R_Chnnl_Digit_Modulat

8/3/2019 R_Chnnl_Digit_Modulat

1/83

ICTP-ITU/BDT-URSI School on Radio-Based Computer Networking for Research and Training in Developing CountriesThe Abdus Salam International Centre for Theoretical Physics ICTP, Trieste (Italy), 7th February - 4th March 2005

Radiocommunication Channeland Digital Modulation: Basics

Prof. Dr. R. [email protected]

Note: These are preliminary notes, intended only for

distribution to participants. Beware of misprints!


2/83

Outline

Radiocommunication channel Modulation

Spreading spectrum

Nonlinearities & intermodulation

Summary

Property of R. Struzak 2


3/83

Microwave radio link



4/83



5/83

Wireless Local Loop


BSS


6/83

PTP, PMP, Mesh A point-to-point (PTP) link is one station (node)communicating with another one

A point-to-multipoint (PMP) network is one node

(base station) communicating with more than one

other nodes Mesh network (fully connected): A network topology

in which there is a direct communication path between

any two nodes Mesh and PMP topologies share communication resources (media)

In a fully connected network with n nodes, there are n(n-1)/2 direct paths, i.e.,

branches.



7/83

FDD radio links Two stations can talk and listen to each other at the same

time (time-sharing).

This requires separate (static) frequency channels a

technique known as Frequency Division Duplex (FDD)


Station 1

TX RX

TXRX

Frequency

Channel 2

Station 2

Frequency

Channel 1


8/83

TDD radio links Two stations can talk and listen to each other using the

same frequency channel (frequency-sharing), one after

another.

This requires time synchronization/ handshaking a

technique known as Time Division Duplex (TDD)

Station 1 Station 2

Single Frequency

ChannelTX

RX

TX

RX



9/83

Radio Link model

Environ

ment

T-antenna

Propagation medium

R-antenna

Noise

Original message/ data

Reconstructed message/ data

EM waves:time-

distance-direction-polarization

ReceiverTime seriesProcessing/De-coding

TransmitterCoding/ProcessingTime series



10/83

Transmitting station

Electrical signal is represented by a function of time.Radio wave transmitted is represented by a function of

time, distance, direction, and polarization.

Radiowave

Transmittingantenna

RF cable(signal attenuation)

Originalsignal

Transmitter(signal processing)

Electrical current EM wave

Focus of the school



11/83

Receiving station

Radio

wave

Receiving

antenna

RF cable(signal attenuation)

Recovered

signal

Receiver(signal processing)

Electrical currentEM wave

Focus of the school

Radio wave received is represented by a function of time,distance, direction, and polarization that depends on signal-path environment

Electrical signal is represented by a function of time.Property of R. Struzak 11


12/83

Modern radio: details

BASEBAND PROCESSING& PC INTERFACE

DAC

CRYSTALREFERENCE

FILTER

SYNTHETIZER

ADC

FILTER

IFFILTER

SYNTHETIZER

RFFILTER RFFILTER

ANTENNA

RFAMPLIFICATION

RFUP/DOWN

CONVERSION

IFGAIN&SELECTIVITY

SWITCH

TRANSMITTER COMMON PART RECEIVER

MOD

ULATION

&DEMO

DULATION



13/83

Modern radio =combination of

radio and computerhardware &software

Software-definedradio

Systems withmost functionsdefined by

software Automatically

and/or at distance

RADIO WAVE PROPAGATION PATH

Beamforming

Freq. spread

Modulation

Multiplex

Format

Encryption

Encoding

Analog/Digital

Information source

Beamforming

Freq. despread

Demodulation

Demultiplex

Format

Decryption

Decoding

Digital/ Analog

Information sink

Fromo

th

ersources

Tootherdestinations



14/83

Outline

Radiocommunication channel

Modulation

Spreading spectrum


Summary



15/83

Modulation = process of translation

the message frombaseband signal tobandpass (modulatedcarrier) signal at

frequencies that are veryhigh compared to thebaseband frequencies.

Demodulation is the

reverse process Note: An information-bearing

signal is non-deterministic, i.e.it changes in an unpredictablemanner.

Modulator/

Signal Processing

Carrier Generator

m(t)

s(t)

f(t)

s'(t)

Demodulator/

Signal Processing

m'(t)

RADIO ENVIRONMENT

TRANSMITTER RECEIVER



16/83

CommunicationChannelOriginal messagem(t)

Transmitter

s(t) = U(m, f)m(t) = message (information, data)

s(t) = signal carrying the message

f = f(a,b,c,, t) (carrier function)

a,b,c, = modulation parameters

U, V, W= operators = noise, fading, perturbations

x(t) = perturbed signal at the receiver input

y(t) = reproduced message

Task: makey m (within anacceptable error)

Transport medium

x(t) = V(s, )

Receiver

y(t) = W(x)

Reproduced

(received) message

y = W{V[,U(m,f)]}



17/83

Modulation Process( )1 2 3

1 2 3

, , ,... , (= carrier)

, , ,... (= modulation parameters)

(= time)

n

n

f f a a a a t

a a a a

t

=

Modulation implies varying one or morecharacteristics (modulation parameters a1, a2, an) ofa carrierfin accordance with the information-bearing(modulating) baseband signal

Each of the parameters a, b, c... carrying informationcan be modulated independently, increasingcommunication capacity at a cost of complexity.



18/83

The carrier is generated in the transmitter

It may be a continuous (e.g. sinusoidal) current ofradio frequency, a sequence of short pulses, ornoise

Systems using pulse sequences are also calledcarrierless or impulse systems

It may also be a number of carriers, such as in

Orthogonal Frequency Division Multiplexing(OFDM) systems. For instance, one of standards Wireless Local Area Networks

(WLANs) foresees 52 carriers spaced 312.5 kHz apart



19/83

Why Carrier?

To radiate EM waves effectively Radiation efficiency requires antenna dimensions to be

comparable with the radiated wavelength Antenna for 30 kHz would be 10 km long

Antenna for 3 GHz carrier is 10 cm long

To assure signal orthogonality (avoiding mutualinterference by using orthogonal frequencies) Note: There are also other methods of avoiding

interference (e.g. time- or code-orthogonality) Standards and RR impose limitations on carrier

frequencies (interference, intercommunications)



20/83



21/83



22/83

Continuous carrier In the case of sinusoidal carrier, three modulation

parameters can be varied: the amplitude, the frequency,and the phase of the sinusoid (+ polarization). Thisgenerates three distinct modulation types: the amplitudemodulation

(AM), thefrequency modulation

(FM) and thephase modulation (PM)

Each of these may be continuous, when the instantaneousamplitude, frequency and phase of the sinusoid are

continuous functions of time, or may be pulsed, when thevariations occur instantaneously



23/83

Amplitude modulation (AM)

A = A(t)

= const

= const

Frequency modulation (FM) A = const

= (t)

= const

Phase modulation (PM)

A = const

= const

= (t) Polarization modulation

Not used in radio

communications(used in some optical

communications)

Carrier:A sin[t +] + polarztn.; A, , , polarztn. = const



24/83

Amplitude Shift Keying (ASK)


1 10

Baseband

Data0 0

ASK

modulatedsignal

Acos(t) Acos(t)

Pulse shaping can be employed to remove spectral spreading

ASK demonstrates poor performance, as it is heavily affected by noise,fading, and interference


25/83

Frequency Shift Keying (FSK)


1 10 0

Baseband

Data

BFSK

modulatedsignalf0 f0f1 f1

where f0 =Acos(c-)t and f1 =Acos(c+)t Example: The ITU-T V.21 modem standard uses FSK

FSK can be expanded to a M-ary scheme, employing multiplefrequencies as different states


26/83

Phase Shift Keying (PSK)


1 10 0

s0 s0s1 s1

Baseband

Data

BPSK

modulatedsignal

where s0

=Acos(c

t) and s1

=Acos(c

t + )

Major drawback rapid amplitude change between symbols due to phasediscontinuity, which requires infinite bandwidth. Binary Phase Shift Keying(BPSK) demonstrates better performance than ASK and BFSK

BPSK can be expanded to a M-ary scheme, employing multiple phases and

amplitudes as different states


27/83

PSK graphic representationThe two signals

s0 =Acos(t)s1 =Acos(t + )can be represented bytwo vectors (or points)

in the signal plane[Re(s), Im(s)]

Noise & interference

can change positions ofthe points and modifydecision: 0 or 1

A-A

Im(s)

Re(s)

Decision: s = s0 Decision: s = s1

10



28/83

Differential Modulation

In the transmitter, each symbol is modulatedrelative to the previous symbol and modulatingsignal, for instance in BPSK 0 = no change,

1 = +1800

In the receiver, the current symbol is demodulatedusing the previous symbol as a reference. The

previous symbol serves as an estimate of thechannel. A no-change condition causes themodulated signal to remain at the same 0 or 1 stateof the previous symbol.



29/83

DPSK = Differential phase-shift keying: In the

transmitter, each symbol is modulated relative to

the phase of the immediately preceding signal

element transmitted Differential modulation is theoretically 3dB

poorer than coherent. This is because the

differential system has 2 sources of error: acorrupted symbol, and a corrupted reference (the

previous symbol)



30/83

Pulse trains as Carrier A carrier = a train of identical

pulses regularly spaced in time

Example 2003 : Ultra Wideband(UWB) systems Systems that use time-domain

modulation and signal processingmethods (e.g.,pulse-positionmodulation)

Used for sensing, short-range radar,and telecommunication applications

Employ short pulses (duration of ~1 to10 ns), occupying the bandwidth ofmore than 1.5 GHz (or more than 25%of the center frequency)



31/83

Inpulse-frequency modulation (PFM), the pulse

repetition rate is varied in accordance with the

modulating signal; in Pulse-Amplitude Modulation

(PAM), the amplitude of individual pulses in thepulse train is varied

Inpulse-time modulation (PTM) generic class, the

time of occurrence of some characteristic of thepulsed carrier is varied, eg. Duration (PDM) or

position (PPM)



32/83

Inpulse-position

modulation (PPM),the temporal

positions of

individual pulses arevaried in relation tothe reference

positions, inaccordance themodulating signal



33/83

Noise (random processes), and pseudo-random

processes can also be used as carriers

Example: spread-spectrum systems

In some systems, the carrier and modulation formatchange during the transmission

Independently of the modulation type, spectra of

signals used in radiocommunications are,contained between 9 kHz and 275 GHz, as defined

in ITU Radio Regulations



34/83

Demodulation & Detection

Demodulation

Is process of removing the carrier signal to

obtain the original signal waveform

Detection extracts the symbols from thewaveform

Coherent detection Non-coherent detection



35/83

Coherent (synchronous) Detection

Signal change introduced by the channel (phase

and attenuation) is estimated. It is then possible to

reproduce the transmitted signal and demodulate.

Requires a replica carrier wave of the samefrequency and phase to be delivered at the

receiver.

The received signal and replica carrier are cross-correlated using information contained in their

amplitudes and phases.



36/83

Carrier recovery methods include

Pilot Tone (such as Transparent Tone in Band) Less power in the information bearing signal, High peak-to-

mean power ratio

Carrier recovery from the information signal E.g. Costas loop

Applicable to

Phase Shift Keying (PSK) Frequency Shift Keying (FSK)

Amplitude Shift Keying (ASK)



37/83


38/83

Geometric Representation

Digital modulation involves choosing a particular

signal si(t) form a finite set S of possible signals.

For binary modulation schemes a binary

information bit is mapped directly to a signal andS contains only 2 signals, representing 0 and 1.

For M-ary keying S contains more than 2 signals

and each represents more than a single bit ofinformation. With a signal set of size M, it is

possible to transmit up to log2Mbits per signal.



39/83

Any element of set S can be represented as a point

in a vector space whose coordinates are basis

signals j(t) such that

( ) ( )

( )

( ) ( )

2

1

0, ; (= are orthogonal)

1; ( normalization)

Then

i j

i

N

i ij j

j

t t dt i j

E t dt

s t s t

=

=

= = =

=



40/83

Example: BPSK Constellation Diagram

( ) ( ) ( ) ( )

( ) ( )

1 2

1

2 2cos 2 , cos 2 ; ; 0

energy per bit; bit period

For this signal set, there is a single basic signal

2 cos 2 ; 0

b bBPSK c c b

b b

b b

c b

b

BPSK

E ES s t f t s t f t t T

T T

E T

t f t t T T

S E

= = =

= =

=

= ( ) ( ){ }1 1,b bt E t -Eb Eb

Q

I

Constellation diagram



41/83

Constellation diagram

= graphical representation of the complex

envelope of each possible symbol state The x-axis represents the in-phase component

and the y-axis the quadrature component of thecomplex envelope

The distance between signals on a constellation

diagram relates to how different the modulationwaveforms are and how easily a receiver can

differentiate between them.



42/83

QPSK

Quadrature Phase Shift Keying (QPSK) can

be interpreted as two independent BPSK

systems (one on the I-channel and one on

Q), and thus the same performance buttwice the bandwidth efficiency

Large envelope variations occur due toabrupt phase transitions, thus requiring

linear amplification



43/83

QPSK Constellation Diagram

Carrier phases

{0, /2, , 3/2}

Q

Carrier phases

{/4, 3/4, 5/4, 7/4}

I

Q

I

Quadrature Phase Shift Keying has twice the bandwidth efficiency ofBPSK since 2 bits are transmitted in a single modulation symbol



44/83

Types of QPSK

I

Q


Conventional QPSK has transitions through zero (i.e. 1800phase transition). Highlylinear amplifiers required.

In Offset QPSK, the phase transitions are limited to 900, the transitions on the I and Qchannels are staggered.

In /4 QPSK the set of constellation points are toggled each symbol, so transitionsthrough zero cannot occur. This scheme produces the lowest envelope variations.

All QPSK schemes require linear power amplifiers

I

QQ

I

Conventional QPSK Offset QPSK /4 QPSK

M lti l l (M ) Ph d


45/83

Multi-level (M-ary) Phase and

Amplitude Modulation

16 QAM 16 PSK 16 APSK

Amplitude and phase shift keying can be combined to transmit several bits persymbol. (Often referred to as linearas they require linear amplification. More

bandwidth-efficient, but more susceptible to noise.)

For M=4, 16QAM has the largest distance between points, but requires verylinear amplification. 16PSK has less stringent linearity requirements, but hasless spacing between constellation points, and is therefore more affected bynoise.

Simulation: http://www.educatorscorner.com/index.cgi?CONTENT_ID=2478Property of R. Struzak 45


46/83

Decision region



47/83

DistortionsDecision region

Perfect channel White noise Phase jitter


i


48/83

Eye Diagram

Eye pattern is an oscilloscopedisplay in which digital data

signal from a receiver isrepetitively superimposed onitself many times

(sampled and applied to thevertical input, while the datarate is used to trigger thehorizontal sweep).

It is so called because thepattern looks like a series ofeyes between a pair of rails.

Time (symbols)

Magnitude

If the eye is not

open at the samplepoint, errors will occurdue to signalcorruption



49/83

GMSK Gaussian Minimum Shift Keying (GMSK) is a form of

continuous-phase FSK in which the phase change ischanged between symbols to provide a constant envelope.Consequently it is a popular alternative to QPSK

The RF bandwidth is controlled by the Gaussian low-passfilter bandwidth. The degree of filtering is expressed bymultiplying the filter 3dB bandwidth (B) by the bit periodof the transmission (T), i.e. by BT

GMSK allows efficient class C non-linear amplifiers to beused



50/83

Outline


Modulation

Spreading spectrum


Summary



51/83

Modulation Spectra The Nyquist bandwidth is the

minimum bandwidth that cancarry a given volume ofinformation

The spectrum occupied by asignal is usually larger and

spill over adjacent channelscausing interference

The spectrum occupied by asignal can be reduced byapplication of filters

Technical standards and RRimpose limits on spectralmasks

Nyquist MinimumBandwidth

Frequency

RelativeMagnitude(dB

)

AdjacentChannel


Capacity of communication system


52/83

Capacity of communication system

C = B*log2{1 + [S/(No*B)]}

Bandwidth, Hz

Noise density, W/Hz

Received signal power, W

Capacity, bit/s

The capacity to transfer error-free information is enhancedwith increased bandwidth B, even though the signal-to-noise

ratio is decreased because of the increased bandwidth.


SS communications basics


53/83

SS communications basics

Original

information

Propagation effects Transmission

Reconstructed

information

Original signal Spread signal

Spread signal+ Reconstr. signal

Spreading

De-spreading

Unwanted signals + Noise


SS: basic characteristics


54/83

SS: basic characteristics

Signal spread over a wide bandwidth >> minimum

bandwidth necessary to transmit information

Spreading by means of a code independent of the data

Data recovered by de-spreading the signal with asynchronous replica of the reference code TR: transmitted reference (separate data-channel and reference-channel, correlation detector)

SR: stored reference (independent generation at T & R pseudo-random identical waveforms,synchronization by signal received, correlation detector)

Other (MT: T-signal generated by pulsing a matched filter having long, pseudo-randomly controlledimpulse response. Signal detection at R by identical filter & correlation computation)


SS communication techniques


55/83

SS communication techniques

FH: frequency hoping (frequency synthesizer controlled by pseudo-random sequence of numbers)

DS: direct sequence (pseudo-random sequence of pulses used forspreading)

TH: time hoping(spreading achieved by randomly spacing transmitted pulses)

Random noise as carrier

Hybrid combination of the above

Other techniques (radar and other applications)



56/83

Multiple-access techniques

FDMA: frequency-division multiple access

TDMA: time-division multiple access

CDMA: code-division multiple access

Other (e.g. OFDM)


FDMA


57/83

FDMA

Freque

ncy

Time

Power density

FDMA

Freq

uency


TimeFrequency channel

Bm

Bc

Transmission is organized

in frequency channels.

Each link is assigneda separate channel.

Example: Telephony Bm = 3-9 kHz

TDMAP d it


58/83

TDMA

Tim

e

Power densityTDMA

Freque

ncy


Frequency

TimeTime slot

Time-frame

Transmission is organized in repetitive

time-frames. Each frame consists of

groups of pulses - time slots. Each user/

link is assigned a separate time-slot.

Example: DECT (Digital enhanced cordless phone) Frame lasts 10 ms, consists of 24 time slots (each 417s)

FH SS (CDMA)


59/83

FH SS (CDMA)


Freq

uency

CDMA

Time

Power density

Frequency

Time-frequency slot

Bm

Bc

Transmission is organized intime-frequency slots. Each link

is assigned a sequence of the slots,

according to a specific code.

Time

DS SS: transmitter


60/83

Modulator X Antenna

[A(t), (t)]Information

[g1(t)]

Modulated signal

S1(t) = A(t) cos(0t + (t))band Bm Hz

Spread signal

g1(t)S1(t)

band Bc Hz

Bc >> Bm

Carrier

cos(0t)

gi(t): pseudo-random noise (PN) spreading functions that spreads the energy of S1(t) over a bandwidth

considerably wider than that of S1(t): ideally gi(t) gj(t) = 1 ifi =j and gi(t) gj(t) = 0 ifi j


DS SS-receiver


61/83

Spreadingfunction

[g1(t)]

Correlator&

bandpass

filter

Xantenna

Tod

emodulator

Linear

combination

g1(t)S1(t)g2(t)S2(t)

.

gn(t)Sn(t)N(t) (noise)

S(t)

g1(t) g1(t)S1(t)

g1(t) g2(t)S2(t)

.

g1(t) gn(t)Sn(t)

g1(t) N(t)g1(t) S(t)

S1(t)


SS-receivers Input


62/83

SS receiver s Input

Unwanted signalsSS s.: g2(t)S2(t); ; gn(t)Sn(t)

Other s. : S(t)

Noise: N(t)

W/Hz

Wanted (spread) signal: g1(t)S1(t)

BcHz

Signal-to-interference ratio (S/ I)in = S/ [I()*Bc]


Bc = Input correlator bandwidth

I() = Average spectral power density of unwanted signals in BcS = Power of the wanted signal

SS-correlator/ filter output


63/83

Bm

Bc


(S/ I)out = S/ [I()*Bm]Bc = Input correlator bandwidth

Bm = Output filter bandwidth

I() = Average spectral power density of unwanted signals & noise in BmS = power of the wanted signal at the correlator output

Wanted (correlated) signal: de-spread to its original bandwidth

as g1(t) g1(t)S1(t) = S1(t) with g1(t) g1(t) = 1

Uncorrelated (unwanted) signalsspread & rejected by correlator + noise

g1(t) S(t); g1(t) N(t); g1(t) gj(t)Sj(t) = 0as gi(t) gj(t) = 0 fori j

Signal-to-interference ratio

Spreading = reducing spectral power density


64/83

SS Processing Gain == [(S/ I)in/ (S/ I)out ] = ~Bc/ Bm

Example: GPS signal

RF bandwidth Bc ~ 2MHz Filter bandwidth Bm ~ 100 Hz

Processing gain ~20000 (+43 dB)

Input S/N = -20 dB (signal power = 1% of noise power)

Output S/N = +23 dB (signal power = 200 x noise power)

(GPS = Global Positioning System)



65/83

Outline


Modulation

Spreading spectrum

Nonlinearities & intermodulation Summary



66/83

Sources of undesired nonlinear effects:

Receiver RF input/ mixing stage Transmitter output stages

Vicinity of the equipment (usually of the

transmitter)



67/83

Types of undesired nonlinear effects:

Receiver blocking

Transmitter spurious radiations & intermodulation

Receiver spurious responses & intermodulation Note: Several nonlinear interactions may occur

simultaneously

(Source: ITU/ CCIR Rep. 524-1, Vol. 1, p. 30, 1986)



68/83

Non-ideal wideband

memory-less linear devicesare often treated byexpressing the output (Y) ofthe system as a power series

of the total input signalX:Y a a X a X a X a X

n

n= + + + + + +0 1 2

2

3

3 ... ...

X(t) Y(t)

X(t) = A1sin(w1t) + A2sin(w2t) + The coefficients a are presumed to be real andindependent onX.



69/83

In practice, one focus only on those impairments

that fall in the desired frequency channel The lowest from these (and often the dominant

one) is the third-order nonlinearity

The second-order nonlinearity may also be a

critical performance parameter for a receiver. Theapproach presented here can easily be extended tothe evaluation of the second-order and othernonlinearities of a receiver.

30 1 3Y a a X a X = + +


Blocking dynamic range (BDR)


70/83

Blocking dynamic range (BDR)2 3

0 1 2 3 ...y a a x a x a x= + + + +

Noise Floor

Output

power(dBm

)

Input

power (dBm)P1dB-inMDS

1dBP1dB-out

BDR

(Blocking Dynamic Range)

MDS = Minimum

Detectable Signal

(Output Noise Floor)


IP1dB_b


71/83

Two-signal Input Referred Blocking 1 dB

Gain Compression Point

Refers to the condition when there are 2 single-

frequency input signalsx(t) = [A1 cos(1t) + A2 cos(2t) and one of

them (the blocker) is significantly stronger than

the other, that is A2 >> A1.( )20 1 3 2 1

3( ) cos 1 ...

2y t a a a A A t

= + + +



72/83

If a3 < 0, the weaker signal A1cos(1t)

experiences progressively less gain as the

stronger signal A2cos(2t) gets stronger.

The gain drops by 1 dB from its ideal valuewhen the blocker amplitude reaches

11 _

3

0.0725IP dB b aAa

=



73/83

Assume a small signal test, i.e. A small enough

such that

The input level for which the output componentsat 1 and 2 have the same amplitude as those at

(212) and (221) is the input referred third-

order intercept point:

2

1 3

9

4a a A

13

3

3

4

3IIP

aA

a=



74/83

Intermodulation Intermodulation spurious signals can be generated

when two or more RF signals are applied to a non-linear device

They could produce interference

The magnitude of the spurious signals depends onthe power of the original signals and on the degreeof device nonlinearity

Technical standards and RR impose limits on out-of-band (spurious) radiations



75/83

Intermodulation products The frequency (Fi) of an intermodulation

product Fi = C1*F1+C2*F2+ .. +Cn*Fn {C1, C2, ...,Cn} are positive or negative integers or

zero, and

{F1, F2, ..., Fn} are the frequencies of the signals

applied to the device

The order of the intermodulation product isthe sum: {|C1| + |C2| + ... + |Cn|}


IIP3


76/83

Two-signal Input-Referred Third-order Intercept

Point

A third-order intermodulation component (IM3)

due to two sinusoidal input signals of equal

amplitude (Acos1t, Acos2t)[ ] [ ]

[ ] ( ) ( )

3

0 1 1 2 3 1 2

2 3 3

0 1 3 1 2 2 3 1 2 3 2 1

( ) cos( ) cos( ) cos( ) cos( )

9 3 3

cos( ) cos( ) cos 2 cos 24 4 4

y t a a A t A t a A t A t

a a a A A t A t a A a A

= + + + + =

= + + + + +



77/83

Example: 3rd order intermodulation Two real signals of frequencies F1 and F2 when applied

to a nonlinearity, produce six false signals (3-rd orderintermodulation products) at the following frequencies:

Fia = 2*F1 - F2

Fib = 2*F2 - F1 Fic = 2*F1 + F2

Fid = 2*F2 + F1

Fie = 3F1

Fif = 3F2

Even if F1 and F2 do not interfereone with another, intermodulationproducts can interfere with one oranother.Frequencies Fia, Fib, can be close

to F1 or F2.More real signals, more thenumber of false signals



78/83

F1 F2

2F1-F2 2F2-F1

2F22F1

2F1+F2 2F2+F1

3F13F2



79/83

All above parameters are defined under assumptions of

small-signal and systems with third-order nonlinearity IP1dB and IP1dB_b can be directly measured

IIP3 and IIP3_h cannot be directly measured: they canonly be extrapolated from small signal measurements asthey are defined under small signal assumptions.

The numerical values of the parameters are inter-related: IP1dB = IIP3 9.6 dB

IP1dB_b = IIP3 12.6 dB IIP3_h = IIP3 + 5 dB



80/83

Summary Radiocommunication channel

Modulation

Spreading spectrum




81/83

References Campbell AT. Untangling the Wireless Web

Radio Channel Issues, Lecture NotesE6951, comet.columbia.edu/~campbell

Proakis J.Digital Communications,McGraw & Hill Int.

Rappaport TS. Wireless Communications,Prentice Hall PTR


Any question?


82/83

Thank you for your attention



83/83

Copyright 2005 Ryszard Struzak. This work is licensed under the

Creative Commons Attribution License

http://creativecommons.org/licenbses/by/1.0 These materials may be used freely for individual study, research, and

education in not-for-profit applications. Any other use (and/or displaying

the material in the WWW) requires the written authors permission

If you cite these materials, please credit the author. If you have

comments or suggestions, please send these directly to the author at

[email protected].

Copyright note


R_Chnnl_Digit_Modulat

Documents

Transcript of R_Chnnl_Digit_Modulat