensive approach forlow number of antenna elements and applications that do notrequire very precise beamforming A more precise control ofthe delay requires higher number of concatenated switchesthat will increase the insertion loss In order to solve thisissue parallel TTDs have been proposed as in [78] where 32antenna elements are fed with 8-bit resolution delay using asingle TDDequippedwith a 3DMEMSNevertheless parallelTTDs achieve better precision and scalability at the expenseof more complex switches that may present significantcrosstalk [79] In addition the high number of fibers requiredincreases the size of the system which can be reduced bytaking advantage of modern bend-insensitive fibers [80] orintegrated polymer integration [81] Even further precisionand scalability are expected from switching matrix technol-ogy [82] TDDs in free-space optics shown in Figure 10are an alternative to those using guided mean These TDDsinclude schemes using a diffraction mirror in combinationwith a rotatable MEMS [83] Figure 10(a) mechanicallypositioned prisms [84] Figure 10(b) and several approachesusing white cells [85] and their derivatives [86] Figure 10(c)These techniques can feed a high number of antenna elements

On

L 2L 2Nminus1L

Switch 1 Switch 2 Switch N Combiner

(a)

L

2L

CombinerMultiportswitch

(N minus 1) middot L

(b)

Combiners

Splitters

Antennaelement 1

Antennaelement N

middot middot middot

(c)

Figure 9 Phase control using different physical paths and guidedmedium (a) serial configurable TTD and (b) parallel configurableTTD and (c) switching matrix based TTD Green lines show theselected path

with pretty high precision (112 antenna elements with 81possible delays each [86]) but they are complicated toconfigure and very sensitive to mechanical vibrations andtherefore they are not suitable for low-cost applications

A time delay can also be applied changing the refrac-tive index of the propagation path This can be achievedin several ways as shown in Figure 11 the most commonemploys a tunable laser source followed by a dispersivemedium In [87] the dispersive medium is composed of abank of standard singlemode fibersdispersion compensatingfibers with different lengths sketched in Figure 11(a) Thistechnique is employed in [88] using a two-stage configurationto enable 2D beam steering The size of the fiber lens canbe significantly reduced by exchanging the fibers by linearlychirped fiber Bragg gratings (FBGs) [89] which is presented


Rotarymirror

Mirror

Collimator

LL998400

(a)

Mirror MirrorL

L998400

Mechanicallycontrolled

prism

Disp

lace

men

t

(b)

L

L998400

Concave mirror Rotaryconcave mirror

(c)

Figure 10 Phase control using different physical paths in free-space optics (a) using a rotary mirror and a plane reflector (b) employing amechanically positioned prism and (c) being based on a white cell Solid and discontinuous time represent paths with different lengths 119871 and1198711015840 Arrows indicate the displacementrotation for obtaining different lengths

in Figure 11(b) An integrable solution to both fiber andFBG bank is a dispersion engineered material such as aphotonic crystal where dispersion slope can be tailored tomeet the required shape [90] All these techniques permitthe continuous control of the phase allowing not only beamswitching but also adaptive beamforming but they require atunable laser This increases the cost and requires a carefuldesign to achieve long-term stability and avoid mode hoping[91]

432 Phase Control Based on Differential Delay The tech-niques based on controlling the differential delay can bedivided into those using different physical paths for theunmodulated and the modulated fields and those where bothfields are propagated over the same medium but at differentspeed The former requires the two components to be spa-tially demultiplexed which can be achieved by means of ademultiplexer the latter needs a dispersive medium whose

dispersion slope is enough to induce the required phase shiftIn both cases the implementation of PAA at low frequenciesis extremely challenging because the demultiplexing of thesignal requires demultiplexers with very narrow bands orbecause highly dispersive material is needed As operationfrequency increases for instance when feeding mm-wavePAAs the control of the differential delay becomes feasible

Figure 12 shows a scheme where the differential delay iscontrolled applying a phase shift to one of the two fields Thephase shift can be performed using different technologies in[92] the phase shift is performed employing thermoelectricalphase shifters while in [68] the phase control is performedemploying electrically controlled semiconductor devices Inboth cases the optical length of the path of one of thecomponents is varied with a minor power penalty howeverthe latter is preferable given the slower dynamics of thethermoelectrical process In addition this technique allowscontinued phase control and with the advection of Si-based


Antennaelement 1Antenna

element 2Antenna

element 3Antenna

element 4

Antennaelement N

DCFSSMFVariablewavelength

input

Split

ter

(a)


element 2Antenna

element 3Antenna

element 4

Antennaelement N

Variablewavelength

input

Split

ter

1205821

1205822

1205823

120582K

(b)

Figure 11 Phase control using (a) a bank of different standard single mode fibers (SSMF)dispersion compensating fibers (DCF) and (b)concatenation of FBGs

AntennaCombiner

PMSplitter

Mux

PM

PM

element 1

Antennaelement 1

Antennaelement N

Figure 12 Phase control applying a differential delay PM phasemodulation

modulators [93] opens the doors to completely integrated Si-based beamformer networks

Alternatively the phase control can be implementedtaking advantage of the frequency separation between themodulated and demodulated fields in combination with adispersive medium such as an optical fiber Furthermore

a multimode source can be used to simultaneously generatethe signals for the different antenna elements The maindrawback of this technique is the required tunable laser thatas already stated increases the cost and reduces the reliability

5 Noise in Optically Fed PAAs

Optical control of phases and amplitudes of the PAA elementspresents a significantly broader bandwidth and smaller sizethan its electrical counterpart However these improvementsare achieved at the expense of an elevated noise level thatreduces the dynamic range of the system deteriorating itsperformance This effect has been analyzed in [94] for asingle-source architecture and therefore performance of thedifferent feeding architectures remains uncertain In thissection we extend (9)ndash(12) to consider the impact of the noiseon the system We first introduce the most important noisesources that contribute to signal degradation We then iden-tify the twomajor effects of noise that is the time fluctuationof the total radiated power and the random amplitude andphase differences between elements that cause variation of theAF Finally the different architectures are evaluated in termsof the number of antenna elements and the configuration of


Table 1 Summary of the noises in optically fed PAAs

Device Origin Type of noisemm-wavegenerator Spontaneous emission Multiplicative noise

Optical amplifier Amplifiedspontaneous emission Beating noise

Photodiode

Carrier Brownianmotion (thermalnoise)

Additive (powerindependent)

Discrete nature ofphotons (shot noise)

Additive (powerdependent)

the mm-wave generator In order to assess the performancethe feeding system is simulated using VPI TransmissionMaker which is capable of modeling realistically opticalcomponents such as lasers external modulators and PDs

51 Noise Sources and Carrier-to-Noise Ratio Noise mech-anisms in optical systems differ significantly from those inelectronics [55] In particular the power spectral densityof the thermal noise drops after several THz [95] andtherefore in optical systems passives do not induce extranoise [96] Consequently only the active components shouldbe considered as noise sources In the case of optically fedPAAs active devices include the mm-wave generator theoptical amplifier and the PD whose main noise features aresummarized in Table 1

511 Noise of the Optical mm-Wave Generator The two tonesat the output of the optical mm-wave generator are corruptedby both amplitude and phase noises However amplitude andphase fluctuations are not independent of each other but arecoupled according to the Kramers-Kronig relations whichhold in causal linear systems [66] This coupling between theamplitude and phase noises is typically expressed in termsof the Henry factor (also known as linewidth enhancementfactor) and depends on many design parameters such as thegain spectrum and the type of carrier confinement (bulkmultiquantum well and quantum-dot) as well as on someoperational parameters that is the bias current and thepresence of optical injection [97] The amplitude and phasefluctuations are a consequence of the spontaneous emissionevents occurring within the active gain medium Since thespontaneous emission rate is reduced when increasing thedensity of photons the power levels of the amplitude andphase noise are reduced at a higher emission power andtherefore at a higher bias current [65]

For each wavelength the output of the mm-wave genera-tor acquires the form of

119864 (119905) = 11986401 (119905) sdot exp 119895 [21205871198911119905 + 1206011 (119905)] + 11986402 (119905)

sdot exp 119895 [21205871198912119905 + 1206012 (119905)] (21)

which corresponds to (9) with119898(119905) = 1 (for the sake of clarityno data transmission is assumed) The amplitudes 11986401(119905) and

11986402(119905) can be decomposed into a constant component 1198641|2and a fluctuating zero-mean term Δ1198641|2(119905) Consequently119864(119905) can be written as

119864 (119905) = [1198641 +Δ1198641 (119905)] sdot exp 119895 [21205871198911119905 + 1206011 (119905)]

+ [1198642 +Δ1198642 (119905)] sdot exp 119895 [21205871198912119905 + 1206012 (119905)] (22)

Regarding the optical phase noise of the lasers inmost opticalmm-wave generators high correlation between 1206011(119905) and1206012(119905) is forced in order to produce highly spectrally pure RFsignals at the output of the PD

512 Noise of the Optical Amplifier When the optical signalis amplified the amplifier adds extra noise the so-calledamplified spontaneous emission (ASE) noise The amount ofnoise added depends on whether the amplifier is a semi-conductor optical amplifier (SOA) or an erbium-doped fiberamplifier (EDFA) the gain and the power of the incidentlight [55] Then the amplified field 119864amp(119905) is expressed interms of the amplifier power gain 119866 and ASE noise 119899ASE(119905)

119864amp (119905) = radic119866 sdot 119864 (119905) + 119899ASE (119905) (23)

The bandwidth of ASE noise is in the order of magnitudeof the gain bandwidth of the active medium which typicallyranges for tens of THz-s [98]Hence even if at large frequencyscales ASE may have some irregular spectrum it can beconsidered spectrally flat (white) for the bandwidth of oursignal

The amount of ASE noise is typically given in terms of thenoise figure of the optical amplifier Typical values are 4-5 dBfor EDFAs and 8-9 dB for SOAs [96]

513 Noise of the PD In addition to the noises associatedwith the mm-wave generator and the optical amplifier thePD constitutes an additional noise source This contribution119899PD(119905) can be further divided into two components onecaused by the thermal agitation of the electrons and the otherinduced by the discrete nature of the electrons which isdenominated shot noise [99] Both can be considered white inthe bandwidth of interest but while the power of the thermalnoise does not depend on the incident light the power of shotnoise increases linearly with the power of the incident lightConsequently shot noise is more significant at high receivedpower levels

Alongside the induced noise the PDs present losses thatare accounted for through the responsivity 119877 introduced in(10)119877 tends to decrease as the bandwidth of the PD increaseswhich may result to be problematic at high RF systems [56]Then the photogenerated current 119894PD(119905) can be written as

119894PD (119905) =

119877 sdot10038161003816100381610038161003816119864amp (119905)

10038161003816100381610038161003816

2

119871+ 119899PD (119905)

(24)

where the power loss 119871 due to passives (including the phaseand amplitude control) between the amplifier and the PD hasbeen considered


514 Amplitude Noise in the Generated RF Signal Afterintroducing (21)ndash(23) in (24) we obtain the next expressionfor 119894PD(119905)

119894PD (119905) =119877

119871(119866 (119864

201 +119864

202)

+11986611986401 (119905) 11986402 (119905) cos [2120587119891mm119905 + Δ120601 (119905)]

+ 2radic119866Re 119899ASE (119905) 11986401 (119905) exp119895 [21205871198911119905 + 1206011]

+ 2radic119866Re 119899ASE (119905) 11986402 (119905) exp119895 [21205871198912119905 + 1206012]

+1003816100381610038161003816119899ASE (119905)

1003816100381610038161003816

2) + 119899PD (119905)

(25)

Since the power of the ASE noise is typically much lowerthan that of the amplified signal the square of theASEnoise isgenerally neglected After this assumption ASE noise appearsas a beating noise

119894PD (119905) asymp119877

119871(119866 (119864

201 +119864

202)

+11986611986401 (119905) 11986402 (119905) cos [2120587119891mm119905 + Δ120601 (119905)]

+ 2radic119866Re 119899ASE (119905) 11986401 (119905) exp119895 [21205871198911119905 + 1206011]

+ 2radic119866Re 119899ASE (119905) 11986402 (119905) exp119895 [21205871198912119905 + 1206012])

+ 119899PD (119905)

(26)

The RF signal is then obtained by filtering out the low-frequency components Hence the RF signal acquires thenext form

119894RF (119905) asymp119877

119871(11986611986401 (119905) 11986402 (119905) cos [2120587119891mm119905 + Δ120601 (119905)]

+ 2radic119866Re 1198991015840ASE (119905) 11986401 (119905) exp119895 [21205871198911119905 + 1206011]

+ 2radic119866Re 1198991015840ASE (119905) 11986402 (119905) exp119895 [21205871198912119905 + 1206012])

+ 1198991015840

PD (119905)

(27)

where 1198991015840

PD(119905) and 1198991015840

ASE(119905) represent the filtered signals of119899PD(119905) and 119899ASE(119905) This expression can be written in termsof the average and fluctuating terms of the fields giving as aresult

119894RF (119905) asymp119877

119871(119866 [1198641 +Δ1198641 (119905)] sdot [1198642 +Δ1198642 (119905)]

sdot cos [2120587119891mm119905 + Δ120601 (119905)]

+ 2radic119866Re 1198991015840ASE (119905) [1198641 +Δ1198641 (119905)]

sdot exp119895 [21205871198911119905 + 1206011]

+ 2radic119866Re 1198991015840ASE (119905) [1198642 +Δ1198642 (119905)]

sdot exp119895 [21205871198912119905 + 1206012]) + 1198991015840

PD (119905)

(28)

Neglecting the beating between different fluctuations we get

119894RF (119905) asymp119877119866

11987111986411198642cos [2120587119891mm119905 + Δ120601 (119905)]

+119877119866

119871[Δ1198641 (119905) 1198642 +Δ1198642 (119905) 1198641]

sdot cos [2120587119891mm119905 + Δ120601 (119905)]

+2119877radic119866

119871Re 1198991015840ASE (119905) 1198641exp119895 [21205871198911119905 + 1206011]

+2119877radic119866

119871Re 1198991015840ASE (119905) 1198642exp119895 [21205871198912119905 + 1206012]

+ 1198991015840

PD (119905)

(29)

The first term in the previous expression corresponds tothe signal whereas the others are the contributions of thedifferent noise sources (amplitude noise of the mm-wavegenerator the amplifier ASE and the PD additive noise) Asstated in Section 22Δ120601(119905) is the phase difference between thetwo beating fields including the phase noise of both tonesTypically optical mm-wave generators are designed to pro-duce highly correlated tones which results in spectrally pureRF signals [32] A priori these tones could be decorrelated ifthey were delayed by a different amount of time for instanceif phase control based on differential delay is applied causinga power penalty and spectral broadening of the generated RFsignal [43] However according to (20) the amount of timerequired to phase-shift the RF signal by 2120587 is 2(1198911 + 1198912)which is much shorter than the correlation time of the source(the inverse of the linewidth) and therefore has a negligibleeffect [45] If the signal amplitude is much higher than theamplitude of the noise signals zero-crossing distortion canbe neglected and the amplitude noise term 119899

119860(119905) acquires

the form

119899119860 (119905) =

119877119866

119871[Δ1198641 (119905) 1198642 +Δ1198642 (119905) 1198641]

+2119877radic119866

119871Re 1198991015840ASE (119905) 1198641

+2119877radic119866

119871Re 1198991015840ASE (119905) 1198642 + 119899

1015840

PD (119905)

(30)

The power of the amplitude noise 119875119899119860 can be calculated

straightforward after recalling that the different noise contri-butions are not correlated

119875119899119860

= 119875119873source

+119875119873amp

+119875119873PD (31)

with

119875119873source

= (119877119866

119871)

2[Δ1198641 (119905) 1198642 + Δ1198642 (119905) 1198641]

2

119875119873amp

= 2(119877radic119866

119871)

2

1198992ASE (119905) (119864

21 +119864

22)

119875119873PD

= 1198992PD (119905)

(32)


with upper bar denoting the time average operation Equation(32) reveals two important points (i) All terms except 119875

119873PDdecay quadratically with 119871 and consequently for high 119871

values 119875119873PD

becomes dominant (ii) On the other hand forlow 119871 values considering that 119866 typically ranges from 20to 30 dB it is envisaged that 119875

119873sourcewould be the limiting

impairment It is then useful to define the carrier-to-noiseratio (CNR) as

CNR =119875119862

119875119899119860

=119875119862

119875119873source

+ 119875119873amp

+ 119875119873PD

(33)

where 119875119862stands for the carrier power and is given by

119875119862

=12(

1198771198662

11987111986411198642)

2

(34)

515 Phase Noise in the Generated RF Signal Even if phasecorrelation between optical tones is preserved the other noisemechanisms induce phase noise on the generated RF signalThe probability density of the phase noise induced in thephotogenerated current can be calculated according to thisexpression [45]

119901Φ(120601) =

exp (minus120574)

2120587[1+radic2120574 sdot exp (120574cos2120601)

sdot int

radic2120574 cos(120601)

minusinfin

exp(minus119909

2

2)119889119909]

(35)

where 120574 is calculated as

120574 =119875119862

119875119873amp

+ 119875119873PD

(36)

It is important to note that 120574 does not account for the mm-wave generator noise since it does not contribute to the phasenoise

Finally the power of the phase noise can be calculated bynumerically computing the following integral

119875119899120601

= int

+infin

minusinfin

1206012119901Φ(120601) 119889120601 (37)

52 Effects of theNoise on the PAAPerformance Thepreviousexpressions considered a single PD and consequently mustbe extended in order to analyze the effect of noise on PAAwith multiple elements In this analysis it is important to payspecial attention to the correlation among noises affectingthe different antenna elements The amount of correlationwill differ for different architectures resulting in diverseperformance According to this criterion three cases can bedifferentiated

Case 1 The noise contributions of the mm-wave generatorand the optical amplifier are the same for all antennaelementsThis corresponds to the architecture where a single-wavelengthmm-wave generator is used to feed all the antennaelements Figure 7(a)

Case 2 The noise contributions of the mm-wave generatorare correlated but the amplifier and PD contributions areindependent This case models architectures based on mul-tiwavelength mm-wave generators that is Figures 8(a) and8(b)

Case 3 None of the noise contributions are correlated Thisis the case of architectures employing different mm-wavegenerators such as Figures 7(b) 8(c) and 8(d)

It is important to note that in the case of architecturesemploying multiple wavelengths the noise induced by theoptical amplifier at different wavelengths is assumed to beuncorrelated because of the low coherence nature of theadded noise [98]

In order to compare the performances of the differentcases the optical feeding system was simulated using VPITransmission Maker This software enables modeling severalnoise mechanisms as well as the correlation among themIn particular we simulated a mm-wave generator based onoptical frequency doubling using an external modulatorpresented in [37] that generated two highly correlated toneswith 60GHz separation The employed laser source wassimulated using the rate-equation model whose parameterswere set to match those of a standard distributed feedback(DFB) laser a threshold current of 15mA a linewidth of1MHz a RIN of minus145 dBHz and an emission power of10 dBm at 100mA The amplifier noise figure and gain wereset to 4 dB and 20 dB respectively which are typical valuesfor an EDFA The responsivity of the PD 119877 was set to06 AW whereas the thermal noise spectral density was setto 10minus12 A2Hz

For the sake of notation simplicity we rename 119894RF(119905) in(29) to distinguish the currents generated by different PDsfrom now on 119894

119899(119905) will denote the photogenerated current at

RF of the 119899th PD

521 Effects on the Total Radiated Power The total radiatedpower can be expressed as

119875total (119905) = 1205980 sdot (119873

sum

119899=1119877 sdot 119894119899 (119905))

2

(38)

where following the notation in (14) 1205980 accounts for theantenna efficiency and 119873 denotes the number of elements ofthe PAA while 119877 as in (10) represents the PD responsivityThe fluctuation of the total radiated power can be measuredin terms of the normalized power standard deviation that isthe standard deviation of the total emitted power normalizedto the average total emitted power

120590Δ119875

1198750=

radic(119875total minus 1198750)2

1198750

(39)

where 1198750 is the average power given by 1198750 = 119875total(119905)Figure 13 shows the fluctuation of the normalized stan-

dard deviation of the emitted power in terms of the numberof fed elements The figure presents curves for the three


2 4 6 8 10 12 14 16Number of elements

Case 1Case 2

Case 3

10minus3

10minus4

10minus5

10minus6

120590ΔPP

0

Figure 13 Normalized standard deviation of the total radiatedpower as a function of the number of elements for the three casesSolid lines are for a bias current of 50mA and discontinuous linesare for 100mA

cases considering two different driving currents of the laserin the mm-wave generator 50mA (continuous line) and100mA (discontinuous line) Comparing the different casesCase 1 presents a rising trend in the normalized standarddeviation of the radiated power as the number of elementsincreases whereas in Cases 2 and 3 the standard deviationdrops This reduction is explained by the partial cancellationresulting from the lack of correlation among the thermaland shot noises affecting each PD Furthermore in Case 2the noise contributions of the mm-wave generator to thedifferent antenna elements add destructively resulting ineven lower power variation In Case 1 the standard deviationreduction due to destructive addition of noises is overcomeby the reduced CNR since the optical power is shared bythe different elements In regard to the effect of the laserbias current in all cases a higher bias current results inlower power fluctuation This is an expected outcome sinceat higher bias currents the RIN of the source is reducedand consequently the noise contribution of the source islower Comparing the different cases Case 1 presents themost significant improvement which was expected sincein this case the effect of the PD-induced noise is criticaland therefore higher optical emission power considerablyenhances the system performance

522 Effects on the AF In addition to the total radiatedpower fluctuation the noise in the photogenerated currentscauses deviation from the nominal amplitude and phasevalues of each element This amplitude and the phase errorsimpact the AF term of the radiation pattern and shouldbe studied In order to analyze the effect of the feedingarchitecture we will first study the amplitude and phasefluctuation in terms of the number of antenna elements andafterwards we focus on the resulting AF

The amplitude and phase of 119894119899(119905) can be extracted from its

associated analytic signal 119899(119905) = 119894

119899(119905) + 119895 sdot HT119894

119899(119905) where

HTsdot denotes theHilbert transform Amplitude and phase of119894119899(119905) are computed as

119860119899 (119905) = radic(Re

119899 (119905))2+ (Im

119899 (119905))2

120601119899 (119905) = atan

Im 119899 (119905)

Re 119899 (119905)

(40)

The time-dependent nominal values of amplitude 1198600(119905)and phase 1206010(119905) are given by the ensemble average of 119860

119899(119905)

and 120601119899(119905) that is

1198600 (119905) =1119873

119873

sum

119899=1119860119899 (119905)

1206010 (119905) =1119873

119873

sum

119899=1

120601119899 (119905)

(41)

The amplitude and phase deviations Δ119860119899(119905) and Δ120601

119899(119905) of

the current generated at the 119899th PD are then given by

Δ119860119899 (119905) = 119860

119899 (119905) minus1198600 (119905)

Δ120601119899 (119905) = 120601

119899 (119905) minus 1206010 (119905) (42)

The amplitude error will be measured using its normal-ized variance which is inversely related to the CNR that is

1205902119860

1205832119860

=

⟨Δ1198602119899(119905)⟩

⟨1198600 (119905)⟩2 (43)

while the power of the phase error will be evaluated throughits variance

1205902120601= ⟨Δ120601

2119899(119905)⟩ (44)

Figures 14(a) and 14(b) show the normalized variance ofthe amplitude error and the variance of the phase error for thethree cases in terms of the number of antenna elements alsoconsidering two bias currents 50mA and 100mA Similar tothe total radiated power the amplitude and phase fluctuationsin Case 1 degrade as the number of fed antenna elementsincreases which is a consequence of the reduction of thereceived power Cases 2 and 3 on the contrary remainindependent of the number of antenna elements for 119873 gt 4Comparing the three cases the best performance is achievedfor Case 3 whichmay be attributed to themutual cancelationnot only of the PD-induced noise but also of the noiseinduced by the mm-wave generator Regarding the effect ofthe bias current on the amplitude and phase error in Cases1 and 3 significant improvements are achieved when the biascurrent is switched from 50 to 100mA on the other handin Case 2 a minimal improvement is observed This minimalimprovement causes the for small number of fed antennaelements architecture in Case 1 to outperform Case 2



Case 1Case 2

Case 3

10minus3

10minus2

10minus4

10minus5

10minus6

1205902 A120583

2 A

(a)


Case 1Case 2

Case 3

10minus3

10minus2

10minus4

10minus5

10minus6

1205902 120601

(b)

Figure 14 (a) Normalized variance of the amplitude error and (b) variance of the phase error as a function of the number of elements for thethree cases Solid lines are for a bias current of 50mA and discontinuous lines are for 100mA

Errors in the amplitudes and phases of the feeding cur-rents cause the AF to vary over time In Figures 15ndash17 the AFsof the three cases are analyzed for a 1 times 8 PAA when the biascurrent of themm-wave is set to 50mA Subfigures labeled (a)show the blurredAFs where the blurring indicates the degreeof variation of theAF Subfigures (b-d) represent the time evo-lution of119866max and the direction of maximum radiation 120579maxrespectively whereas subfigures (c-e) show the histogram ofthese quantities Looking at the AFs it is clear that their vari-ations are more notorious close to the zeros in particular forCase 1 Comparing the different cases Cases 2 and 3 presentsimilar performance in terms of time variation in 119866max and120579max while Case 1 reveals a significantly higher variation inboth figures of merit These results are in agreement with thecurves presented in Figure 14 where Cases 2 and 3 presentalmost the same phase and amplitude variation whose powerlevel is much lower than that of Case 1

In order to analyze the effect of the number of fedelements we focus on Case 1 since in Cases 2 and 3the variances of amplitude and phase errors remain almostconstant In Figures 18ndash20 the same figures of merit as inFigures 15ndash17 are shown but only for Case 1 and differentnumbers of elements Figure 18 is for 1 times 4 PAA elementsFigure 19 is for 1 times 8 PAA and Figure 20 is for 1 times 16 PAAThese figures reveal that variations of 119866max rise with thenumber of elements while the variation of 120579max reducesThe increment in the variation of 119866max seems logical fromFigure 14 however from the same figure wemight think thatvariation in 120579max should also increase which contradicts theobtained resultsThis discrepancy can be explained by notingthat for higher number of antenna elements the shape of themain lobe of the AF narrows This further causes that thedirection of maximum radiation to be more clearly defined

The analysis of the impact of the noise on PAA per-formance drives an important conclusion effectively PAAsoperating at mm-wave frequencies can be optically fed atleast for a moderate number of elements We also concludethat the chosen architecture has a critical effect on the ampli-tude and phase errors of the antenna elements thus feedingarchitecture based on multiple mm-wave generators is theoptimum solution Nevertheless a lower cost approach such

0 05 1 15

0

869

94

08

120579 (rad)minus15 minus1 minus05

minus40

minus20

minus80 5 10 15

Time (120583s)

0 5 10 15Time (120583s)

Gm

ax(d

B)120579

max

(mRa

d)|A

F(120579)|

(dB)

1205902 = 0074

1205902 = 158

Figure 15 Case 1 1 times 8 PAA (a) AF (b) 119866max and (c) its histogram(d) Direction of maximum radiation and (e) its histogram

as an architecture employing a single mm-wave generator isfeasible at the expense of higher variation on the total radiatedpower andAF which requires higher transmission power andcomplicates spatial multiplexing and interference avoidance

6 Research Opportunities

Despite the great effort dedicated to the development ofthe efficient optical control schemes some issues remainunresolved as follows

(i) Integration Using Silicon Photonics Silicon photonicsenables the integration of a huge number of optical vari-able attenuatorsphase shifters alongside the complementarymetal-oxide-semiconductor (CMOS) control circuitry in areduced footprint chip Nevertheless silicon-based devices


0 05 1 15

0

869

94

08


minus40

minus20

minus80 5 10 15 20

Time (120583s)

0 5 10 15 20Time (120583s)

Gm

ax(d

B)120579

max

(mRa

d)|A

F(120579)|

(dB)

1205902 = 33E minus 4

1205902 = 005

Figure 16 Case 2 1 times 8 PAA (a) AF (b)119866max and (c) its histogram(d) Direction of maximum radiation and (e) its histogram

0 05 1 15

0

869

94

08


minus40

minus20

minus80 5 10 15 20

Time (120583s)

0 5 10 15 20Time (120583s)

Gm

ax(d

B)120579

max

(mRa

d)|A

F(120579)|

(dB)

1205902 = 34E minus 4

1205902 = 005


still present significant insertion losses which may becomea limiting impairment hindering their implementation

(ii) Balanced PDs Most of the reported feeding architecturesare based on unbalanced photodetection Balanced photode-tection avoids the requirement for filtering out the low-frequency components and improves the dynamic range ofthe system [100] In this case the integration of the antennawith balanced photodetectors should be analyzed

(iii) Preamplified PDs Since the radiated power dependson the output power of the PDs it is important that

0 05 1 15

0

566

64

08


minus40

minus20

minus80 5 10 15 20

Time (120583s)

0 5 10 15 20Time (120583s)

Gm

ax(d

B)120579

max

(mRa

d)|A

F(120579)|

(dB)

1205902 = 0004

1205902 = 437


0 05 1 15

0

569

64

08


minus40

minus20

minus80 5 10 15 20

Time (120583s)

0 5 10 15 20Time (120583s)

Gm

ax(d

B)120579

max

(mRa

d)|A

F(120579)|

(dB)

1205902 = 0074

1205902 = 158


the incident optical power be high enough This may bedifficult in PAAs with a high number of elements In the caseof multiwavelength mm-wave generators the total power isdivided among all the channels so the power per channelis expected to be relatively low while when a single-channelmm-wave generator is used splitting loss increases as thenumber of antenna elements to be fed In both cases an opti-cal amplifier preceding the PD will increase the maximumnumber of antenna elements This preamplifier may be builtusing semiconductor technology making its integration withthe PD feasible


0 05 1 15

0

11612

124

08


minus40

minus20

minus80 5 10 15 20

Time (120583s)

0 5 10 15 20Time (120583s)

Gm

ax(d

B)120579

max

(mRa

d)|A

F(120579)|

(dB)

1205902 = 0130

1205902 = 077


7 Conclusions

Optical phase and amplitude control of mm-wave PAAelements overcomes the bandwidth limitation of its electricalcounterpart However optical feeding still poses some chal-lenges such as the integration of antenna elements with thehigh-speed PD the efficient implementation of the phase andamplitude control and the noise induced on the generatedfeeding signals which further results in temporal emittedpower and radiation pattern fluctuations In this paper wehave discussed these challenges and listed the most promi-nent techniques in the literature presenting their advantagesand disadvantages In addition we analyzed the impact of thenoise on both the emission power fluctuation and radiationpatter variation considering the correlation among the noisesaffecting the different antenna elements Thus simulationresults revealed that the chosen beamforming architecturehas a critical impact on the PAA performance This workis intended to be a guideline for both antenna engineersinterested in optical phase and amplitude control techniquesand optical engineers keen on applying photonics to thefeeding ofmm-wave PAAWe have included a list of tentativeresearch opportunities that to our criterion deserve furtherstudy

Conflict of Interests

The authors declare that there is no conflict of interestsregarding the publication of this paper

References

[1] Cisco Systems ldquoCisco visual networking index forecast andmethodology 2012ndash2017rdquo Tech Rep Cisco Systems San Fran-cisco Calif USA 2013

[2] Cisco ldquoCisco visual networking index mobile data trafficforecast updaterdquo Tech Rep Cisco 2014

[3] T RappaportW Roh andK Cheun ldquoMobilersquosmillimeter-wavemakeoverrdquo IEEE Spectrum vol 51 no 9 pp 34ndash58 2014

[4] C J Hansen ldquoWiGiG multi-gigabit wireless communicationsin the 60GHz bandrdquo IEEEWireless Communications vol 18 no6 pp 6ndash7 2011

[5] I WPAN Task Group 3c (TG3c) MillimeterWave AlternativePHY httpieee802org15pubTG3chtml

[6] ECMA International ldquoHigh rate 60GHz PHYMAC and PALsrdquoStandard ECMA-387 ECMA International 2010

[7] Z Pi and F Khan ldquoAn introduction to millimeter-wave mobilebroadband systemsrdquo IEEE Communications Magazine vol 49no 6 pp 101ndash107 2011

[8] A Lebedev X Pang J J Vegas Olmos et al ldquoFeasibility studyand experimental verification of simplified fiber-supported 60-GHz picocell mobile backhaul linksrdquo IEEE Photonics Journalvol 5 no 4 pp 1ndash14 2013

[9] T Rappaport S Sun R Mayzus et al ldquoMillimeter wave mobilecommunications for 5G cellular it will workrdquo IEEE Access vol1 pp 335ndash349 2013

[10] C Dehos J Gonzalez A de Domenico D Kteenas andL Dussopt ldquoMillimeter-wave access and backhauling thesolution to the exponential data traffic increase in 5G mobilecommunications systemsrdquo IEEE Communications Magazinevol 52 no 9 pp 88ndash95 2014

[11] R C Daniels and R W Heath Jr ldquo60GHz wireless communi-cations emerging requirements and design recommendationsrdquoIEEE Vehicular Technology Magazine vol 2 no 3 pp 41ndash502007

[12] F Giannetti M Luise and R Reggiannini ldquoMobile and per-sonal communications in the 60 GHz band a surveyrdquoWirelessPersonal Communications vol 10 no 2 pp 207ndash243 1999

[13] S Hur T Kim D J Love J V Krogmeier T A Thomasand A Ghosh ldquoMillimeter wave beamforming for wirelessbackhaul and access in small cell networksrdquo IEEE Transactionson Communications vol 61 no 10 pp 4391ndash4403 2013

[14] W Roh J-Y Seol J Park et al ldquoMillimeter-wave beamformingas an enabling technology for 5G cellular communications the-oretical feasibility and prototype resultsrdquo IEEECommunicationsMagazine vol 52 no 2 pp 106ndash113 2014

[15] L Wang M Elkashlan T Q Duong and R W HeathldquoSecure communication in cellular networks the benefits ofmillimeter wave mobile broadbandrdquo in Proceedings of the IEEE15th International Workshop on Signal Processing Advances inWireless Communications (SPAWC rsquo14) pp 115ndash119 TorontoCanada June 2014

[16] L C Godara ldquoApplications of antenna arrays to mobile com-munications part I performance improvement feasibility andsystem considerationsrdquo Proceedings of the IEEE vol 85 no 7pp 1031ndash1060 1997

[17] C Balanis Antenna Theory Analysis and Design John Wileyand Sons 3rd edition 2005

[18] M Y Frankel and R D Esman ldquoTrue time-delay fiber-opticcontrol of an ultrawideband array transmitterreceiver withmultibeam capabilityrdquo IEEE Transactions on Microwave Theoryand Techniques vol 43 no 9 pp 2387ndash2394 1995

[19] W-Q Che E K-N Yung KWu and X-D Nie ldquoDesign inves-tigation on millimeter-wave ferrite phase shifter in substrateintegrated waveguiderdquo Progress in Electromagnetics Researchvol 45 pp 263ndash275 2004


[20] D Liu B Gaucher U Pfeiffer and J Grzyb Millimeter-WaveTechnologies John Wiley and Sons 2009

[21] A J Seeds ldquoMicrowave photonicsrdquo IEEE Transactions onMicrowave Theory and Techniques vol 50 no 3 pp 877ndash8872002

[22] J Yao ldquoMicrowave photonicsrdquo Journal of Lightwave Technologyvol 27 no 3 pp 314ndash335 2009

[23] M F Jahromi Optical and microwave beamforming for phasedarray antennas [PhD thesis] University of Waterloo 2008

[24] R Mailloux Phased Array Antenna Handbook Artech House2nd edition 2005

[25] H Zmuda and E N Toughlian Photonic Aspects of ModernRadar Artech House 1994

[26] S Saunders and A Aragon-Zavala Antennas and PropagationforWireless Communication SystemsWileyamp Sons 2nd edition2005

[27] K Chang R A York P S Hall and T Itoh ldquoActive integratedantennasrdquo IEEE Transactions on Microwave Theory and Tech-niques vol 50 no 3 pp 937ndash944 2002

[28] H Singh H L Sneha and R M Jha ldquoMutual coupling inphased arrays a reviewrdquo International Journal of Antennas andPropagation vol 2013 Article ID 348123 23 pages 2013

[29] C A Balanis Ed Modern Antenna Handbook John Wiley ampSons Hoboken NJ USA 2008

[30] M A Piqueras G Grosskopf B Vidal et al ldquoOptically beam-formed beam-switched adaptive antennas for fixed and mobilebroad-band wireless access networksrdquo IEEE Transactions onMicrowave Theory and Techniques vol 54 no 2 pp 887ndash8992006

[31] J Beas G Castanon I Aldaya A Aragon-Zavala and G Cam-puzano ldquoMillimeter-wave frequency radio over fiber systemsa surveyrdquo IEEE Communications Surveys and Tutorials vol 15no 4 pp 1593ndash1619 2013

[32] I Aldaya J Beas G Castanon G Campuzano and A Aragon-Zavala ldquoA survey of key-enabling components for remotemillimetric wave generation in radio over fiber networksrdquoOptics and Laser Technology vol 49 pp 213ndash226 2013

[33] P Hartmann X Qian A Wonfor R V Penty and I HWhite ldquo1ndash20GHz directly modulated radio over MMF linkrdquo inProceedings of the International Topical Meeting on MicrowavePhotonics (MWP rsquo05) pp 95ndash98 October 2005

[34] L Goldberg H F Taylor J F Weller and D M BloomldquoMicrowave signal generation with injection-locked laserdiodesrdquo Electronics Letters vol 19 no 13 pp 491ndash493 1983

[35] R P Braun and G Grosskopf ldquoOptical millimeter-wave sys-tems for broadband mobile communications devices andtechniquesrdquo in Proceedings of International Zurich Seminar onBroadband Communications Accessing Transmission Network-ing pp 51ndash58 Zurich Switzerland 1998

[36] D Parekh W Yang A NgrsquoOma et al ldquoMulti-Gbps ASK andQPSK-modulated 60GHz RoF link using an optically injectionlocked VCSELrdquo in Proceedings of the Optical Fiber Communi-cationNational Fiber Optic Engineers Conference (OFCNFOECrsquo10) pp 1ndash3 2010

[37] Z Jia J Yu A Chowdhury G Ellinas and G-K ChangldquoSimultaneous generation of independent wired and wirelessservices using a single modulator in millimeter-wave-bandradio-over-fiber systemsrdquo IEEE Photonics Technology Lettersvol 19 no 20 pp 1691ndash1693 2007

[38] S Makino K Shinoda T Kitatani et al ldquoHigh-speed elec-troabsorption modulator integrated DFB laser for 40 Gbps and

100 Gbps applicationrdquo in Proceedings of the IEEE InternationalConference on Indium Phosphide amp Related Materials (IPRMrsquo09) pp 362ndash366 IEEE Newport Beach Calif USAMay 2009

[39] M Huchard P Chanclou B Charbonnier et al ldquo60GHz radiosignal up-conversion and transport using a directly modulatedmode-locked laserrdquo in Proceedings of the IEEE InternationalTopical Meeting on Microwave Photonics pp 333ndash335 GoldCoast Australia October 2008

[40] M Attygalle C Lim and A Nirmalathas ldquoDispersion-tolerantmultiple WDM channel millimeter-wave signal generationusing a single monolithic mode-locked semiconductor laserrdquoJournal of Lightwave Technology vol 23 no 1 pp 295ndash3032005

[41] K Mori K Sato H Takara and T Ohara ldquoSupercontinuumlightwave source generating 50GHz spaced optical ITU gridseamlessly over S- C- and L-bandsrdquo IEE Electronics Letters vol39 no 6 pp 544ndash546 2003

[42] C-T Lin J Chen W-J Jiang et al ldquoUltra-high data-rate60 GHz radio-over-fiber systems employing optical frequencymultiplication and adaptive OFDM formatsrdquo in Proceedings oftheOptical Fiber CommunicationConference andExposition andthe National Fiber Optic Engineers Conference (OFCNFOECrsquo11) pp 1ndash3 March 2011

[43] G H Smith D Novak and Z Ahmed ldquoOvercomingchromatic-dispersion effects in fiber-wireless systems incorpo-rating external modulatorsrdquo IEEE Transactions on MicrowaveTheory and Techniques vol 45 no 8 pp 1410ndash1415 1997

[44] P B Gallion and G Debarge ldquoQuantum phase noise and fieldcorrelationin single frequency semiconductor laser systemsrdquoIEEE Journal of QuantumElectronics vol 20 no 4 pp 343ndash3491984

[45] U Gliese S Norskov and T N Nielsen ldquoChromatic dispersionin fiber-optic microwave and millimeter-wave linksrdquo IEEETransactions on Microwave Theory and Techniques vol 44 no10 pp 1716ndash1724 1996

[46] A Ngrsquooma and M Sauer ldquoRadio-over-fiber systems for multi-Gbps wireless communicationrdquo in Proceedings of the AsiaCommunications and Photonics Conference and Exhibition (ACPrsquo09) pp 1ndash9 November 2009

[47] L Goldberg R D Esman and K J Williams ldquoGenerationand control of microwave signals by optical techniquesrdquo IEEProceedings J Optoelectronics vol 139 no 4 pp 288ndash295 1992

[48] R Masood and S A Mohsin ldquoCharacterization of a coplanarwaveguide open stub-based discontinuity for mmics and filterapplicationsrdquo International Journal of Antennas and Propaga-tion vol 2012 Article ID 423706 9 pages 2012

[49] H Vettikalladi W T Sethi and M A Alkanhal ldquoHigh gainand high efficient stacked antenna array with integrated hornfor 60GHz communication systemsrdquo International Journal ofAntennas and Propagation vol 2014 Article ID 418056 8 pages2014

[50] Y Liu L-M Si M Wei et al ldquoSome recent developmentsof microstrip antennardquo International Journal of Antennas andPropagation vol 2012 Article ID 428284 10 pages 2012

[51] A Enayati W De Raedt and G A E Vandenbosch ldquoAntenna-in-package solution for millimeter-wave applications slotted-patch in a multilayer PCBrdquo in Proceedings of the IEEE Inter-national Symposium on Antennas and Propagation and USNC-URSI National Radio Science Meeting (APSURSI rsquo12) pp 1ndash2July 2012


[52] B Cheng H Xue C Xue et al ldquoSilicon-based long wavelengthphotodetectorsrdquo inOptoelectronicMaterials andDevices IV vol7631 of Proceedings of SPIE December 2009

[53] M W Geis S J Spector M E Grein et al ldquoCMOS-compatibleall-Si high-speed waveguide photodiodes with high respon-sivity in near-infrared communication bandrdquo IEEE PhotonicsTechnology Letters vol 19 no 3 pp 152ndash154 2007

[54] E Sackinger Broadband Circuits for Optical Fiber Communica-tion John Wiley amp Sons 2005

[55] G P Agrawal Fiber-Optic Communication Systems JohnWileyamp Sons 2002

[56] H Ito S Kodama Y Muramoto T Furuta T Nagatsumaand T Ishibashi ldquoHigh-speed and high-output InP-InGaAsunitraveling-carrier photodiodesrdquo IEEE Journal on SelectedTopics in Quantum Electronics vol 10 no 4 pp 709ndash727 2004

[57] H Ito T Yoshimatsu H Yamamoto and T Ishibashi ldquoBroad-band photonic terahertz-wave emitter integratingUTC-PD andnovel planar antennardquo inTerahertz Physics Devices and SystemsVII Advanced Applications in Industry and Defense vol 8716 ofProceedings of SPIE April 2013

[58] H Ito T Nagatsuma A Hirata et al ldquoHigh-power photonicmillimetre wave generation at 100 GHz usingmatching-circuit-integrated uni-travelling-carrier photodiodesrdquo IEE ProceedingsOptoelectronics vol 150 no 2 pp 138ndash142 2003

[59] C C RenaudM Robertson D Rogers et al ldquoA high responsiv-ity broadband waveguide uni-travelling carrier photodioderdquo inMillimeter-Wave and Terahertz Photonics vol 6194 of Proceed-ings of SPIE Strasbourg France April 2006

[60] H F Pues and A R van de Capelle ldquoImpedance-matchingtechnique for increasing the bandwidth ofmicrostrip antennasrdquoIEEE Transactions on Antennas and Propagation vol 37 no 11pp 1345ndash1354 1989

[61] K Li T Matsui and M Izutsu ldquoPhotonic antennas and itsapplication to radio-over-fiber wireless communication sys-temsrdquo Journal of the National Institute of Information andCommunications Technology vol 51 no 1-2 pp 141ndash149 2004

[62] L Morgan and H Andersson ldquoAn efficient beamformingmethod using a combination of analog true time and digitaldelayrdquo in Proceedings of the IEEE Radar Conference pp 260ndash265 April 2002

[63] H Aliakbarian V Volski E van der Westhuizen R Wolhuterand G A E Vandenbosch ldquoAnalogue versus digital for base-band beam steerable array used for LEO satellite applicationsrdquoin Proceedings of the 4th European Conference on Antennas andPropagation (EuCAP rsquo10) pp 1ndash4 IEEE Barcelona Spain April2010

[64] F van Vliet ldquoPhotonic beamforming for phased-array radarrdquo inProceedings of the International Union of Radio Science vol 1ndash4Maastricht The Netherlands August 2002

[65] J Buus Single Frequency Semiconductor Lasers vol TT5 SPIEOptical Engineering Press BellinghamWash USA 1st edition1990

[66] J Carroll J Whiteway and D Plumb Distributed FeedbackSemiconductor Lasers IEESPIE Optical Engineering Press1998

[67] W S Birkmayer and M J Wale ldquoProof-of-concept model of acoherent optical beam-forming networkrdquo IEE proceedings vol139 no 4 pp 301ndash304 1992

[68] J Stulemeijer F E van Vliet K W Benoist D H Maat andM K Smit ldquoCompact photonic integrated phase and amplitudecontroller for phased-array antennasrdquo IEEE Photonics Technol-ogy Letters vol 11 no 1 pp 122ndash124 1999

[69] H Li T Huang C Ke S Fu P P Shum and D Liu ldquoPhotonicgeneration of frequency-quadrupled microwave signal withtunable phase shiftrdquo IEEE Photonics Technology Letters vol 26no 3 pp 220ndash223 2014

[70] M Tamburrini M Parent L Goldberg and D StillwellldquoOptical feed for a phased arraymicrowave antennardquoElectronicsLetters vol 23 no 13 pp 680ndash681 1987

[71] M Oishi H Matsuno K Nishimura and S Akiba ldquoExper-imental study of chromatic dispersion effects on antennabeam forming by RF over fiberrdquo in Proceedings of the IEEEInternational Topical Meeting on Microwave Photonics (MWPrsquo12) pp 140ndash143 September 2012

[72] M Oishi Y Nishikawa S Akiba J Hirokawa and M Andoldquo2-dimensional beam steering by 2 times 3 photonic antenna usingmillimeter-wave radio over fiberrdquo in Proceedings of the IEEEInternational Topical Meeting on Microwave Photonics (MWPrsquo13) pp 130ndash133 October 2013

[73] J-D Shin B-S Lee and B-G Kim ldquoOptical true time-delayfeeder for X-band phased array antennas composed of 2 times 2

optical MEMS switches and fiber delay linesrdquo IEEE PhotonicsTechnology Letters vol 16 no 5 pp 1364ndash1366 2004

[74] FM Soares F Karouta E J Geluk J H C van Zantvoort H deWaardt and M K Smit ldquoIntegrated InP-based true time delaywith fibermode adapter for beamformingrdquo in Proceedings of the210th ECS Meeting Cancun Mexico October-November 2006

[75] J Xie L Zhou Z Li J Wang and J Chen ldquoSeven-bitreconfigurable optical true time delay line based on siliconintegrationrdquo Optics Express vol 22 no 19 pp 22707ndash227152014

[76] B-M Jung J-D Shin and B-G Kim ldquoOptical true time-delayfor two-dimensional X-band phased array antennasrdquo IEEEPhotonics Technology Letters vol 19 no 12 pp 877ndash879 2007

[77] D T K Tong and M C Wu ldquoMultiwavelength opti-cally controlled phased-array antennasrdquo IEEE Transactions onMicrowave Theory and Techniques vol 46 no 1 pp 108ndash1151998

[78] V Kaman X Zheng R J Helkey C Pusarla and J E BowersldquoA 32-element 8-bit photonic true-time-delay system basedon a 288 times 288 3-D MEMS optical switchrdquo IEEE PhotonicsTechnology Letters vol 15 no 6 pp 849ndash851 2003

[79] T-W Yeow K L Eddie and A Goldenberg ldquoMEMS opticalswitchesrdquo IEEE Communications Magazine vol 39 no 11 pp158ndash163 2001

[80] M-J Li P Tandon D C Bookbinder et al ldquoUltra-low bendingloss single-mode fiber for FTTHrdquo Journal of Lightwave Technol-ogy vol 27 no 3 pp 376ndash382 2009

[81] C Chen Y Yi F Wang Y Yan X Sun and D Zhang ldquoUltra-long compact optical polymeric array waveguide true-time-delay line devicesrdquo IEEE Journal of Quantum Electronics vol46 no 5 pp 754ndash761 2010

[82] A Capozzoli C Curcio andGDrsquoElia ldquoThe design of an opticaltime steered antenna based on a new integrated true time delayunitrdquoProgress in Electromagnetics Research vol 140 pp 681ndash7172013

[83] R T Schermer F Bucholtz andCAVillarruel ldquoContinuously-tunable microwave photonic true-time-delay based on a fiber-coupled beam deflector and diffraction gratingrdquoOptics Expressvol 19 no 6 pp 5371ndash5378 2011

[84] D Dolfi P Joffre J Antoine J-P Huignard D Philippetand P Granger ldquoExperimental demonstration of a phased-array antenna optically controlled with phase and time delaysrdquoApplied Optics vol 35 no 26 pp 5293ndash5300 1996


[85] A Rader and B L Anderson ldquoDemonstration of a linear opticaltrue-time delay device by use of a microelectromechanicalmirror arrayrdquoApplied Optics vol 42 no 8 pp 1409ndash1416 2003

[86] B L Anderson J G Ho W D Cowan et al ldquoHardwaredemonstration of extremely compact optical true time delaydevice for wideband electronically steered antennasrdquo Journalof Lightwave Technology vol 29 no 9 Article ID 5727896 pp1343ndash1353 2011

[87] R D Esman M Y Frankel J L Dexter et al ldquoFiber-opticprism true time-delay antenna feedrdquo IEEE Photonics TechnologyLetters vol 5 no 11 pp 1347ndash1349 1993

[88] P Wu S Tang and D E Raible ldquoA prototype high-speedoptically-steered X-band phased array antennardquoOptics Expressvol 21 no 26 pp 32599ndash32604 2013

[89] H Zmuda R A Soref P Payson S Johns and E N ToughlianldquoPhotonic beamformer for phased array antennas using a fibergrating prismrdquo IEEE Photonics Technology Letters vol 9 no 2pp 241ndash243 1997

[90] H Subbaraman M Y Chen and R T Chen ldquoPhotoniccrystal fiber-based true-time-delay beamformer formultiple RFbeam transmission and reception of an X-band phased-arrayantennardquo Journal of Lightwave Technology vol 26 no 15 pp2803ndash2809 2008

[91] P Matthews and P Biernacki ldquoRecent progress in dispersion-based photonic beamformingrdquo in Technical Digest Interna-tional Topical Meeting on Microwave Photonics (MWP rsquo00) pp1ndash4 Oxford UK 2000

[92] G Grosskopf B Kuhlow R Eggemann G Przyrembel and DRohde ldquoPhotonic beam-forming for millimeter-wave mobilecommunicationsrdquo in Proceedings of the IEEE LEOS AnnualMeeting Conference Proceedings vol 2 pp 859ndash860 October2003

[93] R Soref ldquoThe past present and future of silicon photonicsrdquoIEEE Journal on Selected Topics in Quantum Electronics vol 12no 6 pp 1678ndash1687 2006

[94] T Landolsi L S Tamil and W P Osborne ldquoEffect of noisein optically-fed phased array antennas for CDMA wirelessnetworksrdquo in Proceedings of the IEEE International Conferenceon Personal Wireless Communications pp 244ndash247 December1997

[95] D Abbott B R Davis N J Phillips and K Eshraghian ldquoSimplederivation of the thermal noise formula using window-limitedfourier transforms and other conundrumsrdquo IEEE Transactionson Education vol 39 no 1 pp 1ndash13 1996

[96] R Ramaswami and K N Sivarajan Optical Networks Apractical Perspective Morgan Kaufmann Boston Mass USA2002

[97] L A Coldren and S W Corzine Diode Lasers and PhotonicIntegrated Circuits John Wiley amp Sons 1995

[98] P M Becker A A Olsson and J R Simpson Erbium-DopedFiber Amplifiers Fundamentals and Technology AcademicPress New York NY USA 1999

[99] S B Alenxander Optical Communication Receiver Design volTT22 SPIE Optical Engineering Press 1997

[100] L Zhuang A Meijerink C G H Roeloffzen et al ldquoNovelring resonator-based optical beamformer for broadband phasedarray receive antennasrdquo in Proceedings of the 21st AnnualMeeting of the IEEE Lasers and Electro-Optics Society (LEOSrsquo08) pp 20ndash21 Acapulco Mexico November 2008

International Journal of

AerospaceEngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

RoboticsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014


Active and Passive Electronic Components

Control Scienceand Engineering

Journal of



RotatingMachinery


Hindawi Publishing Corporation httpwwwhindawicom

Journal ofEngineeringVolume 2014

Submit your manuscripts athttpwwwhindawicom

VLSI Design



Shock and Vibration


Civil EngineeringAdvances in

Acoustics and VibrationAdvances in



Electrical and Computer Engineering

Journal of

Advances inOptoElectronics


Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

SensorsJournal of


Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014


Chemical EngineeringInternational Journal of Antennas and

Propagation




Navigation and Observation



DistributedSensor Networks



relied on ferrite nucleus that resulted in bulky and heavyarrays [18] As higher degree of integration was requiredarray weight and size decreased progressively [19] After-wards microelectromechanical systems (MEMSs) emergedenabling the implementation of true time delay (TDD)lines which presented significantly broader bandwidth thanferrite-based phase shifters [20] In parallel since the earlydays of microwave photonics different optical techniquesfor controlling the phase of an RF signal were proposed[21 22] Optical techniques have the advantages of being ableto deal with higher RF frequencies as well as to present asignificantly broader bandwidth and lower losses comparedto their electrical counterpart [23] making optical control anattractive approach for mm-wave smart antennas Howeveroptical feeding still presents two significant challenges on theone hand the integration of a fast photodiode (PD) with anantenna requires a thorough design that should pay specialattention to power budget analysis On the other hand phaseand amplitude control of the antenna elements must be donein an efficient way

Several previous books and tutorials have analyzed PAAs[24] ormicrowave photonics [21 22] systems including someaspects of optical feeding of phased arrays Reference [25] isdevoted completely to the application of photonics inmodernradar applications It includes an extensive review of photonictechniques as well as a detailed background but it does notconsider the particularities of mm-wave systemsThe presentpaper constitutes to the best of our knowledge the firstwork fully devoted to covering the particular problems andchallenges of the optical feeding of PAAs operating at mm-wave frequencies Furthermore the literature review allowedus to classify the different beamforming architectures whichwere compared in terms of their performance We had twoaudiences in mind when we wrote this tutorial it is orientedto antenna engineers that want to get some knowledge onthe work done in the optical domain as well as to opticalengineers that require knowing the characteristics of thesignals that must be generated Therefore this work pretendsto be to some extent self-contained which requires somebasic concepts that are included in the paper

The paper is organized as follows Section 2 introducesthe fundamental concepts required for the rest of the paperas well as the nomenclature that we will use Section 3is dedicated to the integration of fast PDs with antennaelements whereas Section 4 presents the different opticalarchitectures as well as particular techniques to control theamplitude and phases of the elementsThese architectures arecompared in terms of the PAA performance in Section 5 InSection 6 some research opportunities are listed and finallySection 7 concludes the paper

2 Fundamental Concepts

In this section we describe in more detail the PAA and itsdifferent types as well as the expression for its radiationpattern Later on beam steering beam shaping and beam-forming concepts are explained On the other hand theoptical generation of RF signals is presented paying specialattention to the phase noise of the generated RF signal

(r Θ Φ)

rarrr minus

rarrr 1

rarrr minus

rarrr minus

rarrr 2 rarr

r minusrarrr 3

rarrr

rarrr 1

rarrr 2

rarrr 3

rarrr i

(x1 y1 z1)

(x2 y2 z2)(x3 y3 z3)

(xi yi zi)

A1

A2

A3

Ai = Aiej120595119894

Φ

Θ

z

y

x

rarrr i

Figure 1 Sketch of a PAA for the calculation of its radiation patternΘ azimuthal angle Φ elevation angle 119903 = (119903 ΘΦ) position ofthe point of interest in spherical coordinates vec119903

119894= (119909119894 119910119894 119911119894)

position of the 119894th antenna element 119860119894complex amplitude of the

feeding currents which can be expressed in terms of the real-valuedamplitude 119860

119894 and phase 120595

119894

21 Phased Array Antennas The scheme of a PAA is acollection of coherently radiating elements that can be inde-pendently fed [26]The elements which are usually identicalare therefore fed with signals at the same frequency butwith possibly different phases and amplitudes PAAs can beclassified according to different features if each element hasa dedicated oscillator then the PAA is said to be active [27]in contrast to passive phased arrays where all the feedingcurrents derive from the same oscillator Depending on thegeometrical configuration a PAA can be linear if the antennaelements are arranged in a line planar if they are in a planeor conformal when the elements are placed on a 3D surfaceUniformPAAs are thosewhere the element positions conformto a regular grid whereas nonuniformPAAs are arrayswith anirregular grid [17] When the amplitudes relation and relativephases of the feeding currents do not vary on time the PAAis static whereas when phases and amplitudes of the elementsare varied it is denominated dynamic PAA By a properdesign PAAs present high gain and dynamic flexibility thatjustify them as a key element in modern communicationsystems

A general PAA is sketched in Figure 1 where the positionof the 119894th antenna element is denoted by 119903

119894= (119909119894 119910119894 119911119894) and

the complex amplitude of the feeding current by119860119894= 119860119894119890119895120595119894

The radiation pattern of the 119873-element PAA can be foundapplying the superposition principle at an arbitrary position



119864 ( 119903) =

119873

sum

119894=1119864119894 ( 119903)

=

119873

sum

119894=1

radic21205780119866 (ΘΦ)

4120587119860119894119890119895120595119894

1198901198952120587| 119903minus 119903119894|119891RF119888

1003816100381610038161003816 119903 minus 119903119894

1003816100381610038161003816

(1)



119864 ( 119903) =

119873

sum

119894=1radic21205780119866 (ΘΦ)

4120587 1003816100381610038161003816 119903 minus 119903119894

1003816100381610038161003816

2 119860119894

⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟

Amplitude term

119890119895(120595119894+2120587| 119903minus 119903119894|119891RF119888)⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟

Phase term (2)





119894 and a



1205951015840

119894( 119903) =

2120587119891RF119888

(sinΘ sdot (119909119894cosΦ+119910

119894sinΦ)+ 119911

119894cosΘ) (3)


119864 ( 119903) = radic21205780119866 (ΘΦ)

41205871199032sdot

119873

sum

119894=1119860119894119890119895(120595119894+120595

1015840

119894) (4)


119894and 120595



AF (ΘΦ) =

119873

sum

119894=1119860119894119890119895(120595119894+120595

1015840

119894) (5)


0 05 1 15

0

5

10


Θ (rad)

|AF(Θ)|

(dB)


Cosine

(a)

0

1

2


|Ai|

(b)

1 2 3 4 5 6 7 8

02

minus2

Antenna element i

Ang

leA

i

(c)



119866PAA (ΘΦ) = 119866 (ΘΦ)|AF (ΘΦ)|

2

sum119873

119894=11003816100381610038161003816119860 119894

1003816100381610038161003816

2 (6)



2

sum119873

119894=11003816100381610038161003816119860 119894

1003816100381610038161003816

2 (7)




Cosine

0 05 1 15

0

5

10


Θ (rad)

|AF(Θ)|

(dB)

(a)

0

1

2


|Ai|

(b)

1 2 3 4 5 6 7 8

02

minus2

Antenna element i

Ang

leA

i

(c)



ΘMAX = sin (2120591119891RF) (8)






119864 (119905) = 11986401 (119905) sdot exp 119895 [21205871198911119905 + 1206011 (119905)] +119898 (119905)

sdot 11986402 (119905) sdot exp 119895 [21205871198912119905 + 1206012 (119905)] (9)



fRF fRF fRF

fRFfRFf1 f2


m(t)



119894PD (119905) = 119877 |119864 (119905)|2+ 119899 (119905) = 119877 [119864 (119905) sdot 119864 (119905)

lowast] + 119899 (119905) (10)


119894RF (119905) = 119877 sdot 11986401 (119905) 11986402 (119905)

sdot (Re 119898 (119905) cos [2120587119891RF119905 + Δ120601 (119905)]

sdot Im 119898 (119905) sin [2120587119891RF119905 + Δ120601 (119905)]) + 1198991015840(119905)

(11)


119894RF (119905) = 119877 sdot 11986401 (119905) 11986402 (119905) sdot |119898 (119905)|

sdot cos [2120587119891RF119905 + 120601119898 (119905) + Δ120601 (119905)] + 119899

1015840(119905)

(12)










Groundplane

GroundplaneAntenna

Substrate

(a)

Groundplane

Groundplane

Antenna

Substrate

Foam

(b) (c)


h

Conduction band

Absor

ption

Valence

N

P

band

(a)

h

Conduction band

Valence band

Bloc

king

laye

r

Abso

rptio

n

N

P

(b)























mmW generation




Antenna unitOBFNODN

Element 1

Element 2

Element N1205820

1205820

1205820

(a)

mmW generator 1

mmW generator 2

mmW generator N

mmW generation





Element 1

Element 2

Element N1205820

1205820

1205820

(b)








119864 (119905) = 1198641 (119905 minusΔ1198791) + 1198642 (119905 minusΔ1198792)

= 11986401 exp [11989521205871198911 (119905 minusΔ1198791)]

+ 11986402 exp [11989521205871198912 (119905 minusΔ1198792)]

(16)


119894RF (119905) = 2119877 sdot 1198640111986402




119894RF (119905) = 2119877 sdot 1198640111986402


2120575119879]


(18)




mmW generation




Antenna unitOBFNODN

Element 1

Element 2

Element N120582N

1205822

1205821

(a)

OBFN ODN

Antenna unit

Element 1

Element 2

Element N120582N

1205822





mmW generation

(b)

mmW generator 1

mmW generator 2

mmW generator N

mmW generation




Antenna unitOBFNODN

Element 1

Element 2

Element N120582N

1205822

1205821

(c)

mmW generator 1

mmW generator 2

mmW generator N

mmW generation





Element 1

Element 2

Element N120582N

1205822

1205821

120582N

1205822

1205821

(d)



Δ120601CM = 2120587119891RFΔ119879 (19)

Δ120601diff = 21205871198911 + 1198912

2120575119879 (20)






On

L 2L 2Nminus1L


(a)

L

2L



(b)

Combiners

Splitters

Antennaelement 1

Antennaelement N


(c)





Rotarymirror

Mirror

Collimator

LL998400

(a)

Mirror MirrorL

L998400


prism

Disp

lace

men

t

(b)

L

L998400


(c)








element 2Antenna

element 3Antenna

element 4

Antennaelement N


input

Split

ter

(a)


element 2Antenna

element 3Antenna

element 4

Antennaelement N

Variablewavelength

input

Split

ter

1205821

1205822

1205823

120582K

(b)


AntennaCombiner

PMSplitter

Mux

PM

PM

element 1

Antennaelement 1

Antennaelement N











Photodiode









119864 (119905) = 11986401 (119905) sdot exp 119895 [21205871198911119905 + 1206011 (119905)] + 11986402 (119905)

sdot exp 119895 [21205871198912119905 + 1206012 (119905)] (21)



119864 (119905) = [1198641 +Δ1198641 (119905)] sdot exp 119895 [21205871198911119905 + 1206011 (119905)]

+ [1198642 +Δ1198642 (119905)] sdot exp 119895 [21205871198912119905 + 1206012 (119905)] (22)








119894PD (119905) =

119877 sdot10038161003816100381610038161003816119864amp (119905)

10038161003816100381610038161003816

2

119871+ 119899PD (119905)

(24)




119894PD (119905) =119877

119871(119866 (119864

201 +119864

202)

+11986611986401 (119905) 11986402 (119905) cos [2120587119891mm119905 + Δ120601 (119905)]

+ 2radic119866Re 119899ASE (119905) 11986401 (119905) exp119895 [21205871198911119905 + 1206011]

+ 2radic119866Re 119899ASE (119905) 11986402 (119905) exp119895 [21205871198912119905 + 1206012]

+1003816100381610038161003816119899ASE (119905)

1003816100381610038161003816

2) + 119899PD (119905)

(25)


119894PD (119905) asymp119877

119871(119866 (119864

201 +119864

202)

+11986611986401 (119905) 11986402 (119905) cos [2120587119891mm119905 + Δ120601 (119905)]

+ 2radic119866Re 119899ASE (119905) 11986401 (119905) exp119895 [21205871198911119905 + 1206011]

+ 2radic119866Re 119899ASE (119905) 11986402 (119905) exp119895 [21205871198912119905 + 1206012])

+ 119899PD (119905)

(26)


119894RF (119905) asymp119877

119871(11986611986401 (119905) 11986402 (119905) cos [2120587119891mm119905 + Δ120601 (119905)]

+ 2radic119866Re 1198991015840ASE (119905) 11986401 (119905) exp119895 [21205871198911119905 + 1206011]

+ 2radic119866Re 1198991015840ASE (119905) 11986402 (119905) exp119895 [21205871198912119905 + 1206012])

+ 1198991015840

PD (119905)

(27)

where 1198991015840

PD(119905) and 1198991015840


119894RF (119905) asymp119877

119871(119866 [1198641 +Δ1198641 (119905)] sdot [1198642 +Δ1198642 (119905)]

sdot cos [2120587119891mm119905 + Δ120601 (119905)]

+ 2radic119866Re 1198991015840ASE (119905) [1198641 +Δ1198641 (119905)]

sdot exp119895 [21205871198911119905 + 1206011]

+ 2radic119866Re 1198991015840ASE (119905) [1198642 +Δ1198642 (119905)]

sdot exp119895 [21205871198912119905 + 1206012]) + 1198991015840

PD (119905)

(28)


119894RF (119905) asymp119877119866

11987111986411198642cos [2120587119891mm119905 + Δ120601 (119905)]

+119877119866

119871[Δ1198641 (119905) 1198642 +Δ1198642 (119905) 1198641]

sdot cos [2120587119891mm119905 + Δ120601 (119905)]

+2119877radic119866

119871Re 1198991015840ASE (119905) 1198641exp119895 [21205871198911119905 + 1206011]

+2119877radic119866

119871Re 1198991015840ASE (119905) 1198642exp119895 [21205871198912119905 + 1206012]

+ 1198991015840

PD (119905)

(29)


119860(119905) acquires

the form

119899119860 (119905) =

119877119866

119871[Δ1198641 (119905) 1198642 +Δ1198642 (119905) 1198641]

+2119877radic119866

119871Re 1198991015840ASE (119905) 1198641

+2119877radic119866

119871Re 1198991015840ASE (119905) 1198642 + 119899

1015840

PD (119905)

(30)



119875119899119860

= 119875119873source

+119875119873amp

+119875119873PD (31)

with

119875119873source

= (119877119866

119871)

2[Δ1198641 (119905) 1198642 + Δ1198642 (119905) 1198641]

2

119875119873amp

= 2(119877radic119866

119871)

2

1198992ASE (119905) (119864

21 +119864

22)

119875119873PD

= 1198992PD (119905)

(32)




values 119875119873PD




CNR =119875119862

119875119899119860

=119875119862

119875119873source

+ 119875119873amp

+ 119875119873PD

(33)


119875119862

=12(

1198771198662

11987111986411198642)

2

(34)


119901Φ(120601) =

exp (minus120574)


sdot int

radic2120574 cos(120601)

minusinfin

exp(minus119909

2

2)119889119909]

(35)


120574 =119875119862

119875119873amp

+ 119875119873PD

(36)



119875119899120601

= int

+infin

minusinfin

1206012119901Φ(120601) 119889120601 (37)











119875total (119905) = 1205980 sdot (119873

sum

119899=1119877 sdot 119894119899 (119905))

2

(38)


120590Δ119875

1198750=


1198750

(39)





Case 1Case 2

Case 3

10minus3

10minus4

10minus5

10minus6

120590ΔPP

0






119899(119905) + 119895 sdot HT119894

119899(119905) where


119860119899 (119905) = radic(Re

119899 (119905))2+ (Im

119899 (119905))2

120601119899 (119905) = atan

Im 119899 (119905)

Re 119899 (119905)

(40)


119899(119905)

and 120601119899(119905) that is

1198600 (119905) =1119873

119873

sum

119899=1119860119899 (119905)

1206010 (119905) =1119873

119873

sum

119899=1

120601119899 (119905)

(41)


119899(119905) of


Δ119860119899 (119905) = 119860

119899 (119905) minus1198600 (119905)

Δ120601119899 (119905) = 120601

119899 (119905) minus 1206010 (119905) (42)


1205902119860

1205832119860

=

⟨Δ1198602119899(119905)⟩

⟨1198600 (119905)⟩2 (43)


1205902120601= ⟨Δ120601

2119899(119905)⟩ (44)




Case 1Case 2

Case 3

10minus3

10minus2

10minus4

10minus5

10minus6

1205902 A120583

2 A

(a)


Case 1Case 2

Case 3

10minus3

10minus2

10minus4

10minus5

10minus6

1205902 120601

(b)





0 05 1 15

0

869

94

08


minus40

minus20

minus80 5 10 15

Time (120583s)

0 5 10 15Time (120583s)

Gm

ax(d

B)120579

max

(mRa

d)|A

F(120579)|

(dB)

1205902 = 0074

1205902 = 158







0 05 1 15

0

869

94

08


minus40

minus20

minus80 5 10 15 20

Time (120583s)

0 5 10 15 20Time (120583s)

Gm

ax(d

B)120579

max

(mRa

d)|A

F(120579)|

(dB)

1205902 = 33E minus 4

1205902 = 005


0 05 1 15

0

869

94

08


minus40

minus20

minus80 5 10 15 20

Time (120583s)

0 5 10 15 20Time (120583s)

Gm

ax(d

B)120579

max

(mRa

d)|A

F(120579)|

(dB)

1205902 = 34E minus 4

1205902 = 005





0 05 1 15

0

566

64

08


minus40

minus20

minus80 5 10 15 20

Time (120583s)

0 5 10 15 20Time (120583s)

Gm

ax(d

B)120579

max

(mRa

d)|A

F(120579)|

(dB)

1205902 = 0004

1205902 = 437


0 05 1 15

0

569

64

08


minus40

minus20

minus80 5 10 15 20

Time (120583s)

0 5 10 15 20Time (120583s)

Gm

ax(d

B)120579

max

(mRa

d)|A

F(120579)|

(dB)

1205902 = 0074

1205902 = 158




0 05 1 15

0

11612

124

08


minus40

minus20

minus80 5 10 15 20

Time (120583s)

0 5 10 15 20Time (120583s)

Gm

ax(d

B)120579

max

(mRa

d)|A

F(120579)|

(dB)

1205902 = 0130

1205902 = 077


7 Conclusions




References












































































































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation











119864 ( 119903) =

119873

sum

119894=1119864119894 ( 119903)

=

119873

sum

119894=1

radic21205780119866 (ΘΦ)

4120587119860119894119890119895120595119894

1198901198952120587| 119903minus 119903119894|119891RF119888

1003816100381610038161003816 119903 minus 119903119894

1003816100381610038161003816

(1)



119864 ( 119903) =

119873

sum

119894=1radic21205780119866 (ΘΦ)

4120587 1003816100381610038161003816 119903 minus 119903119894

1003816100381610038161003816

2 119860119894

⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟

Amplitude term

119890119895(120595119894+2120587| 119903minus 119903119894|119891RF119888)⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟

Phase term (2)





119894 and a



1205951015840

119894( 119903) =

2120587119891RF119888

(sinΘ sdot (119909119894cosΦ+119910

119894sinΦ)+ 119911

119894cosΘ) (3)


119864 ( 119903) = radic21205780119866 (ΘΦ)

41205871199032sdot

119873

sum

119894=1119860119894119890119895(120595119894+120595

1015840

119894) (4)


119894and 120595



AF (ΘΦ) =

119873

sum

119894=1119860119894119890119895(120595119894+120595

1015840

119894) (5)


0 05 1 15

0

5

10


Θ (rad)

|AF(Θ)|

(dB)


Cosine

(a)

0

1

2


|Ai|

(b)

1 2 3 4 5 6 7 8

02

minus2

Antenna element i

Ang

leA

i

(c)



119866PAA (ΘΦ) = 119866 (ΘΦ)|AF (ΘΦ)|

2

sum119873

119894=11003816100381610038161003816119860 119894

1003816100381610038161003816

2 (6)



2

sum119873

119894=11003816100381610038161003816119860 119894

1003816100381610038161003816

2 (7)




Cosine

0 05 1 15

0

5

10


Θ (rad)

|AF(Θ)|

(dB)

(a)

0

1

2


|Ai|

(b)

1 2 3 4 5 6 7 8

02

minus2

Antenna element i

Ang

leA

i

(c)



ΘMAX = sin (2120591119891RF) (8)






119864 (119905) = 11986401 (119905) sdot exp 119895 [21205871198911119905 + 1206011 (119905)] +119898 (119905)

sdot 11986402 (119905) sdot exp 119895 [21205871198912119905 + 1206012 (119905)] (9)



fRF fRF fRF

fRFfRFf1 f2


m(t)



119894PD (119905) = 119877 |119864 (119905)|2+ 119899 (119905) = 119877 [119864 (119905) sdot 119864 (119905)

lowast] + 119899 (119905) (10)


119894RF (119905) = 119877 sdot 11986401 (119905) 11986402 (119905)

sdot (Re 119898 (119905) cos [2120587119891RF119905 + Δ120601 (119905)]

sdot Im 119898 (119905) sin [2120587119891RF119905 + Δ120601 (119905)]) + 1198991015840(119905)

(11)


119894RF (119905) = 119877 sdot 11986401 (119905) 11986402 (119905) sdot |119898 (119905)|

sdot cos [2120587119891RF119905 + 120601119898 (119905) + Δ120601 (119905)] + 119899

1015840(119905)

(12)










Groundplane

GroundplaneAntenna

Substrate

(a)

Groundplane

Groundplane

Antenna

Substrate

Foam

(b) (c)


h

Conduction band

Absor

ption

Valence

N

P

band

(a)

h

Conduction band

Valence band

Bloc

king

laye

r

Abso

rptio

n

N

P

(b)























mmW generation




Antenna unitOBFNODN

Element 1

Element 2

Element N1205820

1205820

1205820

(a)

mmW generator 1

mmW generator 2

mmW generator N

mmW generation





Element 1

Element 2

Element N1205820

1205820

1205820

(b)








119864 (119905) = 1198641 (119905 minusΔ1198791) + 1198642 (119905 minusΔ1198792)

= 11986401 exp [11989521205871198911 (119905 minusΔ1198791)]

+ 11986402 exp [11989521205871198912 (119905 minusΔ1198792)]

(16)


119894RF (119905) = 2119877 sdot 1198640111986402




119894RF (119905) = 2119877 sdot 1198640111986402


2120575119879]


(18)




mmW generation




Antenna unitOBFNODN

Element 1

Element 2

Element N120582N

1205822

1205821

(a)

OBFN ODN

Antenna unit

Element 1

Element 2

Element N120582N

1205822





mmW generation

(b)

mmW generator 1

mmW generator 2

mmW generator N

mmW generation




Antenna unitOBFNODN

Element 1

Element 2

Element N120582N

1205822

1205821

(c)

mmW generator 1

mmW generator 2

mmW generator N

mmW generation





Element 1

Element 2

Element N120582N

1205822

1205821

120582N

1205822

1205821

(d)



Δ120601CM = 2120587119891RFΔ119879 (19)

Δ120601diff = 21205871198911 + 1198912

2120575119879 (20)






On

L 2L 2Nminus1L


(a)

L

2L



(b)

Combiners

Splitters

Antennaelement 1

Antennaelement N


(c)





Rotarymirror

Mirror

Collimator

LL998400

(a)

Mirror MirrorL

L998400


prism

Disp

lace

men

t

(b)

L

L998400


(c)








element 2Antenna

element 3Antenna

element 4

Antennaelement N


input

Split

ter

(a)


element 2Antenna

element 3Antenna

element 4

Antennaelement N

Variablewavelength

input

Split

ter

1205821

1205822

1205823

120582K

(b)


AntennaCombiner

PMSplitter

Mux

PM

PM

element 1

Antennaelement 1

Antennaelement N











Photodiode









119864 (119905) = 11986401 (119905) sdot exp 119895 [21205871198911119905 + 1206011 (119905)] + 11986402 (119905)

sdot exp 119895 [21205871198912119905 + 1206012 (119905)] (21)



119864 (119905) = [1198641 +Δ1198641 (119905)] sdot exp 119895 [21205871198911119905 + 1206011 (119905)]

+ [1198642 +Δ1198642 (119905)] sdot exp 119895 [21205871198912119905 + 1206012 (119905)] (22)








119894PD (119905) =

119877 sdot10038161003816100381610038161003816119864amp (119905)

10038161003816100381610038161003816

2

119871+ 119899PD (119905)

(24)




119894PD (119905) =119877

119871(119866 (119864

201 +119864

202)

+11986611986401 (119905) 11986402 (119905) cos [2120587119891mm119905 + Δ120601 (119905)]

+ 2radic119866Re 119899ASE (119905) 11986401 (119905) exp119895 [21205871198911119905 + 1206011]

+ 2radic119866Re 119899ASE (119905) 11986402 (119905) exp119895 [21205871198912119905 + 1206012]

+1003816100381610038161003816119899ASE (119905)

1003816100381610038161003816

2) + 119899PD (119905)

(25)


119894PD (119905) asymp119877

119871(119866 (119864

201 +119864

202)

+11986611986401 (119905) 11986402 (119905) cos [2120587119891mm119905 + Δ120601 (119905)]

+ 2radic119866Re 119899ASE (119905) 11986401 (119905) exp119895 [21205871198911119905 + 1206011]

+ 2radic119866Re 119899ASE (119905) 11986402 (119905) exp119895 [21205871198912119905 + 1206012])

+ 119899PD (119905)

(26)


119894RF (119905) asymp119877

119871(11986611986401 (119905) 11986402 (119905) cos [2120587119891mm119905 + Δ120601 (119905)]

+ 2radic119866Re 1198991015840ASE (119905) 11986401 (119905) exp119895 [21205871198911119905 + 1206011]

+ 2radic119866Re 1198991015840ASE (119905) 11986402 (119905) exp119895 [21205871198912119905 + 1206012])

+ 1198991015840

PD (119905)

(27)

where 1198991015840

PD(119905) and 1198991015840


119894RF (119905) asymp119877

119871(119866 [1198641 +Δ1198641 (119905)] sdot [1198642 +Δ1198642 (119905)]

sdot cos [2120587119891mm119905 + Δ120601 (119905)]

+ 2radic119866Re 1198991015840ASE (119905) [1198641 +Δ1198641 (119905)]

sdot exp119895 [21205871198911119905 + 1206011]

+ 2radic119866Re 1198991015840ASE (119905) [1198642 +Δ1198642 (119905)]

sdot exp119895 [21205871198912119905 + 1206012]) + 1198991015840

PD (119905)

(28)


119894RF (119905) asymp119877119866

11987111986411198642cos [2120587119891mm119905 + Δ120601 (119905)]

+119877119866

119871[Δ1198641 (119905) 1198642 +Δ1198642 (119905) 1198641]

sdot cos [2120587119891mm119905 + Δ120601 (119905)]

+2119877radic119866

119871Re 1198991015840ASE (119905) 1198641exp119895 [21205871198911119905 + 1206011]

+2119877radic119866

119871Re 1198991015840ASE (119905) 1198642exp119895 [21205871198912119905 + 1206012]

+ 1198991015840

PD (119905)

(29)


119860(119905) acquires

the form

119899119860 (119905) =

119877119866

119871[Δ1198641 (119905) 1198642 +Δ1198642 (119905) 1198641]

+2119877radic119866

119871Re 1198991015840ASE (119905) 1198641

+2119877radic119866

119871Re 1198991015840ASE (119905) 1198642 + 119899

1015840

PD (119905)

(30)



119875119899119860

= 119875119873source

+119875119873amp

+119875119873PD (31)

with

119875119873source

= (119877119866

119871)

2[Δ1198641 (119905) 1198642 + Δ1198642 (119905) 1198641]

2

119875119873amp

= 2(119877radic119866

119871)

2

1198992ASE (119905) (119864

21 +119864

22)

119875119873PD

= 1198992PD (119905)

(32)




values 119875119873PD




CNR =119875119862

119875119899119860

=119875119862

119875119873source

+ 119875119873amp

+ 119875119873PD

(33)


119875119862

=12(

1198771198662

11987111986411198642)

2

(34)


119901Φ(120601) =

exp (minus120574)


sdot int

radic2120574 cos(120601)

minusinfin

exp(minus119909

2

2)119889119909]

(35)


120574 =119875119862

119875119873amp

+ 119875119873PD

(36)



119875119899120601

= int

+infin

minusinfin

1206012119901Φ(120601) 119889120601 (37)











119875total (119905) = 1205980 sdot (119873

sum

119899=1119877 sdot 119894119899 (119905))

2

(38)


120590Δ119875

1198750=


1198750

(39)





Case 1Case 2

Case 3

10minus3

10minus4

10minus5

10minus6

120590ΔPP

0






119899(119905) + 119895 sdot HT119894

119899(119905) where


119860119899 (119905) = radic(Re

119899 (119905))2+ (Im

119899 (119905))2

120601119899 (119905) = atan

Im 119899 (119905)

Re 119899 (119905)

(40)


119899(119905)

and 120601119899(119905) that is

1198600 (119905) =1119873

119873

sum

119899=1119860119899 (119905)

1206010 (119905) =1119873

119873

sum

119899=1

120601119899 (119905)

(41)


119899(119905) of


Δ119860119899 (119905) = 119860

119899 (119905) minus1198600 (119905)

Δ120601119899 (119905) = 120601

119899 (119905) minus 1206010 (119905) (42)


1205902119860

1205832119860

=

⟨Δ1198602119899(119905)⟩

⟨1198600 (119905)⟩2 (43)


1205902120601= ⟨Δ120601

2119899(119905)⟩ (44)




Case 1Case 2

Case 3

10minus3

10minus2

10minus4

10minus5

10minus6

1205902 A120583

2 A

(a)


Case 1Case 2

Case 3

10minus3

10minus2

10minus4

10minus5

10minus6

1205902 120601

(b)





0 05 1 15

0

869

94

08


minus40

minus20

minus80 5 10 15

Time (120583s)

0 5 10 15Time (120583s)

Gm

ax(d

B)120579

max

(mRa

d)|A

F(120579)|

(dB)

1205902 = 0074

1205902 = 158







0 05 1 15

0

869

94

08


minus40

minus20

minus80 5 10 15 20

Time (120583s)

0 5 10 15 20Time (120583s)

Gm

ax(d

B)120579

max

(mRa

d)|A

F(120579)|

(dB)

1205902 = 33E minus 4

1205902 = 005


0 05 1 15

0

869

94

08


minus40

minus20

minus80 5 10 15 20

Time (120583s)

0 5 10 15 20Time (120583s)

Gm

ax(d

B)120579

max

(mRa

d)|A

F(120579)|

(dB)

1205902 = 34E minus 4

1205902 = 005





0 05 1 15

0

566

64

08


minus40

minus20

minus80 5 10 15 20

Time (120583s)

0 5 10 15 20Time (120583s)

Gm

ax(d

B)120579

max

(mRa

d)|A

F(120579)|

(dB)

1205902 = 0004

1205902 = 437


0 05 1 15

0

569

64

08


minus40

minus20

minus80 5 10 15 20

Time (120583s)

0 5 10 15 20Time (120583s)

Gm

ax(d

B)120579

max

(mRa

d)|A

F(120579)|

(dB)

1205902 = 0074

1205902 = 158




0 05 1 15

0

11612

124

08


minus40

minus20

minus80 5 10 15 20

Time (120583s)

0 5 10 15 20Time (120583s)

Gm

ax(d

B)120579

max

(mRa

d)|A

F(120579)|

(dB)

1205902 = 0130

1205902 = 077


7 Conclusions




References












































































































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation











Cosine

0 05 1 15

0

5

10


Θ (rad)

|AF(Θ)|

(dB)

(a)

0

1

2


|Ai|

(b)

1 2 3 4 5 6 7 8

02

minus2

Antenna element i

Ang

leA

i

(c)



ΘMAX = sin (2120591119891RF) (8)






119864 (119905) = 11986401 (119905) sdot exp 119895 [21205871198911119905 + 1206011 (119905)] +119898 (119905)

sdot 11986402 (119905) sdot exp 119895 [21205871198912119905 + 1206012 (119905)] (9)



fRF fRF fRF

fRFfRFf1 f2


m(t)



119894PD (119905) = 119877 |119864 (119905)|2+ 119899 (119905) = 119877 [119864 (119905) sdot 119864 (119905)

lowast] + 119899 (119905) (10)


119894RF (119905) = 119877 sdot 11986401 (119905) 11986402 (119905)

sdot (Re 119898 (119905) cos [2120587119891RF119905 + Δ120601 (119905)]

sdot Im 119898 (119905) sin [2120587119891RF119905 + Δ120601 (119905)]) + 1198991015840(119905)

(11)


119894RF (119905) = 119877 sdot 11986401 (119905) 11986402 (119905) sdot |119898 (119905)|

sdot cos [2120587119891RF119905 + 120601119898 (119905) + Δ120601 (119905)] + 119899

1015840(119905)

(12)










Groundplane

GroundplaneAntenna

Substrate

(a)

Groundplane

Groundplane

Antenna

Substrate

Foam

(b) (c)


h

Conduction band

Absor

ption

Valence

N

P

band

(a)

h

Conduction band

Valence band

Bloc

king

laye

r

Abso

rptio

n

N

P

(b)























mmW generation




Antenna unitOBFNODN

Element 1

Element 2

Element N1205820

1205820

1205820

(a)

mmW generator 1

mmW generator 2

mmW generator N

mmW generation





Element 1

Element 2

Element N1205820

1205820

1205820

(b)








119864 (119905) = 1198641 (119905 minusΔ1198791) + 1198642 (119905 minusΔ1198792)

= 11986401 exp [11989521205871198911 (119905 minusΔ1198791)]

+ 11986402 exp [11989521205871198912 (119905 minusΔ1198792)]

(16)


119894RF (119905) = 2119877 sdot 1198640111986402




119894RF (119905) = 2119877 sdot 1198640111986402


2120575119879]


(18)




mmW generation




Antenna unitOBFNODN

Element 1

Element 2

Element N120582N

1205822

1205821

(a)

OBFN ODN

Antenna unit

Element 1

Element 2

Element N120582N

1205822





mmW generation

(b)

mmW generator 1

mmW generator 2

mmW generator N

mmW generation




Antenna unitOBFNODN

Element 1

Element 2

Element N120582N

1205822

1205821

(c)

mmW generator 1

mmW generator 2

mmW generator N

mmW generation





Element 1

Element 2

Element N120582N

1205822

1205821

120582N

1205822

1205821

(d)



Δ120601CM = 2120587119891RFΔ119879 (19)

Δ120601diff = 21205871198911 + 1198912

2120575119879 (20)






On

L 2L 2Nminus1L


(a)

L

2L



(b)

Combiners

Splitters

Antennaelement 1

Antennaelement N


(c)





Rotarymirror

Mirror

Collimator

LL998400

(a)

Mirror MirrorL

L998400


prism

Disp

lace

men

t

(b)

L

L998400


(c)








element 2Antenna

element 3Antenna

element 4

Antennaelement N


input

Split

ter

(a)


element 2Antenna

element 3Antenna

element 4

Antennaelement N

Variablewavelength

input

Split

ter

1205821

1205822

1205823

120582K

(b)


AntennaCombiner

PMSplitter

Mux

PM

PM

element 1

Antennaelement 1

Antennaelement N











Photodiode









119864 (119905) = 11986401 (119905) sdot exp 119895 [21205871198911119905 + 1206011 (119905)] + 11986402 (119905)

sdot exp 119895 [21205871198912119905 + 1206012 (119905)] (21)



119864 (119905) = [1198641 +Δ1198641 (119905)] sdot exp 119895 [21205871198911119905 + 1206011 (119905)]

+ [1198642 +Δ1198642 (119905)] sdot exp 119895 [21205871198912119905 + 1206012 (119905)] (22)








119894PD (119905) =

119877 sdot10038161003816100381610038161003816119864amp (119905)

10038161003816100381610038161003816

2

119871+ 119899PD (119905)

(24)




119894PD (119905) =119877

119871(119866 (119864

201 +119864

202)

+11986611986401 (119905) 11986402 (119905) cos [2120587119891mm119905 + Δ120601 (119905)]

+ 2radic119866Re 119899ASE (119905) 11986401 (119905) exp119895 [21205871198911119905 + 1206011]

+ 2radic119866Re 119899ASE (119905) 11986402 (119905) exp119895 [21205871198912119905 + 1206012]

+1003816100381610038161003816119899ASE (119905)

1003816100381610038161003816

2) + 119899PD (119905)

(25)


119894PD (119905) asymp119877

119871(119866 (119864

201 +119864

202)

+11986611986401 (119905) 11986402 (119905) cos [2120587119891mm119905 + Δ120601 (119905)]

+ 2radic119866Re 119899ASE (119905) 11986401 (119905) exp119895 [21205871198911119905 + 1206011]

+ 2radic119866Re 119899ASE (119905) 11986402 (119905) exp119895 [21205871198912119905 + 1206012])

+ 119899PD (119905)

(26)


119894RF (119905) asymp119877

119871(11986611986401 (119905) 11986402 (119905) cos [2120587119891mm119905 + Δ120601 (119905)]

+ 2radic119866Re 1198991015840ASE (119905) 11986401 (119905) exp119895 [21205871198911119905 + 1206011]

+ 2radic119866Re 1198991015840ASE (119905) 11986402 (119905) exp119895 [21205871198912119905 + 1206012])

+ 1198991015840

PD (119905)

(27)

where 1198991015840

PD(119905) and 1198991015840


119894RF (119905) asymp119877

119871(119866 [1198641 +Δ1198641 (119905)] sdot [1198642 +Δ1198642 (119905)]

sdot cos [2120587119891mm119905 + Δ120601 (119905)]

+ 2radic119866Re 1198991015840ASE (119905) [1198641 +Δ1198641 (119905)]

sdot exp119895 [21205871198911119905 + 1206011]

+ 2radic119866Re 1198991015840ASE (119905) [1198642 +Δ1198642 (119905)]

sdot exp119895 [21205871198912119905 + 1206012]) + 1198991015840

PD (119905)

(28)


119894RF (119905) asymp119877119866

11987111986411198642cos [2120587119891mm119905 + Δ120601 (119905)]

+119877119866

119871[Δ1198641 (119905) 1198642 +Δ1198642 (119905) 1198641]

sdot cos [2120587119891mm119905 + Δ120601 (119905)]

+2119877radic119866

119871Re 1198991015840ASE (119905) 1198641exp119895 [21205871198911119905 + 1206011]

+2119877radic119866

119871Re 1198991015840ASE (119905) 1198642exp119895 [21205871198912119905 + 1206012]

+ 1198991015840

PD (119905)

(29)


119860(119905) acquires

the form

119899119860 (119905) =

119877119866

119871[Δ1198641 (119905) 1198642 +Δ1198642 (119905) 1198641]

+2119877radic119866

119871Re 1198991015840ASE (119905) 1198641

+2119877radic119866

119871Re 1198991015840ASE (119905) 1198642 + 119899

1015840

PD (119905)

(30)



119875119899119860

= 119875119873source

+119875119873amp

+119875119873PD (31)

with

119875119873source

= (119877119866

119871)

2[Δ1198641 (119905) 1198642 + Δ1198642 (119905) 1198641]

2

119875119873amp

= 2(119877radic119866

119871)

2

1198992ASE (119905) (119864

21 +119864

22)

119875119873PD

= 1198992PD (119905)

(32)




values 119875119873PD




CNR =119875119862

119875119899119860

=119875119862

119875119873source

+ 119875119873amp

+ 119875119873PD

(33)


119875119862

=12(

1198771198662

11987111986411198642)

2

(34)


119901Φ(120601) =

exp (minus120574)


sdot int

radic2120574 cos(120601)

minusinfin

exp(minus119909

2

2)119889119909]

(35)


120574 =119875119862

119875119873amp

+ 119875119873PD

(36)



119875119899120601

= int

+infin

minusinfin

1206012119901Φ(120601) 119889120601 (37)











119875total (119905) = 1205980 sdot (119873

sum

119899=1119877 sdot 119894119899 (119905))

2

(38)


120590Δ119875

1198750=


1198750

(39)





Case 1Case 2

Case 3

10minus3

10minus4

10minus5

10minus6

120590ΔPP

0






119899(119905) + 119895 sdot HT119894

119899(119905) where


119860119899 (119905) = radic(Re

119899 (119905))2+ (Im

119899 (119905))2

120601119899 (119905) = atan

Im 119899 (119905)

Re 119899 (119905)

(40)


119899(119905)

and 120601119899(119905) that is

1198600 (119905) =1119873

119873

sum

119899=1119860119899 (119905)

1206010 (119905) =1119873

119873

sum

119899=1

120601119899 (119905)

(41)


119899(119905) of


Δ119860119899 (119905) = 119860

119899 (119905) minus1198600 (119905)

Δ120601119899 (119905) = 120601

119899 (119905) minus 1206010 (119905) (42)


1205902119860

1205832119860

=

⟨Δ1198602119899(119905)⟩

⟨1198600 (119905)⟩2 (43)


1205902120601= ⟨Δ120601

2119899(119905)⟩ (44)




Case 1Case 2

Case 3

10minus3

10minus2

10minus4

10minus5

10minus6

1205902 A120583

2 A

(a)


Case 1Case 2

Case 3

10minus3

10minus2

10minus4

10minus5

10minus6

1205902 120601

(b)





0 05 1 15

0

869

94

08


minus40

minus20

minus80 5 10 15

Time (120583s)

0 5 10 15Time (120583s)

Gm

ax(d

B)120579

max

(mRa

d)|A

F(120579)|

(dB)

1205902 = 0074

1205902 = 158







0 05 1 15

0

869

94

08


minus40

minus20

minus80 5 10 15 20

Time (120583s)

0 5 10 15 20Time (120583s)

Gm

ax(d

B)120579

max

(mRa

d)|A

F(120579)|

(dB)

1205902 = 33E minus 4

1205902 = 005


0 05 1 15

0

869

94

08


minus40

minus20

minus80 5 10 15 20

Time (120583s)

0 5 10 15 20Time (120583s)

Gm

ax(d

B)120579

max

(mRa

d)|A

F(120579)|

(dB)

1205902 = 34E minus 4

1205902 = 005





0 05 1 15

0

566

64

08


minus40

minus20

minus80 5 10 15 20

Time (120583s)

0 5 10 15 20Time (120583s)

Gm

ax(d

B)120579

max

(mRa

d)|A

F(120579)|

(dB)

1205902 = 0004

1205902 = 437


0 05 1 15

0

569

64

08


minus40

minus20

minus80 5 10 15 20

Time (120583s)

0 5 10 15 20Time (120583s)

Gm

ax(d

B)120579

max

(mRa

d)|A

F(120579)|

(dB)

1205902 = 0074

1205902 = 158




0 05 1 15

0

11612

124

08


minus40

minus20

minus80 5 10 15 20

Time (120583s)

0 5 10 15 20Time (120583s)

Gm

ax(d

B)120579

max

(mRa

d)|A

F(120579)|

(dB)

1205902 = 0130

1205902 = 077


7 Conclusions




References












































































































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










fRF fRF fRF

fRFfRFf1 f2


m(t)



119894PD (119905) = 119877 |119864 (119905)|2+ 119899 (119905) = 119877 [119864 (119905) sdot 119864 (119905)

lowast] + 119899 (119905) (10)


119894RF (119905) = 119877 sdot 11986401 (119905) 11986402 (119905)

sdot (Re 119898 (119905) cos [2120587119891RF119905 + Δ120601 (119905)]

sdot Im 119898 (119905) sin [2120587119891RF119905 + Δ120601 (119905)]) + 1198991015840(119905)

(11)


119894RF (119905) = 119877 sdot 11986401 (119905) 11986402 (119905) sdot |119898 (119905)|

sdot cos [2120587119891RF119905 + 120601119898 (119905) + Δ120601 (119905)] + 119899

1015840(119905)

(12)










Groundplane

GroundplaneAntenna

Substrate

(a)

Groundplane

Groundplane

Antenna

Substrate

Foam

(b) (c)


h

Conduction band

Absor

ption

Valence

N

P

band

(a)

h

Conduction band

Valence band

Bloc

king

laye

r

Abso

rptio

n

N

P

(b)























mmW generation




Antenna unitOBFNODN

Element 1

Element 2

Element N1205820

1205820

1205820

(a)

mmW generator 1

mmW generator 2

mmW generator N

mmW generation





Element 1

Element 2

Element N1205820

1205820

1205820

(b)








119864 (119905) = 1198641 (119905 minusΔ1198791) + 1198642 (119905 minusΔ1198792)

= 11986401 exp [11989521205871198911 (119905 minusΔ1198791)]

+ 11986402 exp [11989521205871198912 (119905 minusΔ1198792)]

(16)


119894RF (119905) = 2119877 sdot 1198640111986402




119894RF (119905) = 2119877 sdot 1198640111986402


2120575119879]


(18)




mmW generation




Antenna unitOBFNODN

Element 1

Element 2

Element N120582N

1205822

1205821

(a)

OBFN ODN

Antenna unit

Element 1

Element 2

Element N120582N

1205822





mmW generation

(b)

mmW generator 1

mmW generator 2

mmW generator N

mmW generation




Antenna unitOBFNODN

Element 1

Element 2

Element N120582N

1205822

1205821

(c)

mmW generator 1

mmW generator 2

mmW generator N

mmW generation





Element 1

Element 2

Element N120582N

1205822

1205821

120582N

1205822

1205821

(d)



Δ120601CM = 2120587119891RFΔ119879 (19)

Δ120601diff = 21205871198911 + 1198912

2120575119879 (20)






On

L 2L 2Nminus1L


(a)

L

2L



(b)

Combiners

Splitters

Antennaelement 1

Antennaelement N


(c)





Rotarymirror

Mirror

Collimator

LL998400

(a)

Mirror MirrorL

L998400


prism

Disp

lace

men

t

(b)

L

L998400


(c)








element 2Antenna

element 3Antenna

element 4

Antennaelement N


input

Split

ter

(a)


element 2Antenna

element 3Antenna

element 4

Antennaelement N

Variablewavelength

input

Split

ter

1205821

1205822

1205823

120582K

(b)


AntennaCombiner

PMSplitter

Mux

PM

PM

element 1

Antennaelement 1

Antennaelement N











Photodiode









119864 (119905) = 11986401 (119905) sdot exp 119895 [21205871198911119905 + 1206011 (119905)] + 11986402 (119905)

sdot exp 119895 [21205871198912119905 + 1206012 (119905)] (21)



119864 (119905) = [1198641 +Δ1198641 (119905)] sdot exp 119895 [21205871198911119905 + 1206011 (119905)]

+ [1198642 +Δ1198642 (119905)] sdot exp 119895 [21205871198912119905 + 1206012 (119905)] (22)








119894PD (119905) =

119877 sdot10038161003816100381610038161003816119864amp (119905)

10038161003816100381610038161003816

2

119871+ 119899PD (119905)

(24)




119894PD (119905) =119877

119871(119866 (119864

201 +119864

202)

+11986611986401 (119905) 11986402 (119905) cos [2120587119891mm119905 + Δ120601 (119905)]

+ 2radic119866Re 119899ASE (119905) 11986401 (119905) exp119895 [21205871198911119905 + 1206011]

+ 2radic119866Re 119899ASE (119905) 11986402 (119905) exp119895 [21205871198912119905 + 1206012]

+1003816100381610038161003816119899ASE (119905)

1003816100381610038161003816

2) + 119899PD (119905)

(25)


119894PD (119905) asymp119877

119871(119866 (119864

201 +119864

202)

+11986611986401 (119905) 11986402 (119905) cos [2120587119891mm119905 + Δ120601 (119905)]

+ 2radic119866Re 119899ASE (119905) 11986401 (119905) exp119895 [21205871198911119905 + 1206011]

+ 2radic119866Re 119899ASE (119905) 11986402 (119905) exp119895 [21205871198912119905 + 1206012])

+ 119899PD (119905)

(26)


119894RF (119905) asymp119877

119871(11986611986401 (119905) 11986402 (119905) cos [2120587119891mm119905 + Δ120601 (119905)]

+ 2radic119866Re 1198991015840ASE (119905) 11986401 (119905) exp119895 [21205871198911119905 + 1206011]

+ 2radic119866Re 1198991015840ASE (119905) 11986402 (119905) exp119895 [21205871198912119905 + 1206012])

+ 1198991015840

PD (119905)

(27)

where 1198991015840

PD(119905) and 1198991015840


119894RF (119905) asymp119877

119871(119866 [1198641 +Δ1198641 (119905)] sdot [1198642 +Δ1198642 (119905)]

sdot cos [2120587119891mm119905 + Δ120601 (119905)]

+ 2radic119866Re 1198991015840ASE (119905) [1198641 +Δ1198641 (119905)]

sdot exp119895 [21205871198911119905 + 1206011]

+ 2radic119866Re 1198991015840ASE (119905) [1198642 +Δ1198642 (119905)]

sdot exp119895 [21205871198912119905 + 1206012]) + 1198991015840

PD (119905)

(28)


119894RF (119905) asymp119877119866

11987111986411198642cos [2120587119891mm119905 + Δ120601 (119905)]

+119877119866

119871[Δ1198641 (119905) 1198642 +Δ1198642 (119905) 1198641]

sdot cos [2120587119891mm119905 + Δ120601 (119905)]

+2119877radic119866

119871Re 1198991015840ASE (119905) 1198641exp119895 [21205871198911119905 + 1206011]

+2119877radic119866

119871Re 1198991015840ASE (119905) 1198642exp119895 [21205871198912119905 + 1206012]

+ 1198991015840

PD (119905)

(29)


119860(119905) acquires

the form

119899119860 (119905) =

119877119866

119871[Δ1198641 (119905) 1198642 +Δ1198642 (119905) 1198641]

+2119877radic119866

119871Re 1198991015840ASE (119905) 1198641

+2119877radic119866

119871Re 1198991015840ASE (119905) 1198642 + 119899

1015840

PD (119905)

(30)



119875119899119860

= 119875119873source

+119875119873amp

+119875119873PD (31)

with

119875119873source

= (119877119866

119871)

2[Δ1198641 (119905) 1198642 + Δ1198642 (119905) 1198641]

2

119875119873amp

= 2(119877radic119866

119871)

2

1198992ASE (119905) (119864

21 +119864

22)

119875119873PD

= 1198992PD (119905)

(32)




values 119875119873PD




CNR =119875119862

119875119899119860

=119875119862

119875119873source

+ 119875119873amp

+ 119875119873PD

(33)


119875119862

=12(

1198771198662

11987111986411198642)

2

(34)


119901Φ(120601) =

exp (minus120574)


sdot int

radic2120574 cos(120601)

minusinfin

exp(minus119909

2

2)119889119909]

(35)


120574 =119875119862

119875119873amp

+ 119875119873PD

(36)



119875119899120601

= int

+infin

minusinfin

1206012119901Φ(120601) 119889120601 (37)











119875total (119905) = 1205980 sdot (119873

sum

119899=1119877 sdot 119894119899 (119905))

2

(38)


120590Δ119875

1198750=


1198750

(39)





Case 1Case 2

Case 3

10minus3

10minus4

10minus5

10minus6

120590ΔPP

0






119899(119905) + 119895 sdot HT119894

119899(119905) where


119860119899 (119905) = radic(Re

119899 (119905))2+ (Im

119899 (119905))2

120601119899 (119905) = atan

Im 119899 (119905)

Re 119899 (119905)

(40)


119899(119905)

and 120601119899(119905) that is

1198600 (119905) =1119873

119873

sum

119899=1119860119899 (119905)

1206010 (119905) =1119873

119873

sum

119899=1

120601119899 (119905)

(41)


119899(119905) of


Δ119860119899 (119905) = 119860

119899 (119905) minus1198600 (119905)

Δ120601119899 (119905) = 120601

119899 (119905) minus 1206010 (119905) (42)


1205902119860

1205832119860

=

⟨Δ1198602119899(119905)⟩

⟨1198600 (119905)⟩2 (43)


1205902120601= ⟨Δ120601

2119899(119905)⟩ (44)




Case 1Case 2

Case 3

10minus3

10minus2

10minus4

10minus5

10minus6

1205902 A120583

2 A

(a)


Case 1Case 2

Case 3

10minus3

10minus2

10minus4

10minus5

10minus6

1205902 120601

(b)





0 05 1 15

0

869

94

08


minus40

minus20

minus80 5 10 15

Time (120583s)

0 5 10 15Time (120583s)

Gm

ax(d

B)120579

max

(mRa

d)|A

F(120579)|

(dB)

1205902 = 0074

1205902 = 158







0 05 1 15

0

869

94

08


minus40

minus20

minus80 5 10 15 20

Time (120583s)

0 5 10 15 20Time (120583s)

Gm

ax(d

B)120579

max

(mRa

d)|A

F(120579)|

(dB)

1205902 = 33E minus 4

1205902 = 005


0 05 1 15

0

869

94

08


minus40

minus20

minus80 5 10 15 20

Time (120583s)

0 5 10 15 20Time (120583s)

Gm

ax(d

B)120579

max

(mRa

d)|A

F(120579)|

(dB)

1205902 = 34E minus 4

1205902 = 005





0 05 1 15

0

566

64

08


minus40

minus20

minus80 5 10 15 20

Time (120583s)

0 5 10 15 20Time (120583s)

Gm

ax(d

B)120579

max

(mRa

d)|A

F(120579)|

(dB)

1205902 = 0004

1205902 = 437


0 05 1 15

0

569

64

08


minus40

minus20

minus80 5 10 15 20

Time (120583s)

0 5 10 15 20Time (120583s)

Gm

ax(d

B)120579

max

(mRa

d)|A

F(120579)|

(dB)

1205902 = 0074

1205902 = 158




0 05 1 15

0

11612

124

08


minus40

minus20

minus80 5 10 15 20

Time (120583s)

0 5 10 15 20Time (120583s)

Gm

ax(d

B)120579

max

(mRa

d)|A

F(120579)|

(dB)

1205902 = 0130

1205902 = 077


7 Conclusions




References












































































































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










Groundplane

GroundplaneAntenna

Substrate

(a)

Groundplane

Groundplane

Antenna

Substrate

Foam

(b) (c)


h

Conduction band

Absor

ption

Valence

N

P

band

(a)

h

Conduction band

Valence band

Bloc

king

laye

r

Abso

rptio

n

N

P

(b)























mmW generation




Antenna unitOBFNODN

Element 1

Element 2

Element N1205820

1205820

1205820

(a)

mmW generator 1

mmW generator 2

mmW generator N

mmW generation





Element 1

Element 2

Element N1205820

1205820

1205820

(b)








119864 (119905) = 1198641 (119905 minusΔ1198791) + 1198642 (119905 minusΔ1198792)

= 11986401 exp [11989521205871198911 (119905 minusΔ1198791)]

+ 11986402 exp [11989521205871198912 (119905 minusΔ1198792)]

(16)


119894RF (119905) = 2119877 sdot 1198640111986402




119894RF (119905) = 2119877 sdot 1198640111986402


2120575119879]


(18)




mmW generation




Antenna unitOBFNODN

Element 1

Element 2

Element N120582N

1205822

1205821

(a)

OBFN ODN

Antenna unit

Element 1

Element 2

Element N120582N

1205822





mmW generation

(b)

mmW generator 1

mmW generator 2

mmW generator N

mmW generation




Antenna unitOBFNODN

Element 1

Element 2

Element N120582N

1205822

1205821

(c)

mmW generator 1

mmW generator 2

mmW generator N

mmW generation





Element 1

Element 2

Element N120582N

1205822

1205821

120582N

1205822

1205821

(d)



Δ120601CM = 2120587119891RFΔ119879 (19)

Δ120601diff = 21205871198911 + 1198912

2120575119879 (20)






On

L 2L 2Nminus1L


(a)

L

2L



(b)

Combiners

Splitters

Antennaelement 1

Antennaelement N


(c)





Rotarymirror

Mirror

Collimator

LL998400

(a)

Mirror MirrorL

L998400


prism

Disp

lace

men

t

(b)

L

L998400


(c)








element 2Antenna

element 3Antenna

element 4

Antennaelement N


input

Split

ter

(a)


element 2Antenna

element 3Antenna

element 4

Antennaelement N

Variablewavelength

input

Split

ter

1205821

1205822

1205823

120582K

(b)


AntennaCombiner

PMSplitter

Mux

PM

PM

element 1

Antennaelement 1

Antennaelement N











Photodiode









119864 (119905) = 11986401 (119905) sdot exp 119895 [21205871198911119905 + 1206011 (119905)] + 11986402 (119905)

sdot exp 119895 [21205871198912119905 + 1206012 (119905)] (21)



119864 (119905) = [1198641 +Δ1198641 (119905)] sdot exp 119895 [21205871198911119905 + 1206011 (119905)]

+ [1198642 +Δ1198642 (119905)] sdot exp 119895 [21205871198912119905 + 1206012 (119905)] (22)








119894PD (119905) =

119877 sdot10038161003816100381610038161003816119864amp (119905)

10038161003816100381610038161003816

2

119871+ 119899PD (119905)

(24)




119894PD (119905) =119877

119871(119866 (119864

201 +119864

202)

+11986611986401 (119905) 11986402 (119905) cos [2120587119891mm119905 + Δ120601 (119905)]

+ 2radic119866Re 119899ASE (119905) 11986401 (119905) exp119895 [21205871198911119905 + 1206011]

+ 2radic119866Re 119899ASE (119905) 11986402 (119905) exp119895 [21205871198912119905 + 1206012]

+1003816100381610038161003816119899ASE (119905)

1003816100381610038161003816

2) + 119899PD (119905)

(25)


119894PD (119905) asymp119877

119871(119866 (119864

201 +119864

202)

+11986611986401 (119905) 11986402 (119905) cos [2120587119891mm119905 + Δ120601 (119905)]

+ 2radic119866Re 119899ASE (119905) 11986401 (119905) exp119895 [21205871198911119905 + 1206011]

+ 2radic119866Re 119899ASE (119905) 11986402 (119905) exp119895 [21205871198912119905 + 1206012])

+ 119899PD (119905)

(26)


119894RF (119905) asymp119877

119871(11986611986401 (119905) 11986402 (119905) cos [2120587119891mm119905 + Δ120601 (119905)]

+ 2radic119866Re 1198991015840ASE (119905) 11986401 (119905) exp119895 [21205871198911119905 + 1206011]

+ 2radic119866Re 1198991015840ASE (119905) 11986402 (119905) exp119895 [21205871198912119905 + 1206012])

+ 1198991015840

PD (119905)

(27)

where 1198991015840

PD(119905) and 1198991015840


119894RF (119905) asymp119877

119871(119866 [1198641 +Δ1198641 (119905)] sdot [1198642 +Δ1198642 (119905)]

sdot cos [2120587119891mm119905 + Δ120601 (119905)]

+ 2radic119866Re 1198991015840ASE (119905) [1198641 +Δ1198641 (119905)]

sdot exp119895 [21205871198911119905 + 1206011]

+ 2radic119866Re 1198991015840ASE (119905) [1198642 +Δ1198642 (119905)]

sdot exp119895 [21205871198912119905 + 1206012]) + 1198991015840

PD (119905)

(28)


119894RF (119905) asymp119877119866

11987111986411198642cos [2120587119891mm119905 + Δ120601 (119905)]

+119877119866

119871[Δ1198641 (119905) 1198642 +Δ1198642 (119905) 1198641]

sdot cos [2120587119891mm119905 + Δ120601 (119905)]

+2119877radic119866

119871Re 1198991015840ASE (119905) 1198641exp119895 [21205871198911119905 + 1206011]

+2119877radic119866

119871Re 1198991015840ASE (119905) 1198642exp119895 [21205871198912119905 + 1206012]

+ 1198991015840

PD (119905)

(29)


119860(119905) acquires

the form

119899119860 (119905) =

119877119866

119871[Δ1198641 (119905) 1198642 +Δ1198642 (119905) 1198641]

+2119877radic119866

119871Re 1198991015840ASE (119905) 1198641

+2119877radic119866

119871Re 1198991015840ASE (119905) 1198642 + 119899

1015840

PD (119905)

(30)



119875119899119860

= 119875119873source

+119875119873amp

+119875119873PD (31)

with

119875119873source

= (119877119866

119871)

2[Δ1198641 (119905) 1198642 + Δ1198642 (119905) 1198641]

2

119875119873amp

= 2(119877radic119866

119871)

2

1198992ASE (119905) (119864

21 +119864

22)

119875119873PD

= 1198992PD (119905)

(32)




values 119875119873PD




CNR =119875119862

119875119899119860

=119875119862

119875119873source

+ 119875119873amp

+ 119875119873PD

(33)


119875119862

=12(

1198771198662

11987111986411198642)

2

(34)


119901Φ(120601) =

exp (minus120574)


sdot int

radic2120574 cos(120601)

minusinfin

exp(minus119909

2

2)119889119909]

(35)


120574 =119875119862

119875119873amp

+ 119875119873PD

(36)



119875119899120601

= int

+infin

minusinfin

1206012119901Φ(120601) 119889120601 (37)











119875total (119905) = 1205980 sdot (119873

sum

119899=1119877 sdot 119894119899 (119905))

2

(38)


120590Δ119875

1198750=


1198750

(39)





Case 1Case 2

Case 3

10minus3

10minus4

10minus5

10minus6

120590ΔPP

0






119899(119905) + 119895 sdot HT119894

119899(119905) where


119860119899 (119905) = radic(Re

119899 (119905))2+ (Im

119899 (119905))2

120601119899 (119905) = atan

Im 119899 (119905)

Re 119899 (119905)

(40)


119899(119905)

and 120601119899(119905) that is

1198600 (119905) =1119873

119873

sum

119899=1119860119899 (119905)

1206010 (119905) =1119873

119873

sum

119899=1

120601119899 (119905)

(41)


119899(119905) of


Δ119860119899 (119905) = 119860

119899 (119905) minus1198600 (119905)

Δ120601119899 (119905) = 120601

119899 (119905) minus 1206010 (119905) (42)


1205902119860

1205832119860

=

⟨Δ1198602119899(119905)⟩

⟨1198600 (119905)⟩2 (43)


1205902120601= ⟨Δ120601

2119899(119905)⟩ (44)




Case 1Case 2

Case 3

10minus3

10minus2

10minus4

10minus5

10minus6

1205902 A120583

2 A

(a)


Case 1Case 2

Case 3

10minus3

10minus2

10minus4

10minus5

10minus6

1205902 120601

(b)





0 05 1 15

0

869

94

08


minus40

minus20

minus80 5 10 15

Time (120583s)

0 5 10 15Time (120583s)

Gm

ax(d

B)120579

max

(mRa

d)|A

F(120579)|

(dB)

1205902 = 0074

1205902 = 158







0 05 1 15

0

869

94

08


minus40

minus20

minus80 5 10 15 20

Time (120583s)

0 5 10 15 20Time (120583s)

Gm

ax(d

B)120579

max

(mRa

d)|A

F(120579)|

(dB)

1205902 = 33E minus 4

1205902 = 005


0 05 1 15

0

869

94

08


minus40

minus20

minus80 5 10 15 20

Time (120583s)

0 5 10 15 20Time (120583s)

Gm

ax(d

B)120579

max

(mRa

d)|A

F(120579)|

(dB)

1205902 = 34E minus 4

1205902 = 005





0 05 1 15

0

566

64

08


minus40

minus20

minus80 5 10 15 20

Time (120583s)

0 5 10 15 20Time (120583s)

Gm

ax(d

B)120579

max

(mRa

d)|A

F(120579)|

(dB)

1205902 = 0004

1205902 = 437


0 05 1 15

0

569

64

08


minus40

minus20

minus80 5 10 15 20

Time (120583s)

0 5 10 15 20Time (120583s)

Gm

ax(d

B)120579

max

(mRa

d)|A

F(120579)|

(dB)

1205902 = 0074

1205902 = 158




0 05 1 15

0

11612

124

08


minus40

minus20

minus80 5 10 15 20

Time (120583s)

0 5 10 15 20Time (120583s)

Gm

ax(d

B)120579

max

(mRa

d)|A

F(120579)|

(dB)

1205902 = 0130

1205902 = 077


7 Conclusions




References












































































































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation

























mmW generation




Antenna unitOBFNODN

Element 1

Element 2

Element N1205820

1205820

1205820

(a)

mmW generator 1

mmW generator 2

mmW generator N

mmW generation





Element 1

Element 2

Element N1205820

1205820

1205820

(b)








119864 (119905) = 1198641 (119905 minusΔ1198791) + 1198642 (119905 minusΔ1198792)

= 11986401 exp [11989521205871198911 (119905 minusΔ1198791)]

+ 11986402 exp [11989521205871198912 (119905 minusΔ1198792)]

(16)


119894RF (119905) = 2119877 sdot 1198640111986402




119894RF (119905) = 2119877 sdot 1198640111986402


2120575119879]


(18)




mmW generation




Antenna unitOBFNODN

Element 1

Element 2

Element N120582N

1205822

1205821

(a)

OBFN ODN

Antenna unit

Element 1

Element 2

Element N120582N

1205822





mmW generation

(b)

mmW generator 1

mmW generator 2

mmW generator N

mmW generation




Antenna unitOBFNODN

Element 1

Element 2

Element N120582N

1205822

1205821

(c)

mmW generator 1

mmW generator 2

mmW generator N

mmW generation





Element 1

Element 2

Element N120582N

1205822

1205821

120582N

1205822

1205821

(d)



Δ120601CM = 2120587119891RFΔ119879 (19)

Δ120601diff = 21205871198911 + 1198912

2120575119879 (20)






On

L 2L 2Nminus1L


(a)

L

2L



(b)

Combiners

Splitters

Antennaelement 1

Antennaelement N


(c)





Rotarymirror

Mirror

Collimator

LL998400

(a)

Mirror MirrorL

L998400


prism

Disp

lace

men

t

(b)

L

L998400


(c)








element 2Antenna

element 3Antenna

element 4

Antennaelement N


input

Split

ter

(a)


element 2Antenna

element 3Antenna

element 4

Antennaelement N

Variablewavelength

input

Split

ter

1205821

1205822

1205823

120582K

(b)


AntennaCombiner

PMSplitter

Mux

PM

PM

element 1

Antennaelement 1

Antennaelement N











Photodiode









119864 (119905) = 11986401 (119905) sdot exp 119895 [21205871198911119905 + 1206011 (119905)] + 11986402 (119905)

sdot exp 119895 [21205871198912119905 + 1206012 (119905)] (21)



119864 (119905) = [1198641 +Δ1198641 (119905)] sdot exp 119895 [21205871198911119905 + 1206011 (119905)]

+ [1198642 +Δ1198642 (119905)] sdot exp 119895 [21205871198912119905 + 1206012 (119905)] (22)








119894PD (119905) =

119877 sdot10038161003816100381610038161003816119864amp (119905)

10038161003816100381610038161003816

2

119871+ 119899PD (119905)

(24)




119894PD (119905) =119877

119871(119866 (119864

201 +119864

202)

+11986611986401 (119905) 11986402 (119905) cos [2120587119891mm119905 + Δ120601 (119905)]

+ 2radic119866Re 119899ASE (119905) 11986401 (119905) exp119895 [21205871198911119905 + 1206011]

+ 2radic119866Re 119899ASE (119905) 11986402 (119905) exp119895 [21205871198912119905 + 1206012]

+1003816100381610038161003816119899ASE (119905)

1003816100381610038161003816

2) + 119899PD (119905)

(25)


119894PD (119905) asymp119877

119871(119866 (119864

201 +119864

202)

+11986611986401 (119905) 11986402 (119905) cos [2120587119891mm119905 + Δ120601 (119905)]

+ 2radic119866Re 119899ASE (119905) 11986401 (119905) exp119895 [21205871198911119905 + 1206011]

+ 2radic119866Re 119899ASE (119905) 11986402 (119905) exp119895 [21205871198912119905 + 1206012])

+ 119899PD (119905)

(26)


119894RF (119905) asymp119877

119871(11986611986401 (119905) 11986402 (119905) cos [2120587119891mm119905 + Δ120601 (119905)]

+ 2radic119866Re 1198991015840ASE (119905) 11986401 (119905) exp119895 [21205871198911119905 + 1206011]

+ 2radic119866Re 1198991015840ASE (119905) 11986402 (119905) exp119895 [21205871198912119905 + 1206012])

+ 1198991015840

PD (119905)

(27)

where 1198991015840

PD(119905) and 1198991015840


119894RF (119905) asymp119877

119871(119866 [1198641 +Δ1198641 (119905)] sdot [1198642 +Δ1198642 (119905)]

sdot cos [2120587119891mm119905 + Δ120601 (119905)]

+ 2radic119866Re 1198991015840ASE (119905) [1198641 +Δ1198641 (119905)]

sdot exp119895 [21205871198911119905 + 1206011]

+ 2radic119866Re 1198991015840ASE (119905) [1198642 +Δ1198642 (119905)]

sdot exp119895 [21205871198912119905 + 1206012]) + 1198991015840

PD (119905)

(28)


119894RF (119905) asymp119877119866

11987111986411198642cos [2120587119891mm119905 + Δ120601 (119905)]

+119877119866

119871[Δ1198641 (119905) 1198642 +Δ1198642 (119905) 1198641]

sdot cos [2120587119891mm119905 + Δ120601 (119905)]

+2119877radic119866

119871Re 1198991015840ASE (119905) 1198641exp119895 [21205871198911119905 + 1206011]

+2119877radic119866

119871Re 1198991015840ASE (119905) 1198642exp119895 [21205871198912119905 + 1206012]

+ 1198991015840

PD (119905)

(29)


119860(119905) acquires

the form

119899119860 (119905) =

119877119866

119871[Δ1198641 (119905) 1198642 +Δ1198642 (119905) 1198641]

+2119877radic119866

119871Re 1198991015840ASE (119905) 1198641

+2119877radic119866

119871Re 1198991015840ASE (119905) 1198642 + 119899

1015840

PD (119905)

(30)



119875119899119860

= 119875119873source

+119875119873amp

+119875119873PD (31)

with

119875119873source

= (119877119866

119871)

2[Δ1198641 (119905) 1198642 + Δ1198642 (119905) 1198641]

2

119875119873amp

= 2(119877radic119866

119871)

2

1198992ASE (119905) (119864

21 +119864

22)

119875119873PD

= 1198992PD (119905)

(32)




values 119875119873PD




CNR =119875119862

119875119899119860

=119875119862

119875119873source

+ 119875119873amp

+ 119875119873PD

(33)


119875119862

=12(

1198771198662

11987111986411198642)

2

(34)


119901Φ(120601) =

exp (minus120574)


sdot int

radic2120574 cos(120601)

minusinfin

exp(minus119909

2

2)119889119909]

(35)


120574 =119875119862

119875119873amp

+ 119875119873PD

(36)



119875119899120601

= int

+infin

minusinfin

1206012119901Φ(120601) 119889120601 (37)











119875total (119905) = 1205980 sdot (119873

sum

119899=1119877 sdot 119894119899 (119905))

2

(38)


120590Δ119875

1198750=


1198750

(39)





Case 1Case 2

Case 3

10minus3

10minus4

10minus5

10minus6

120590ΔPP

0






119899(119905) + 119895 sdot HT119894

119899(119905) where


119860119899 (119905) = radic(Re

119899 (119905))2+ (Im

119899 (119905))2

120601119899 (119905) = atan

Im 119899 (119905)

Re 119899 (119905)

(40)


119899(119905)

and 120601119899(119905) that is

1198600 (119905) =1119873

119873

sum

119899=1119860119899 (119905)

1206010 (119905) =1119873

119873

sum

119899=1

120601119899 (119905)

(41)


119899(119905) of


Δ119860119899 (119905) = 119860

119899 (119905) minus1198600 (119905)

Δ120601119899 (119905) = 120601

119899 (119905) minus 1206010 (119905) (42)


1205902119860

1205832119860

=

⟨Δ1198602119899(119905)⟩

⟨1198600 (119905)⟩2 (43)


1205902120601= ⟨Δ120601

2119899(119905)⟩ (44)




Case 1Case 2

Case 3

10minus3

10minus2

10minus4

10minus5

10minus6

1205902 A120583

2 A

(a)


Case 1Case 2

Case 3

10minus3

10minus2

10minus4

10minus5

10minus6

1205902 120601

(b)





0 05 1 15

0

869

94

08


minus40

minus20

minus80 5 10 15

Time (120583s)

0 5 10 15Time (120583s)

Gm

ax(d

B)120579

max

(mRa

d)|A

F(120579)|

(dB)

1205902 = 0074

1205902 = 158







0 05 1 15

0

869

94

08


minus40

minus20

minus80 5 10 15 20

Time (120583s)

0 5 10 15 20Time (120583s)

Gm

ax(d

B)120579

max

(mRa

d)|A

F(120579)|

(dB)

1205902 = 33E minus 4

1205902 = 005


0 05 1 15

0

869

94

08


minus40

minus20

minus80 5 10 15 20

Time (120583s)

0 5 10 15 20Time (120583s)

Gm

ax(d

B)120579

max

(mRa

d)|A

F(120579)|

(dB)

1205902 = 34E minus 4

1205902 = 005





0 05 1 15

0

566

64

08


minus40

minus20

minus80 5 10 15 20

Time (120583s)

0 5 10 15 20Time (120583s)

Gm

ax(d

B)120579

max

(mRa

d)|A

F(120579)|

(dB)

1205902 = 0004

1205902 = 437


0 05 1 15

0

569

64

08


minus40

minus20

minus80 5 10 15 20

Time (120583s)

0 5 10 15 20Time (120583s)

Gm

ax(d

B)120579

max

(mRa

d)|A

F(120579)|

(dB)

1205902 = 0074

1205902 = 158




0 05 1 15

0

11612

124

08


minus40

minus20

minus80 5 10 15 20

Time (120583s)

0 5 10 15 20Time (120583s)

Gm

ax(d

B)120579

max

(mRa

d)|A

F(120579)|

(dB)

1205902 = 0130

1205902 = 077


7 Conclusions




References












































































































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation











mmW generation




Antenna unitOBFNODN

Element 1

Element 2

Element N120582N

1205822

1205821

(a)

OBFN ODN

Antenna unit

Element 1

Element 2

Element N120582N

1205822





mmW generation

(b)

mmW generator 1

mmW generator 2

mmW generator N

mmW generation




Antenna unitOBFNODN

Element 1

Element 2

Element N120582N

1205822

1205821

(c)

mmW generator 1

mmW generator 2

mmW generator N

mmW generation





Element 1

Element 2

Element N120582N

1205822

1205821

120582N

1205822

1205821

(d)



Δ120601CM = 2120587119891RFΔ119879 (19)

Δ120601diff = 21205871198911 + 1198912

2120575119879 (20)






On

L 2L 2Nminus1L


(a)

L

2L



(b)

Combiners

Splitters

Antennaelement 1

Antennaelement N


(c)





Rotarymirror

Mirror

Collimator

LL998400

(a)

Mirror MirrorL

L998400


prism

Disp

lace

men

t

(b)

L

L998400


(c)








element 2Antenna

element 3Antenna

element 4

Antennaelement N


input

Split

ter

(a)


element 2Antenna

element 3Antenna

element 4

Antennaelement N

Variablewavelength

input

Split

ter

1205821

1205822

1205823

120582K

(b)


AntennaCombiner

PMSplitter

Mux

PM

PM

element 1

Antennaelement 1

Antennaelement N











Photodiode









119864 (119905) = 11986401 (119905) sdot exp 119895 [21205871198911119905 + 1206011 (119905)] + 11986402 (119905)

sdot exp 119895 [21205871198912119905 + 1206012 (119905)] (21)



119864 (119905) = [1198641 +Δ1198641 (119905)] sdot exp 119895 [21205871198911119905 + 1206011 (119905)]

+ [1198642 +Δ1198642 (119905)] sdot exp 119895 [21205871198912119905 + 1206012 (119905)] (22)








119894PD (119905) =

119877 sdot10038161003816100381610038161003816119864amp (119905)

10038161003816100381610038161003816

2

119871+ 119899PD (119905)

(24)




119894PD (119905) =119877

119871(119866 (119864

201 +119864

202)

+11986611986401 (119905) 11986402 (119905) cos [2120587119891mm119905 + Δ120601 (119905)]

+ 2radic119866Re 119899ASE (119905) 11986401 (119905) exp119895 [21205871198911119905 + 1206011]

+ 2radic119866Re 119899ASE (119905) 11986402 (119905) exp119895 [21205871198912119905 + 1206012]

+1003816100381610038161003816119899ASE (119905)

1003816100381610038161003816

2) + 119899PD (119905)

(25)


119894PD (119905) asymp119877

119871(119866 (119864

201 +119864

202)

+11986611986401 (119905) 11986402 (119905) cos [2120587119891mm119905 + Δ120601 (119905)]

+ 2radic119866Re 119899ASE (119905) 11986401 (119905) exp119895 [21205871198911119905 + 1206011]

+ 2radic119866Re 119899ASE (119905) 11986402 (119905) exp119895 [21205871198912119905 + 1206012])

+ 119899PD (119905)

(26)


119894RF (119905) asymp119877

119871(11986611986401 (119905) 11986402 (119905) cos [2120587119891mm119905 + Δ120601 (119905)]

+ 2radic119866Re 1198991015840ASE (119905) 11986401 (119905) exp119895 [21205871198911119905 + 1206011]

+ 2radic119866Re 1198991015840ASE (119905) 11986402 (119905) exp119895 [21205871198912119905 + 1206012])

+ 1198991015840

PD (119905)

(27)

where 1198991015840

PD(119905) and 1198991015840


119894RF (119905) asymp119877

119871(119866 [1198641 +Δ1198641 (119905)] sdot [1198642 +Δ1198642 (119905)]

sdot cos [2120587119891mm119905 + Δ120601 (119905)]

+ 2radic119866Re 1198991015840ASE (119905) [1198641 +Δ1198641 (119905)]

sdot exp119895 [21205871198911119905 + 1206011]

+ 2radic119866Re 1198991015840ASE (119905) [1198642 +Δ1198642 (119905)]

sdot exp119895 [21205871198912119905 + 1206012]) + 1198991015840

PD (119905)

(28)


119894RF (119905) asymp119877119866

11987111986411198642cos [2120587119891mm119905 + Δ120601 (119905)]

+119877119866

119871[Δ1198641 (119905) 1198642 +Δ1198642 (119905) 1198641]

sdot cos [2120587119891mm119905 + Δ120601 (119905)]

+2119877radic119866

119871Re 1198991015840ASE (119905) 1198641exp119895 [21205871198911119905 + 1206011]

+2119877radic119866

119871Re 1198991015840ASE (119905) 1198642exp119895 [21205871198912119905 + 1206012]

+ 1198991015840

PD (119905)

(29)


119860(119905) acquires

the form

119899119860 (119905) =

119877119866

119871[Δ1198641 (119905) 1198642 +Δ1198642 (119905) 1198641]

+2119877radic119866

119871Re 1198991015840ASE (119905) 1198641

+2119877radic119866

119871Re 1198991015840ASE (119905) 1198642 + 119899

1015840

PD (119905)

(30)



119875119899119860

= 119875119873source

+119875119873amp

+119875119873PD (31)

with

119875119873source

= (119877119866

119871)

2[Δ1198641 (119905) 1198642 + Δ1198642 (119905) 1198641]

2

119875119873amp

= 2(119877radic119866

119871)

2

1198992ASE (119905) (119864

21 +119864

22)

119875119873PD

= 1198992PD (119905)

(32)




values 119875119873PD




CNR =119875119862

119875119899119860

=119875119862

119875119873source

+ 119875119873amp

+ 119875119873PD

(33)


119875119862

=12(

1198771198662

11987111986411198642)

2

(34)


119901Φ(120601) =

exp (minus120574)


sdot int

radic2120574 cos(120601)

minusinfin

exp(minus119909

2

2)119889119909]

(35)


120574 =119875119862

119875119873amp

+ 119875119873PD

(36)



119875119899120601

= int

+infin

minusinfin

1206012119901Φ(120601) 119889120601 (37)











119875total (119905) = 1205980 sdot (119873

sum

119899=1119877 sdot 119894119899 (119905))

2

(38)


120590Δ119875

1198750=


1198750

(39)





Case 1Case 2

Case 3

10minus3

10minus4

10minus5

10minus6

120590ΔPP

0






119899(119905) + 119895 sdot HT119894

119899(119905) where


119860119899 (119905) = radic(Re

119899 (119905))2+ (Im

119899 (119905))2

120601119899 (119905) = atan

Im 119899 (119905)

Re 119899 (119905)

(40)


119899(119905)

and 120601119899(119905) that is

1198600 (119905) =1119873

119873

sum

119899=1119860119899 (119905)

1206010 (119905) =1119873

119873

sum

119899=1

120601119899 (119905)

(41)


119899(119905) of


Δ119860119899 (119905) = 119860

119899 (119905) minus1198600 (119905)

Δ120601119899 (119905) = 120601

119899 (119905) minus 1206010 (119905) (42)


1205902119860

1205832119860

=

⟨Δ1198602119899(119905)⟩

⟨1198600 (119905)⟩2 (43)


1205902120601= ⟨Δ120601

2119899(119905)⟩ (44)




Case 1Case 2

Case 3

10minus3

10minus2

10minus4

10minus5

10minus6

1205902 A120583

2 A

(a)


Case 1Case 2

Case 3

10minus3

10minus2

10minus4

10minus5

10minus6

1205902 120601

(b)





0 05 1 15

0

869

94

08


minus40

minus20

minus80 5 10 15

Time (120583s)

0 5 10 15Time (120583s)

Gm

ax(d

B)120579

max

(mRa

d)|A

F(120579)|

(dB)

1205902 = 0074

1205902 = 158







0 05 1 15

0

869

94

08


minus40

minus20

minus80 5 10 15 20

Time (120583s)

0 5 10 15 20Time (120583s)

Gm

ax(d

B)120579

max

(mRa

d)|A

F(120579)|

(dB)

1205902 = 33E minus 4

1205902 = 005


0 05 1 15

0

869

94

08


minus40

minus20

minus80 5 10 15 20

Time (120583s)

0 5 10 15 20Time (120583s)

Gm

ax(d

B)120579

max

(mRa

d)|A

F(120579)|

(dB)

1205902 = 34E minus 4

1205902 = 005





0 05 1 15

0

566

64

08


minus40

minus20

minus80 5 10 15 20

Time (120583s)

0 5 10 15 20Time (120583s)

Gm

ax(d

B)120579

max

(mRa

d)|A

F(120579)|

(dB)

1205902 = 0004

1205902 = 437


0 05 1 15

0

569

64

08


minus40

minus20

minus80 5 10 15 20

Time (120583s)

0 5 10 15 20Time (120583s)

Gm

ax(d

B)120579

max

(mRa

d)|A

F(120579)|

(dB)

1205902 = 0074

1205902 = 158




0 05 1 15

0

11612

124

08


minus40

minus20

minus80 5 10 15 20

Time (120583s)

0 5 10 15 20Time (120583s)

Gm

ax(d

B)120579

max

(mRa

d)|A

F(120579)|

(dB)

1205902 = 0130

1205902 = 077


7 Conclusions




References












































































































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation













On

L 2L 2Nminus1L


(a)

L

2L



(b)

Combiners

Splitters

Antennaelement 1

Antennaelement N


(c)





Rotarymirror

Mirror

Collimator

LL998400

(a)

Mirror MirrorL

L998400


prism

Disp

lace

men

t

(b)

L

L998400


(c)








element 2Antenna

element 3Antenna

element 4

Antennaelement N


input

Split

ter

(a)


element 2Antenna

element 3Antenna

element 4

Antennaelement N

Variablewavelength

input

Split

ter

1205821

1205822

1205823

120582K

(b)


AntennaCombiner

PMSplitter

Mux

PM

PM

element 1

Antennaelement 1

Antennaelement N











Photodiode









119864 (119905) = 11986401 (119905) sdot exp 119895 [21205871198911119905 + 1206011 (119905)] + 11986402 (119905)

sdot exp 119895 [21205871198912119905 + 1206012 (119905)] (21)



119864 (119905) = [1198641 +Δ1198641 (119905)] sdot exp 119895 [21205871198911119905 + 1206011 (119905)]

+ [1198642 +Δ1198642 (119905)] sdot exp 119895 [21205871198912119905 + 1206012 (119905)] (22)








119894PD (119905) =

119877 sdot10038161003816100381610038161003816119864amp (119905)

10038161003816100381610038161003816

2

119871+ 119899PD (119905)

(24)




119894PD (119905) =119877

119871(119866 (119864

201 +119864

202)

+11986611986401 (119905) 11986402 (119905) cos [2120587119891mm119905 + Δ120601 (119905)]

+ 2radic119866Re 119899ASE (119905) 11986401 (119905) exp119895 [21205871198911119905 + 1206011]

+ 2radic119866Re 119899ASE (119905) 11986402 (119905) exp119895 [21205871198912119905 + 1206012]

+1003816100381610038161003816119899ASE (119905)

1003816100381610038161003816

2) + 119899PD (119905)

(25)


119894PD (119905) asymp119877

119871(119866 (119864

201 +119864

202)

+11986611986401 (119905) 11986402 (119905) cos [2120587119891mm119905 + Δ120601 (119905)]

+ 2radic119866Re 119899ASE (119905) 11986401 (119905) exp119895 [21205871198911119905 + 1206011]

+ 2radic119866Re 119899ASE (119905) 11986402 (119905) exp119895 [21205871198912119905 + 1206012])

+ 119899PD (119905)

(26)


119894RF (119905) asymp119877

119871(11986611986401 (119905) 11986402 (119905) cos [2120587119891mm119905 + Δ120601 (119905)]

+ 2radic119866Re 1198991015840ASE (119905) 11986401 (119905) exp119895 [21205871198911119905 + 1206011]

+ 2radic119866Re 1198991015840ASE (119905) 11986402 (119905) exp119895 [21205871198912119905 + 1206012])

+ 1198991015840

PD (119905)

(27)

where 1198991015840

PD(119905) and 1198991015840


119894RF (119905) asymp119877

119871(119866 [1198641 +Δ1198641 (119905)] sdot [1198642 +Δ1198642 (119905)]

sdot cos [2120587119891mm119905 + Δ120601 (119905)]

+ 2radic119866Re 1198991015840ASE (119905) [1198641 +Δ1198641 (119905)]

sdot exp119895 [21205871198911119905 + 1206011]

+ 2radic119866Re 1198991015840ASE (119905) [1198642 +Δ1198642 (119905)]

sdot exp119895 [21205871198912119905 + 1206012]) + 1198991015840

PD (119905)

(28)


119894RF (119905) asymp119877119866

11987111986411198642cos [2120587119891mm119905 + Δ120601 (119905)]

+119877119866

119871[Δ1198641 (119905) 1198642 +Δ1198642 (119905) 1198641]

sdot cos [2120587119891mm119905 + Δ120601 (119905)]

+2119877radic119866

119871Re 1198991015840ASE (119905) 1198641exp119895 [21205871198911119905 + 1206011]

+2119877radic119866

119871Re 1198991015840ASE (119905) 1198642exp119895 [21205871198912119905 + 1206012]

+ 1198991015840

PD (119905)

(29)


119860(119905) acquires

the form

119899119860 (119905) =

119877119866

119871[Δ1198641 (119905) 1198642 +Δ1198642 (119905) 1198641]

+2119877radic119866

119871Re 1198991015840ASE (119905) 1198641

+2119877radic119866

119871Re 1198991015840ASE (119905) 1198642 + 119899

1015840

PD (119905)

(30)



119875119899119860

= 119875119873source

+119875119873amp

+119875119873PD (31)

with

119875119873source

= (119877119866

119871)

2[Δ1198641 (119905) 1198642 + Δ1198642 (119905) 1198641]

2

119875119873amp

= 2(119877radic119866

119871)

2

1198992ASE (119905) (119864

21 +119864

22)

119875119873PD

= 1198992PD (119905)

(32)




values 119875119873PD




CNR =119875119862

119875119899119860

=119875119862

119875119873source

+ 119875119873amp

+ 119875119873PD

(33)


119875119862

=12(

1198771198662

11987111986411198642)

2

(34)


119901Φ(120601) =

exp (minus120574)


sdot int

radic2120574 cos(120601)

minusinfin

exp(minus119909

2

2)119889119909]

(35)


120574 =119875119862

119875119873amp

+ 119875119873PD

(36)



119875119899120601

= int

+infin

minusinfin

1206012119901Φ(120601) 119889120601 (37)











119875total (119905) = 1205980 sdot (119873

sum

119899=1119877 sdot 119894119899 (119905))

2

(38)


120590Δ119875

1198750=


1198750

(39)





Case 1Case 2

Case 3

10minus3

10minus4

10minus5

10minus6

120590ΔPP

0






119899(119905) + 119895 sdot HT119894

119899(119905) where


119860119899 (119905) = radic(Re

119899 (119905))2+ (Im

119899 (119905))2

120601119899 (119905) = atan

Im 119899 (119905)

Re 119899 (119905)

(40)


119899(119905)

and 120601119899(119905) that is

1198600 (119905) =1119873

119873

sum

119899=1119860119899 (119905)

1206010 (119905) =1119873

119873

sum

119899=1

120601119899 (119905)

(41)


119899(119905) of


Δ119860119899 (119905) = 119860

119899 (119905) minus1198600 (119905)

Δ120601119899 (119905) = 120601

119899 (119905) minus 1206010 (119905) (42)


1205902119860

1205832119860

=

⟨Δ1198602119899(119905)⟩

⟨1198600 (119905)⟩2 (43)


1205902120601= ⟨Δ120601

2119899(119905)⟩ (44)




Case 1Case 2

Case 3

10minus3

10minus2

10minus4

10minus5

10minus6

1205902 A120583

2 A

(a)


Case 1Case 2

Case 3

10minus3

10minus2

10minus4

10minus5

10minus6

1205902 120601

(b)





0 05 1 15

0

869

94

08


minus40

minus20

minus80 5 10 15

Time (120583s)

0 5 10 15Time (120583s)

Gm

ax(d

B)120579

max

(mRa

d)|A

F(120579)|

(dB)

1205902 = 0074

1205902 = 158







0 05 1 15

0

869

94

08


minus40

minus20

minus80 5 10 15 20

Time (120583s)

0 5 10 15 20Time (120583s)

Gm

ax(d

B)120579

max

(mRa

d)|A

F(120579)|

(dB)

1205902 = 33E minus 4

1205902 = 005


0 05 1 15

0

869

94

08


minus40

minus20

minus80 5 10 15 20

Time (120583s)

0 5 10 15 20Time (120583s)

Gm

ax(d

B)120579

max

(mRa

d)|A

F(120579)|

(dB)

1205902 = 34E minus 4

1205902 = 005





0 05 1 15

0

566

64

08


minus40

minus20

minus80 5 10 15 20

Time (120583s)

0 5 10 15 20Time (120583s)

Gm

ax(d

B)120579

max

(mRa

d)|A

F(120579)|

(dB)

1205902 = 0004

1205902 = 437


0 05 1 15

0

569

64

08


minus40

minus20

minus80 5 10 15 20

Time (120583s)

0 5 10 15 20Time (120583s)

Gm

ax(d

B)120579

max

(mRa

d)|A

F(120579)|

(dB)

1205902 = 0074

1205902 = 158




0 05 1 15

0

11612

124

08


minus40

minus20

minus80 5 10 15 20

Time (120583s)

0 5 10 15 20Time (120583s)

Gm

ax(d

B)120579

max

(mRa

d)|A

F(120579)|

(dB)

1205902 = 0130

1205902 = 077


7 Conclusions




References












































































































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










Rotarymirror

Mirror

Collimator

LL998400

(a)

Mirror MirrorL

L998400


prism

Disp

lace

men

t

(b)

L

L998400


(c)








element 2Antenna

element 3Antenna

element 4

Antennaelement N


input

Split

ter

(a)


element 2Antenna

element 3Antenna

element 4

Antennaelement N

Variablewavelength

input

Split

ter

1205821

1205822

1205823

120582K

(b)


AntennaCombiner

PMSplitter

Mux

PM

PM

element 1

Antennaelement 1

Antennaelement N











Photodiode









119864 (119905) = 11986401 (119905) sdot exp 119895 [21205871198911119905 + 1206011 (119905)] + 11986402 (119905)

sdot exp 119895 [21205871198912119905 + 1206012 (119905)] (21)



119864 (119905) = [1198641 +Δ1198641 (119905)] sdot exp 119895 [21205871198911119905 + 1206011 (119905)]

+ [1198642 +Δ1198642 (119905)] sdot exp 119895 [21205871198912119905 + 1206012 (119905)] (22)








119894PD (119905) =

119877 sdot10038161003816100381610038161003816119864amp (119905)

10038161003816100381610038161003816

2

119871+ 119899PD (119905)

(24)




119894PD (119905) =119877

119871(119866 (119864

201 +119864

202)

+11986611986401 (119905) 11986402 (119905) cos [2120587119891mm119905 + Δ120601 (119905)]

+ 2radic119866Re 119899ASE (119905) 11986401 (119905) exp119895 [21205871198911119905 + 1206011]

+ 2radic119866Re 119899ASE (119905) 11986402 (119905) exp119895 [21205871198912119905 + 1206012]

+1003816100381610038161003816119899ASE (119905)

1003816100381610038161003816

2) + 119899PD (119905)

(25)


119894PD (119905) asymp119877

119871(119866 (119864

201 +119864

202)

+11986611986401 (119905) 11986402 (119905) cos [2120587119891mm119905 + Δ120601 (119905)]

+ 2radic119866Re 119899ASE (119905) 11986401 (119905) exp119895 [21205871198911119905 + 1206011]

+ 2radic119866Re 119899ASE (119905) 11986402 (119905) exp119895 [21205871198912119905 + 1206012])

+ 119899PD (119905)

(26)


119894RF (119905) asymp119877

119871(11986611986401 (119905) 11986402 (119905) cos [2120587119891mm119905 + Δ120601 (119905)]

+ 2radic119866Re 1198991015840ASE (119905) 11986401 (119905) exp119895 [21205871198911119905 + 1206011]

+ 2radic119866Re 1198991015840ASE (119905) 11986402 (119905) exp119895 [21205871198912119905 + 1206012])

+ 1198991015840

PD (119905)

(27)

where 1198991015840

PD(119905) and 1198991015840


119894RF (119905) asymp119877

119871(119866 [1198641 +Δ1198641 (119905)] sdot [1198642 +Δ1198642 (119905)]

sdot cos [2120587119891mm119905 + Δ120601 (119905)]

+ 2radic119866Re 1198991015840ASE (119905) [1198641 +Δ1198641 (119905)]

sdot exp119895 [21205871198911119905 + 1206011]

+ 2radic119866Re 1198991015840ASE (119905) [1198642 +Δ1198642 (119905)]

sdot exp119895 [21205871198912119905 + 1206012]) + 1198991015840

PD (119905)

(28)


119894RF (119905) asymp119877119866

11987111986411198642cos [2120587119891mm119905 + Δ120601 (119905)]

+119877119866

119871[Δ1198641 (119905) 1198642 +Δ1198642 (119905) 1198641]

sdot cos [2120587119891mm119905 + Δ120601 (119905)]

+2119877radic119866

119871Re 1198991015840ASE (119905) 1198641exp119895 [21205871198911119905 + 1206011]

+2119877radic119866

119871Re 1198991015840ASE (119905) 1198642exp119895 [21205871198912119905 + 1206012]

+ 1198991015840

PD (119905)

(29)


119860(119905) acquires

the form

119899119860 (119905) =

119877119866

119871[Δ1198641 (119905) 1198642 +Δ1198642 (119905) 1198641]

+2119877radic119866

119871Re 1198991015840ASE (119905) 1198641

+2119877radic119866

119871Re 1198991015840ASE (119905) 1198642 + 119899

1015840

PD (119905)

(30)



119875119899119860

= 119875119873source

+119875119873amp

+119875119873PD (31)

with

119875119873source

= (119877119866

119871)

2[Δ1198641 (119905) 1198642 + Δ1198642 (119905) 1198641]

2

119875119873amp

= 2(119877radic119866

119871)

2

1198992ASE (119905) (119864

21 +119864

22)

119875119873PD

= 1198992PD (119905)

(32)




values 119875119873PD




CNR =119875119862

119875119899119860

=119875119862

119875119873source

+ 119875119873amp

+ 119875119873PD

(33)


119875119862

=12(

1198771198662

11987111986411198642)

2

(34)


119901Φ(120601) =

exp (minus120574)


sdot int

radic2120574 cos(120601)

minusinfin

exp(minus119909

2

2)119889119909]

(35)


120574 =119875119862

119875119873amp

+ 119875119873PD

(36)



119875119899120601

= int

+infin

minusinfin

1206012119901Φ(120601) 119889120601 (37)











119875total (119905) = 1205980 sdot (119873

sum

119899=1119877 sdot 119894119899 (119905))

2

(38)


120590Δ119875

1198750=


1198750

(39)





Case 1Case 2

Case 3

10minus3

10minus4

10minus5

10minus6

120590ΔPP

0






119899(119905) + 119895 sdot HT119894

119899(119905) where


119860119899 (119905) = radic(Re

119899 (119905))2+ (Im

119899 (119905))2

120601119899 (119905) = atan

Im 119899 (119905)

Re 119899 (119905)

(40)


119899(119905)

and 120601119899(119905) that is

1198600 (119905) =1119873

119873

sum

119899=1119860119899 (119905)

1206010 (119905) =1119873

119873

sum

119899=1

120601119899 (119905)

(41)


119899(119905) of


Δ119860119899 (119905) = 119860

119899 (119905) minus1198600 (119905)

Δ120601119899 (119905) = 120601

119899 (119905) minus 1206010 (119905) (42)


1205902119860

1205832119860

=

⟨Δ1198602119899(119905)⟩

⟨1198600 (119905)⟩2 (43)


1205902120601= ⟨Δ120601

2119899(119905)⟩ (44)




Case 1Case 2

Case 3

10minus3

10minus2

10minus4

10minus5

10minus6

1205902 A120583

2 A

(a)


Case 1Case 2

Case 3

10minus3

10minus2

10minus4

10minus5

10minus6

1205902 120601

(b)





0 05 1 15

0

869

94

08


minus40

minus20

minus80 5 10 15

Time (120583s)

0 5 10 15Time (120583s)

Gm

ax(d

B)120579

max

(mRa

d)|A

F(120579)|

(dB)

1205902 = 0074

1205902 = 158







0 05 1 15

0

869

94

08


minus40

minus20

minus80 5 10 15 20

Time (120583s)

0 5 10 15 20Time (120583s)

Gm

ax(d

B)120579

max

(mRa

d)|A

F(120579)|

(dB)

1205902 = 33E minus 4

1205902 = 005


0 05 1 15

0

869

94

08


minus40

minus20

minus80 5 10 15 20

Time (120583s)

0 5 10 15 20Time (120583s)

Gm

ax(d

B)120579

max

(mRa

d)|A

F(120579)|

(dB)

1205902 = 34E minus 4

1205902 = 005





0 05 1 15

0

566

64

08


minus40

minus20

minus80 5 10 15 20

Time (120583s)

0 5 10 15 20Time (120583s)

Gm

ax(d

B)120579

max

(mRa

d)|A

F(120579)|

(dB)

1205902 = 0004

1205902 = 437


0 05 1 15

0

569

64

08


minus40

minus20

minus80 5 10 15 20

Time (120583s)

0 5 10 15 20Time (120583s)

Gm

ax(d

B)120579

max

(mRa

d)|A

F(120579)|

(dB)

1205902 = 0074

1205902 = 158




0 05 1 15

0

11612

124

08


minus40

minus20

minus80 5 10 15 20

Time (120583s)

0 5 10 15 20Time (120583s)

Gm

ax(d

B)120579

max

(mRa

d)|A

F(120579)|

(dB)

1205902 = 0130

1205902 = 077


7 Conclusions




References












































































































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation











element 2Antenna

element 3Antenna

element 4

Antennaelement N


input

Split

ter

(a)


element 2Antenna

element 3Antenna

element 4

Antennaelement N

Variablewavelength

input

Split

ter

1205821

1205822

1205823

120582K

(b)


AntennaCombiner

PMSplitter

Mux

PM

PM

element 1

Antennaelement 1

Antennaelement N











Photodiode









119864 (119905) = 11986401 (119905) sdot exp 119895 [21205871198911119905 + 1206011 (119905)] + 11986402 (119905)

sdot exp 119895 [21205871198912119905 + 1206012 (119905)] (21)



119864 (119905) = [1198641 +Δ1198641 (119905)] sdot exp 119895 [21205871198911119905 + 1206011 (119905)]

+ [1198642 +Δ1198642 (119905)] sdot exp 119895 [21205871198912119905 + 1206012 (119905)] (22)








119894PD (119905) =

119877 sdot10038161003816100381610038161003816119864amp (119905)

10038161003816100381610038161003816

2

119871+ 119899PD (119905)

(24)




119894PD (119905) =119877

119871(119866 (119864

201 +119864

202)

+11986611986401 (119905) 11986402 (119905) cos [2120587119891mm119905 + Δ120601 (119905)]

+ 2radic119866Re 119899ASE (119905) 11986401 (119905) exp119895 [21205871198911119905 + 1206011]

+ 2radic119866Re 119899ASE (119905) 11986402 (119905) exp119895 [21205871198912119905 + 1206012]

+1003816100381610038161003816119899ASE (119905)

1003816100381610038161003816

2) + 119899PD (119905)

(25)


119894PD (119905) asymp119877

119871(119866 (119864

201 +119864

202)

+11986611986401 (119905) 11986402 (119905) cos [2120587119891mm119905 + Δ120601 (119905)]

+ 2radic119866Re 119899ASE (119905) 11986401 (119905) exp119895 [21205871198911119905 + 1206011]

+ 2radic119866Re 119899ASE (119905) 11986402 (119905) exp119895 [21205871198912119905 + 1206012])

+ 119899PD (119905)

(26)


119894RF (119905) asymp119877

119871(11986611986401 (119905) 11986402 (119905) cos [2120587119891mm119905 + Δ120601 (119905)]

+ 2radic119866Re 1198991015840ASE (119905) 11986401 (119905) exp119895 [21205871198911119905 + 1206011]

+ 2radic119866Re 1198991015840ASE (119905) 11986402 (119905) exp119895 [21205871198912119905 + 1206012])

+ 1198991015840

PD (119905)

(27)

where 1198991015840

PD(119905) and 1198991015840


119894RF (119905) asymp119877

119871(119866 [1198641 +Δ1198641 (119905)] sdot [1198642 +Δ1198642 (119905)]

sdot cos [2120587119891mm119905 + Δ120601 (119905)]

+ 2radic119866Re 1198991015840ASE (119905) [1198641 +Δ1198641 (119905)]

sdot exp119895 [21205871198911119905 + 1206011]

+ 2radic119866Re 1198991015840ASE (119905) [1198642 +Δ1198642 (119905)]

sdot exp119895 [21205871198912119905 + 1206012]) + 1198991015840

PD (119905)

(28)


119894RF (119905) asymp119877119866

11987111986411198642cos [2120587119891mm119905 + Δ120601 (119905)]

+119877119866

119871[Δ1198641 (119905) 1198642 +Δ1198642 (119905) 1198641]

sdot cos [2120587119891mm119905 + Δ120601 (119905)]

+2119877radic119866

119871Re 1198991015840ASE (119905) 1198641exp119895 [21205871198911119905 + 1206011]

+2119877radic119866

119871Re 1198991015840ASE (119905) 1198642exp119895 [21205871198912119905 + 1206012]

+ 1198991015840

PD (119905)

(29)


119860(119905) acquires

the form

119899119860 (119905) =

119877119866

119871[Δ1198641 (119905) 1198642 +Δ1198642 (119905) 1198641]

+2119877radic119866

119871Re 1198991015840ASE (119905) 1198641

+2119877radic119866

119871Re 1198991015840ASE (119905) 1198642 + 119899

1015840

PD (119905)

(30)



119875119899119860

= 119875119873source

+119875119873amp

+119875119873PD (31)

with

119875119873source

= (119877119866

119871)

2[Δ1198641 (119905) 1198642 + Δ1198642 (119905) 1198641]

2

119875119873amp

= 2(119877radic119866

119871)

2

1198992ASE (119905) (119864

21 +119864

22)

119875119873PD

= 1198992PD (119905)

(32)




values 119875119873PD




CNR =119875119862

119875119899119860

=119875119862

119875119873source

+ 119875119873amp

+ 119875119873PD

(33)


119875119862

=12(

1198771198662

11987111986411198642)

2

(34)


119901Φ(120601) =

exp (minus120574)


sdot int

radic2120574 cos(120601)

minusinfin

exp(minus119909

2

2)119889119909]

(35)


120574 =119875119862

119875119873amp

+ 119875119873PD

(36)



119875119899120601

= int

+infin

minusinfin

1206012119901Φ(120601) 119889120601 (37)











119875total (119905) = 1205980 sdot (119873

sum

119899=1119877 sdot 119894119899 (119905))

2

(38)


120590Δ119875

1198750=


1198750

(39)





Case 1Case 2

Case 3

10minus3

10minus4

10minus5

10minus6

120590ΔPP

0






119899(119905) + 119895 sdot HT119894

119899(119905) where


119860119899 (119905) = radic(Re

119899 (119905))2+ (Im

119899 (119905))2

120601119899 (119905) = atan

Im 119899 (119905)

Re 119899 (119905)

(40)


119899(119905)

and 120601119899(119905) that is

1198600 (119905) =1119873

119873

sum

119899=1119860119899 (119905)

1206010 (119905) =1119873

119873

sum

119899=1

120601119899 (119905)

(41)


119899(119905) of


Δ119860119899 (119905) = 119860

119899 (119905) minus1198600 (119905)

Δ120601119899 (119905) = 120601

119899 (119905) minus 1206010 (119905) (42)


1205902119860

1205832119860

=

⟨Δ1198602119899(119905)⟩

⟨1198600 (119905)⟩2 (43)


1205902120601= ⟨Δ120601

2119899(119905)⟩ (44)




Case 1Case 2

Case 3

10minus3

10minus2

10minus4

10minus5

10minus6

1205902 A120583

2 A

(a)


Case 1Case 2

Case 3

10minus3

10minus2

10minus4

10minus5

10minus6

1205902 120601

(b)





0 05 1 15

0

869

94

08


minus40

minus20

minus80 5 10 15

Time (120583s)

0 5 10 15Time (120583s)

Gm

ax(d

B)120579

max

(mRa

d)|A

F(120579)|

(dB)

1205902 = 0074

1205902 = 158







0 05 1 15

0

869

94

08


minus40

minus20

minus80 5 10 15 20

Time (120583s)

0 5 10 15 20Time (120583s)

Gm

ax(d

B)120579

max

(mRa

d)|A

F(120579)|

(dB)

1205902 = 33E minus 4

1205902 = 005


0 05 1 15

0

869

94

08


minus40

minus20

minus80 5 10 15 20

Time (120583s)

0 5 10 15 20Time (120583s)

Gm

ax(d

B)120579

max

(mRa

d)|A

F(120579)|

(dB)

1205902 = 34E minus 4

1205902 = 005





0 05 1 15

0

566

64

08


minus40

minus20

minus80 5 10 15 20

Time (120583s)

0 5 10 15 20Time (120583s)

Gm

ax(d

B)120579

max

(mRa

d)|A

F(120579)|

(dB)

1205902 = 0004

1205902 = 437


0 05 1 15

0

569

64

08


minus40

minus20

minus80 5 10 15 20

Time (120583s)

0 5 10 15 20Time (120583s)

Gm

ax(d

B)120579

max

(mRa

d)|A

F(120579)|

(dB)

1205902 = 0074

1205902 = 158




0 05 1 15

0

11612

124

08


minus40

minus20

minus80 5 10 15 20

Time (120583s)

0 5 10 15 20Time (120583s)

Gm

ax(d

B)120579

max

(mRa

d)|A

F(120579)|

(dB)

1205902 = 0130

1205902 = 077


7 Conclusions




References












































































































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation













Photodiode









119864 (119905) = 11986401 (119905) sdot exp 119895 [21205871198911119905 + 1206011 (119905)] + 11986402 (119905)

sdot exp 119895 [21205871198912119905 + 1206012 (119905)] (21)



119864 (119905) = [1198641 +Δ1198641 (119905)] sdot exp 119895 [21205871198911119905 + 1206011 (119905)]

+ [1198642 +Δ1198642 (119905)] sdot exp 119895 [21205871198912119905 + 1206012 (119905)] (22)








119894PD (119905) =

119877 sdot10038161003816100381610038161003816119864amp (119905)

10038161003816100381610038161003816

2

119871+ 119899PD (119905)

(24)




119894PD (119905) =119877

119871(119866 (119864

201 +119864

202)

+11986611986401 (119905) 11986402 (119905) cos [2120587119891mm119905 + Δ120601 (119905)]

+ 2radic119866Re 119899ASE (119905) 11986401 (119905) exp119895 [21205871198911119905 + 1206011]

+ 2radic119866Re 119899ASE (119905) 11986402 (119905) exp119895 [21205871198912119905 + 1206012]

+1003816100381610038161003816119899ASE (119905)

1003816100381610038161003816

2) + 119899PD (119905)

(25)


119894PD (119905) asymp119877

119871(119866 (119864

201 +119864

202)

+11986611986401 (119905) 11986402 (119905) cos [2120587119891mm119905 + Δ120601 (119905)]

+ 2radic119866Re 119899ASE (119905) 11986401 (119905) exp119895 [21205871198911119905 + 1206011]

+ 2radic119866Re 119899ASE (119905) 11986402 (119905) exp119895 [21205871198912119905 + 1206012])

+ 119899PD (119905)

(26)


119894RF (119905) asymp119877

119871(11986611986401 (119905) 11986402 (119905) cos [2120587119891mm119905 + Δ120601 (119905)]

+ 2radic119866Re 1198991015840ASE (119905) 11986401 (119905) exp119895 [21205871198911119905 + 1206011]

+ 2radic119866Re 1198991015840ASE (119905) 11986402 (119905) exp119895 [21205871198912119905 + 1206012])

+ 1198991015840

PD (119905)

(27)

where 1198991015840

PD(119905) and 1198991015840


119894RF (119905) asymp119877

119871(119866 [1198641 +Δ1198641 (119905)] sdot [1198642 +Δ1198642 (119905)]

sdot cos [2120587119891mm119905 + Δ120601 (119905)]

+ 2radic119866Re 1198991015840ASE (119905) [1198641 +Δ1198641 (119905)]

sdot exp119895 [21205871198911119905 + 1206011]

+ 2radic119866Re 1198991015840ASE (119905) [1198642 +Δ1198642 (119905)]

sdot exp119895 [21205871198912119905 + 1206012]) + 1198991015840

PD (119905)

(28)


119894RF (119905) asymp119877119866

11987111986411198642cos [2120587119891mm119905 + Δ120601 (119905)]

+119877119866

119871[Δ1198641 (119905) 1198642 +Δ1198642 (119905) 1198641]

sdot cos [2120587119891mm119905 + Δ120601 (119905)]

+2119877radic119866

119871Re 1198991015840ASE (119905) 1198641exp119895 [21205871198911119905 + 1206011]

+2119877radic119866

119871Re 1198991015840ASE (119905) 1198642exp119895 [21205871198912119905 + 1206012]

+ 1198991015840

PD (119905)

(29)


119860(119905) acquires

the form

119899119860 (119905) =

119877119866

119871[Δ1198641 (119905) 1198642 +Δ1198642 (119905) 1198641]

+2119877radic119866

119871Re 1198991015840ASE (119905) 1198641

+2119877radic119866

119871Re 1198991015840ASE (119905) 1198642 + 119899

1015840

PD (119905)

(30)



119875119899119860

= 119875119873source

+119875119873amp

+119875119873PD (31)

with

119875119873source

= (119877119866

119871)

2[Δ1198641 (119905) 1198642 + Δ1198642 (119905) 1198641]

2

119875119873amp

= 2(119877radic119866

119871)

2

1198992ASE (119905) (119864

21 +119864

22)

119875119873PD

= 1198992PD (119905)

(32)




values 119875119873PD




CNR =119875119862

119875119899119860

=119875119862

119875119873source

+ 119875119873amp

+ 119875119873PD

(33)


119875119862

=12(

1198771198662

11987111986411198642)

2

(34)


119901Φ(120601) =

exp (minus120574)


sdot int

radic2120574 cos(120601)

minusinfin

exp(minus119909

2

2)119889119909]

(35)


120574 =119875119862

119875119873amp

+ 119875119873PD

(36)



119875119899120601

= int

+infin

minusinfin

1206012119901Φ(120601) 119889120601 (37)











119875total (119905) = 1205980 sdot (119873

sum

119899=1119877 sdot 119894119899 (119905))

2

(38)


120590Δ119875

1198750=


1198750

(39)





Case 1Case 2

Case 3

10minus3

10minus4

10minus5

10minus6

120590ΔPP

0






119899(119905) + 119895 sdot HT119894

119899(119905) where


119860119899 (119905) = radic(Re

119899 (119905))2+ (Im

119899 (119905))2

120601119899 (119905) = atan

Im 119899 (119905)

Re 119899 (119905)

(40)


119899(119905)

and 120601119899(119905) that is

1198600 (119905) =1119873

119873

sum

119899=1119860119899 (119905)

1206010 (119905) =1119873

119873

sum

119899=1

120601119899 (119905)

(41)


119899(119905) of


Δ119860119899 (119905) = 119860

119899 (119905) minus1198600 (119905)

Δ120601119899 (119905) = 120601

119899 (119905) minus 1206010 (119905) (42)


1205902119860

1205832119860

=

⟨Δ1198602119899(119905)⟩

⟨1198600 (119905)⟩2 (43)


1205902120601= ⟨Δ120601

2119899(119905)⟩ (44)




Case 1Case 2

Case 3

10minus3

10minus2

10minus4

10minus5

10minus6

1205902 A120583

2 A

(a)


Case 1Case 2

Case 3

10minus3

10minus2

10minus4

10minus5

10minus6

1205902 120601

(b)





0 05 1 15

0

869

94

08


minus40

minus20

minus80 5 10 15

Time (120583s)

0 5 10 15Time (120583s)

Gm

ax(d

B)120579

max

(mRa

d)|A

F(120579)|

(dB)

1205902 = 0074

1205902 = 158







0 05 1 15

0

869

94

08


minus40

minus20

minus80 5 10 15 20

Time (120583s)

0 5 10 15 20Time (120583s)

Gm

ax(d

B)120579

max

(mRa

d)|A

F(120579)|

(dB)

1205902 = 33E minus 4

1205902 = 005


0 05 1 15

0

869

94

08


minus40

minus20

minus80 5 10 15 20

Time (120583s)

0 5 10 15 20Time (120583s)

Gm

ax(d

B)120579

max

(mRa

d)|A

F(120579)|

(dB)

1205902 = 34E minus 4

1205902 = 005





0 05 1 15

0

566

64

08


minus40

minus20

minus80 5 10 15 20

Time (120583s)

0 5 10 15 20Time (120583s)

Gm

ax(d

B)120579

max

(mRa

d)|A

F(120579)|

(dB)

1205902 = 0004

1205902 = 437


0 05 1 15

0

569

64

08


minus40

minus20

minus80 5 10 15 20

Time (120583s)

0 5 10 15 20Time (120583s)

Gm

ax(d

B)120579

max

(mRa

d)|A

F(120579)|

(dB)

1205902 = 0074

1205902 = 158




0 05 1 15

0

11612

124

08


minus40

minus20

minus80 5 10 15 20

Time (120583s)

0 5 10 15 20Time (120583s)

Gm

ax(d

B)120579

max

(mRa

d)|A

F(120579)|

(dB)

1205902 = 0130

1205902 = 077


7 Conclusions




References












































































































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation











119894PD (119905) =119877

119871(119866 (119864

201 +119864

202)

+11986611986401 (119905) 11986402 (119905) cos [2120587119891mm119905 + Δ120601 (119905)]

+ 2radic119866Re 119899ASE (119905) 11986401 (119905) exp119895 [21205871198911119905 + 1206011]

+ 2radic119866Re 119899ASE (119905) 11986402 (119905) exp119895 [21205871198912119905 + 1206012]

+1003816100381610038161003816119899ASE (119905)

1003816100381610038161003816

2) + 119899PD (119905)

(25)


119894PD (119905) asymp119877

119871(119866 (119864

201 +119864

202)

+11986611986401 (119905) 11986402 (119905) cos [2120587119891mm119905 + Δ120601 (119905)]

+ 2radic119866Re 119899ASE (119905) 11986401 (119905) exp119895 [21205871198911119905 + 1206011]

+ 2radic119866Re 119899ASE (119905) 11986402 (119905) exp119895 [21205871198912119905 + 1206012])

+ 119899PD (119905)

(26)


119894RF (119905) asymp119877

119871(11986611986401 (119905) 11986402 (119905) cos [2120587119891mm119905 + Δ120601 (119905)]

+ 2radic119866Re 1198991015840ASE (119905) 11986401 (119905) exp119895 [21205871198911119905 + 1206011]

+ 2radic119866Re 1198991015840ASE (119905) 11986402 (119905) exp119895 [21205871198912119905 + 1206012])

+ 1198991015840

PD (119905)

(27)

where 1198991015840

PD(119905) and 1198991015840


119894RF (119905) asymp119877

119871(119866 [1198641 +Δ1198641 (119905)] sdot [1198642 +Δ1198642 (119905)]

sdot cos [2120587119891mm119905 + Δ120601 (119905)]

+ 2radic119866Re 1198991015840ASE (119905) [1198641 +Δ1198641 (119905)]

sdot exp119895 [21205871198911119905 + 1206011]

+ 2radic119866Re 1198991015840ASE (119905) [1198642 +Δ1198642 (119905)]

sdot exp119895 [21205871198912119905 + 1206012]) + 1198991015840

PD (119905)

(28)


119894RF (119905) asymp119877119866

11987111986411198642cos [2120587119891mm119905 + Δ120601 (119905)]

+119877119866

119871[Δ1198641 (119905) 1198642 +Δ1198642 (119905) 1198641]

sdot cos [2120587119891mm119905 + Δ120601 (119905)]

+2119877radic119866

119871Re 1198991015840ASE (119905) 1198641exp119895 [21205871198911119905 + 1206011]

+2119877radic119866

119871Re 1198991015840ASE (119905) 1198642exp119895 [21205871198912119905 + 1206012]

+ 1198991015840

PD (119905)

(29)


119860(119905) acquires

the form

119899119860 (119905) =

119877119866

119871[Δ1198641 (119905) 1198642 +Δ1198642 (119905) 1198641]

+2119877radic119866

119871Re 1198991015840ASE (119905) 1198641

+2119877radic119866

119871Re 1198991015840ASE (119905) 1198642 + 119899

1015840

PD (119905)

(30)



119875119899119860

= 119875119873source

+119875119873amp

+119875119873PD (31)

with

119875119873source

= (119877119866

119871)

2[Δ1198641 (119905) 1198642 + Δ1198642 (119905) 1198641]

2

119875119873amp

= 2(119877radic119866

119871)

2

1198992ASE (119905) (119864

21 +119864

22)

119875119873PD

= 1198992PD (119905)

(32)




values 119875119873PD




CNR =119875119862

119875119899119860

=119875119862

119875119873source

+ 119875119873amp

+ 119875119873PD

(33)


119875119862

=12(

1198771198662

11987111986411198642)

2

(34)


119901Φ(120601) =

exp (minus120574)


sdot int

radic2120574 cos(120601)

minusinfin

exp(minus119909

2

2)119889119909]

(35)


120574 =119875119862

119875119873amp

+ 119875119873PD

(36)



119875119899120601

= int

+infin

minusinfin

1206012119901Φ(120601) 119889120601 (37)











119875total (119905) = 1205980 sdot (119873

sum

119899=1119877 sdot 119894119899 (119905))

2

(38)


120590Δ119875

1198750=


1198750

(39)





Case 1Case 2

Case 3

10minus3

10minus4

10minus5

10minus6

120590ΔPP

0






119899(119905) + 119895 sdot HT119894

119899(119905) where


119860119899 (119905) = radic(Re

119899 (119905))2+ (Im

119899 (119905))2

120601119899 (119905) = atan

Im 119899 (119905)

Re 119899 (119905)

(40)


119899(119905)

and 120601119899(119905) that is

1198600 (119905) =1119873

119873

sum

119899=1119860119899 (119905)

1206010 (119905) =1119873

119873

sum

119899=1

120601119899 (119905)

(41)


119899(119905) of


Δ119860119899 (119905) = 119860

119899 (119905) minus1198600 (119905)

Δ120601119899 (119905) = 120601

119899 (119905) minus 1206010 (119905) (42)


1205902119860

1205832119860

=

⟨Δ1198602119899(119905)⟩

⟨1198600 (119905)⟩2 (43)


1205902120601= ⟨Δ120601

2119899(119905)⟩ (44)




Case 1Case 2

Case 3

10minus3

10minus2

10minus4

10minus5

10minus6

1205902 A120583

2 A

(a)


Case 1Case 2

Case 3

10minus3

10minus2

10minus4

10minus5

10minus6

1205902 120601

(b)





0 05 1 15

0

869

94

08


minus40

minus20

minus80 5 10 15

Time (120583s)

0 5 10 15Time (120583s)

Gm

ax(d

B)120579

max

(mRa

d)|A

F(120579)|

(dB)

1205902 = 0074

1205902 = 158







0 05 1 15

0

869

94

08


minus40

minus20

minus80 5 10 15 20

Time (120583s)

0 5 10 15 20Time (120583s)

Gm

ax(d

B)120579

max

(mRa

d)|A

F(120579)|

(dB)

1205902 = 33E minus 4

1205902 = 005


0 05 1 15

0

869

94

08


minus40

minus20

minus80 5 10 15 20

Time (120583s)

0 5 10 15 20Time (120583s)

Gm

ax(d

B)120579

max

(mRa

d)|A

F(120579)|

(dB)

1205902 = 34E minus 4

1205902 = 005





0 05 1 15

0

566

64

08


minus40

minus20

minus80 5 10 15 20

Time (120583s)

0 5 10 15 20Time (120583s)

Gm

ax(d

B)120579

max

(mRa

d)|A

F(120579)|

(dB)

1205902 = 0004

1205902 = 437


0 05 1 15

0

569

64

08


minus40

minus20

minus80 5 10 15 20

Time (120583s)

0 5 10 15 20Time (120583s)

Gm

ax(d

B)120579

max

(mRa

d)|A

F(120579)|

(dB)

1205902 = 0074

1205902 = 158




0 05 1 15

0

11612

124

08


minus40

minus20

minus80 5 10 15 20

Time (120583s)

0 5 10 15 20Time (120583s)

Gm

ax(d

B)120579

max

(mRa

d)|A

F(120579)|

(dB)

1205902 = 0130

1205902 = 077


7 Conclusions




References












































































































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation












values 119875119873PD




CNR =119875119862

119875119899119860

=119875119862

119875119873source

+ 119875119873amp

+ 119875119873PD

(33)


119875119862

=12(

1198771198662

11987111986411198642)

2

(34)


119901Φ(120601) =

exp (minus120574)


sdot int

radic2120574 cos(120601)

minusinfin

exp(minus119909

2

2)119889119909]

(35)


120574 =119875119862

119875119873amp

+ 119875119873PD

(36)



119875119899120601

= int

+infin

minusinfin

1206012119901Φ(120601) 119889120601 (37)











119875total (119905) = 1205980 sdot (119873

sum

119899=1119877 sdot 119894119899 (119905))

2

(38)


120590Δ119875

1198750=


1198750

(39)





Case 1Case 2

Case 3

10minus3

10minus4

10minus5

10minus6

120590ΔPP

0






119899(119905) + 119895 sdot HT119894

119899(119905) where


119860119899 (119905) = radic(Re

119899 (119905))2+ (Im

119899 (119905))2

120601119899 (119905) = atan

Im 119899 (119905)

Re 119899 (119905)

(40)


119899(119905)

and 120601119899(119905) that is

1198600 (119905) =1119873

119873

sum

119899=1119860119899 (119905)

1206010 (119905) =1119873

119873

sum

119899=1

120601119899 (119905)

(41)


119899(119905) of


Δ119860119899 (119905) = 119860

119899 (119905) minus1198600 (119905)

Δ120601119899 (119905) = 120601

119899 (119905) minus 1206010 (119905) (42)


1205902119860

1205832119860

=

⟨Δ1198602119899(119905)⟩

⟨1198600 (119905)⟩2 (43)


1205902120601= ⟨Δ120601

2119899(119905)⟩ (44)




Case 1Case 2

Case 3

10minus3

10minus2

10minus4

10minus5

10minus6

1205902 A120583

2 A

(a)


Case 1Case 2

Case 3

10minus3

10minus2

10minus4

10minus5

10minus6

1205902 120601

(b)





0 05 1 15

0

869

94

08


minus40

minus20

minus80 5 10 15

Time (120583s)

0 5 10 15Time (120583s)

Gm

ax(d

B)120579

max

(mRa

d)|A

F(120579)|

(dB)

1205902 = 0074

1205902 = 158







0 05 1 15

0

869

94

08


minus40

minus20

minus80 5 10 15 20

Time (120583s)

0 5 10 15 20Time (120583s)

Gm

ax(d

B)120579

max

(mRa

d)|A

F(120579)|

(dB)

1205902 = 33E minus 4

1205902 = 005


0 05 1 15

0

869

94

08


minus40

minus20

minus80 5 10 15 20

Time (120583s)

0 5 10 15 20Time (120583s)

Gm

ax(d

B)120579

max

(mRa

d)|A

F(120579)|

(dB)

1205902 = 34E minus 4

1205902 = 005





0 05 1 15

0

566

64

08


minus40

minus20

minus80 5 10 15 20

Time (120583s)

0 5 10 15 20Time (120583s)

Gm

ax(d

B)120579

max

(mRa

d)|A

F(120579)|

(dB)

1205902 = 0004

1205902 = 437


0 05 1 15

0

569

64

08


minus40

minus20

minus80 5 10 15 20

Time (120583s)

0 5 10 15 20Time (120583s)

Gm

ax(d

B)120579

max

(mRa

d)|A

F(120579)|

(dB)

1205902 = 0074

1205902 = 158




0 05 1 15

0

11612

124

08


minus40

minus20

minus80 5 10 15 20

Time (120583s)

0 5 10 15 20Time (120583s)

Gm

ax(d

B)120579

max

(mRa

d)|A

F(120579)|

(dB)

1205902 = 0130

1205902 = 077


7 Conclusions




References












































































































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation











Case 1Case 2

Case 3

10minus3

10minus4

10minus5

10minus6

120590ΔPP

0






119899(119905) + 119895 sdot HT119894

119899(119905) where


119860119899 (119905) = radic(Re

119899 (119905))2+ (Im

119899 (119905))2

120601119899 (119905) = atan

Im 119899 (119905)

Re 119899 (119905)

(40)


119899(119905)

and 120601119899(119905) that is

1198600 (119905) =1119873

119873

sum

119899=1119860119899 (119905)

1206010 (119905) =1119873

119873

sum

119899=1

120601119899 (119905)

(41)


119899(119905) of


Δ119860119899 (119905) = 119860

119899 (119905) minus1198600 (119905)

Δ120601119899 (119905) = 120601

119899 (119905) minus 1206010 (119905) (42)


1205902119860

1205832119860

=

⟨Δ1198602119899(119905)⟩

⟨1198600 (119905)⟩2 (43)


1205902120601= ⟨Δ120601

2119899(119905)⟩ (44)




Case 1Case 2

Case 3

10minus3

10minus2

10minus4

10minus5

10minus6

1205902 A120583

2 A

(a)


Case 1Case 2

Case 3

10minus3

10minus2

10minus4

10minus5

10minus6

1205902 120601

(b)





0 05 1 15

0

869

94

08


minus40

minus20

minus80 5 10 15

Time (120583s)

0 5 10 15Time (120583s)

Gm

ax(d

B)120579

max

(mRa

d)|A

F(120579)|

(dB)

1205902 = 0074

1205902 = 158







0 05 1 15

0

869

94

08


minus40

minus20

minus80 5 10 15 20

Time (120583s)

0 5 10 15 20Time (120583s)

Gm

ax(d

B)120579

max

(mRa

d)|A

F(120579)|

(dB)

1205902 = 33E minus 4

1205902 = 005


0 05 1 15

0

869

94

08


minus40

minus20

minus80 5 10 15 20

Time (120583s)

0 5 10 15 20Time (120583s)

Gm

ax(d

B)120579

max

(mRa

d)|A

F(120579)|

(dB)

1205902 = 34E minus 4

1205902 = 005





0 05 1 15

0

566

64

08


minus40

minus20

minus80 5 10 15 20

Time (120583s)

0 5 10 15 20Time (120583s)

Gm

ax(d

B)120579

max

(mRa

d)|A

F(120579)|

(dB)

1205902 = 0004

1205902 = 437


0 05 1 15

0

569

64

08


minus40

minus20

minus80 5 10 15 20

Time (120583s)

0 5 10 15 20Time (120583s)

Gm

ax(d

B)120579

max

(mRa

d)|A

F(120579)|

(dB)

1205902 = 0074

1205902 = 158




0 05 1 15

0

11612

124

08


minus40

minus20

minus80 5 10 15 20

Time (120583s)

0 5 10 15 20Time (120583s)

Gm

ax(d

B)120579

max

(mRa

d)|A

F(120579)|

(dB)

1205902 = 0130

1205902 = 077


7 Conclusions




References












































































































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation











Case 1Case 2

Case 3

10minus3

10minus2

10minus4

10minus5

10minus6

1205902 A120583

2 A

(a)


Case 1Case 2

Case 3

10minus3

10minus2

10minus4

10minus5

10minus6

1205902 120601

(b)





0 05 1 15

0

869

94

08


minus40

minus20

minus80 5 10 15

Time (120583s)

0 5 10 15Time (120583s)

Gm

ax(d

B)120579

max

(mRa

d)|A

F(120579)|

(dB)

1205902 = 0074

1205902 = 158







0 05 1 15

0

869

94

08


minus40

minus20

minus80 5 10 15 20

Time (120583s)

0 5 10 15 20Time (120583s)

Gm

ax(d

B)120579

max

(mRa

d)|A

F(120579)|

(dB)

1205902 = 33E minus 4

1205902 = 005


0 05 1 15

0

869

94

08


minus40

minus20

minus80 5 10 15 20

Time (120583s)

0 5 10 15 20Time (120583s)

Gm

ax(d

B)120579

max

(mRa

d)|A

F(120579)|

(dB)

1205902 = 34E minus 4

1205902 = 005





0 05 1 15

0

566

64

08


minus40

minus20

minus80 5 10 15 20

Time (120583s)

0 5 10 15 20Time (120583s)

Gm

ax(d

B)120579

max

(mRa

d)|A

F(120579)|

(dB)

1205902 = 0004

1205902 = 437


0 05 1 15

0

569

64

08


minus40

minus20

minus80 5 10 15 20

Time (120583s)

0 5 10 15 20Time (120583s)

Gm

ax(d

B)120579

max

(mRa

d)|A

F(120579)|

(dB)

1205902 = 0074

1205902 = 158




0 05 1 15

0

11612

124

08


minus40

minus20

minus80 5 10 15 20

Time (120583s)

0 5 10 15 20Time (120583s)

Gm

ax(d

B)120579

max

(mRa

d)|A

F(120579)|

(dB)

1205902 = 0130

1205902 = 077


7 Conclusions




References












































































































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










0 05 1 15

0

869

94

08


minus40

minus20

minus80 5 10 15 20

Time (120583s)

0 5 10 15 20Time (120583s)

Gm

ax(d

B)120579

max

(mRa

d)|A

F(120579)|

(dB)

1205902 = 33E minus 4

1205902 = 005


0 05 1 15

0

869

94

08


minus40

minus20

minus80 5 10 15 20

Time (120583s)

0 5 10 15 20Time (120583s)

Gm

ax(d

B)120579

max

(mRa

d)|A

F(120579)|

(dB)

1205902 = 34E minus 4

1205902 = 005





0 05 1 15

0

566

64

08


minus40

minus20

minus80 5 10 15 20

Time (120583s)

0 5 10 15 20Time (120583s)

Gm

ax(d

B)120579

max

(mRa

d)|A

F(120579)|

(dB)

1205902 = 0004

1205902 = 437


0 05 1 15

0

569

64

08


minus40

minus20

minus80 5 10 15 20

Time (120583s)

0 5 10 15 20Time (120583s)

Gm

ax(d

B)120579

max

(mRa

d)|A

F(120579)|

(dB)

1205902 = 0074

1205902 = 158




0 05 1 15

0

11612

124

08


minus40

minus20

minus80 5 10 15 20

Time (120583s)

0 5 10 15 20Time (120583s)

Gm

ax(d

B)120579

max

(mRa

d)|A

F(120579)|

(dB)

1205902 = 0130

1205902 = 077


7 Conclusions




References












































































































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










0 05 1 15

0

11612

124

08


minus40

minus20

minus80 5 10 15 20

Time (120583s)

0 5 10 15 20Time (120583s)

Gm

ax(d

B)120579

max

(mRa

d)|A

F(120579)|

(dB)

1205902 = 0130

1205902 = 077


7 Conclusions




References












































































































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation

































































































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation









Review Article A Tutorial on Optical Feeding of Millimeter...

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