arX

iv:1

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3v1

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20 J

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Spectrum Monitoring Using Energy RatioAlgorithm For OFDM-Based Cognitive Radio

NetworksAbdelmohsen Ali,Student Member, IEEEand Walaa Hamouda,Senior Member, IEEE

Abstract—This paper presents a spectrum monitoring algo-rithm for Orthogonal Frequency Division Multiplexing (OFD M)based cognitive radios by which the primary user reappearancecan be detected during the secondary user transmission. Theproposed technique reduces the frequency with which spectrumsensing must be performed and greatly decreases the elapsedtimebetween the start of a primary transmission and its detection bythe secondary network. This is done by sensing the change insignal strength over a number of reserved OFDM sub-carriersso that the reappearance of the primary user is quickly detected.Moreover, the OFDM impairments such as power leakage,Narrow Band Interference (NBI), and Inter-Carrier Interfe rence(ICI) are investigated and their impact on the proposed techniqueis studied. Both analysis and simulation show that theenergy ratioalgorithm can effectively and accurately detect the appearanceof the primary user. Furthermore, our method achieves highimmunity to frequency-selective fading channels for both singleand multiple receive antenna systems, with a complexity that isapproximately twice that of a conventional energy detector.

Index Terms—Cognitive networks, cognitive radio, fadingchannels, OFDM, spectrum sensing/monitoring

I. I NTRODUCTION

Nowadays, static spectrum access is the main policy forwireless communications. Under this policy, fixed channelsare assigned to licensed users or primary users (PUs) forexclusive use while unlicensed users or secondary users (SUs)are prohibited from accessing those channels even when theyare unoccupied. The idea of a cognitive radio (CR) wasproposed in order to achieve more efficient utilization of theRF spectrum [1]. One of the main approaches utilized bycognitive networks is the interweave network model [2] inwhich SUs seek to opportunistically use the spectrum whenthe PUs are idle. Primary and secondary users are not allowedto operate simultaneously. In this method, secondary usersmust sense the spectrum to detect whether it is availableor not prior to communication. If the PU is idle, the SUcan then use the spectrum, but it must be able to detectvery weak signals from the primary user by monitoring theshared band in order to quickly vacate the occupied spectrum.During this process, the CR system may spend a long time,known as the sensing interval, during which the secondarytransmitters are silent while the frequency band is sensed.

This research was supported by the Natural Sciences and EngineeringResearch Council of Canada (NSERC) Grants N008861 and N01268.

The authors are with the Department of Electrical and Computer Engi-neering, Concordia University, Montreal, Quebec, H3G 1M8,Canada (e-mail:(ali_abde,hamouda)@ece.concordia.ca).

Since the CR users do not utilize the spectrum during thedetection time, these periods are also called quiet periods(QPs) [3]. In the IEEE 802.22 system, a quiet period consistsof a series of consecutive spectrum sensing intervals usingenergy detection to determine if the signal level is higher thana predefined value, which indicates a non-zero probability ofprimary user transmission. The energy detection is followedby feature detection to distinguish whether the source ofenergy is a primary user or noise [4] [5]. This mechanismis repeated periodically to monitor the spectrum. Once the PUis detected, the SU abandons the spectrum for a finite periodand chooses another valid spectrum band in the spectrum poolfor communication.

If the SU must periodically stop communicating in order todetect the emergence of the PU, two important effects shouldbe studied. (1) During quite periods, the SU receiver maylose its synchronization to the SU transmitter which causesan overall degradation in the secondary network performance.This is a problem when the underlying communication tech-nique is sensitive to synchronization errors as in OFDM [6].(2) The throughput of the secondary network during sensingintervals is reduced to zero which degrades the Quality ofService (QoS) for those real-time applications like Voice overIP (VoIP) [7]. The impact becomes more severe if the durationof the sensing intervals is too large as the average throughputof the secondary network becomes very low. On the otherhand, if this duration is too small, then the interference totheprimary users is increased since spectrum sensing providesno information about the frequency band of interest betweenconsecutive sensing intervals.

In this area, there have been research efforts which attemptto minimize the time duration for spectrum monitoring byjointly optimizing the sensing time with the detection thresh-old [8]. The PU throughput statistics are considered to protectthe PU while the sensing time is minimized. In conventionalsystems, traditional spectrum sensing is applied once beforethe SU communication and is not be repeated again unlessthe monitoring algorithm indicates that a primary signal maybe present in the band. If monitoring determines correctlythat there is no primary signal in the band, then the timethat would have been spent performing spectrum sensing isused to deliver packets in the secondary network. Thereforethe spectrum efficiency of the secondary network is improved.If spectrum monitoring detects a primary signal in the bandduring a time period in which spectrum sensing would not havebeen scheduled, then the disruption to the primary user can be

terminated more quickly and hence the impact of secondarycommunications on the primary user is reduced. Based on thisdescription, the SU receiver should follow two consecutivephases, namely sensing phase and monitoring phase, wherethe former is applied once for a predefined period.

Yet, another approach is utilized by [9] where the spec-trum is monitored by the CR receiver during reception andwithout any quiet periods. The idea is to compare the biterror count, that is produced by a strong channel code likea Low Density Parity Check (LDPC) code, for each receivedpacket to a threshold value. If the number of detected errorsis above certain value, the monitoring algorithm indicatesthat the primary user is active. The threshold is obtained byconsidering the hypothesis test for the receiver statistics whenthe primary signal is absent and the receiver statistics forthedesired Secondary-to-Primary power Ratio (SPR). Althoughthis technique is simple and adds almost no complexity to thesystem, the receiver statistics are subject to change by varyingthe system operating conditions. In real systems, there aremany parameters that can affect the receiver error count suchas RF impairments including Phase Noise (PN) and CarrierFrequency Offset (CFO), Sampling Frequency Offset (SFO),and NBI. The error count will depend not only on the presenceof a primary signal but it will also depend on the characteristicsof those impairments. Also, the receiver statistics may changefrom one receiver to the other based on the residual errorsgenerated from estimating and compensating for differentimpairments. Since it is difficult to characterize the receiverstatistics for all CR receivers, it is better to devise an algorithmthat is robust to synchronization errors and channel effects.

OFDM is a multi-carrier modulation technique that is usedin many wireless systems and proven as a reliable and effectivetransmission method. For these reasons, OFDM is utilized asthe physical layer modulation technique for many wirelesssystems including DVB-T/T2, LTE, IEEE 802.16d/e, andIEEE 802.11a/g. Similar to other wireless networks, OFDMis preferred for cognitive networks and has been alreadyin use for the current cognitive standard IEEE 802.22. Onthe other hand, OFDM systems have their own challengesthat need special treatment [10]. These challenges includeitssensitivity to frequency errors and the large dynamic rangeofthe time domain signal. Moreover, the finite time-window inthe receiver DFT results in a spectral leakage from any in-bandand narrow band signal onto all OFDM sub-carriers.

The traditional spectrum monitoring techniques, that relyon the periodic spectrum sensing during quiet periods, applytheir processing over the received time domain samples toexplore a specific feature to the primary user. Further, it istotally encouraged to remove the quiet periods during themonitoring phase in order to improve the network throughput.In fact, the signal construction for the secondary user canassist the spectrum monitoring to happen without involvingQPs. When the secondary user utilizes OFDM as the physicaltransmission technique, a frequency domain based approachcan be employed to monitor the spectrum during the CRreception only if the SU transmitter adds an additional featureto the ordinary OFDM signal. In this paper, we proposea spectrum monitoring technique, namely theenergy ratio

(ER) technique, that is suitable for OFDM-based cognitiveradios. Here, the transmitter helps this frequency domain basedspectrum monitoring approach by introducing scheduled null-tones by which the spectrum can be monitored during CRreception. This monitoring technique is designed to detectthe reappearance of the primary user which also uses OFDMtechnique. Here, different signal chain impairments due toCFO, SFO, and NBI as well as frequency selective fadingchannels are considered. The technique operates over theOFDM signal chain and hence, it does not require to waitfor the decoded bits. This implies fast response to PU appear-ance. Furthermore, the most important OFDM challenges forcognitive radios like power leakage are investigated and theireffects on the proposed monitoring technique are considered.

The paper is organized as follows. Section II summarizesthe overall system model. In section III, theenergy ratiotechnique is discussed. In addition, we present performanceanalysis for AWGN channels under perfect synchronizationand neglecting power leakage in section IV. OFDM challengesand non-perfect synchronization environment are consideredin section V. Further, we extend the analysis and study tofrequency selective fading channels and multi-antenna systemsin section VI. The complexity of theenergy ratiois analyzedand an architecture is also proposed in VII. Finally, the perfor-mance is evaluated with computer simulations in section VIII.

II. SYSTEM MODEL

The secondary user physical layer model is designed inorder to investigate and verify our spectrum monitoring al-gorithm. This model is very close to the OFDM systemfollowed by [10]. At the transmitter side, data coming fromthe source is firstly segmented into blocks where each blockis randomized, channel encoded, and interleaved separately.After interleaving, the data is modulated by the constellationmapper. The frequency domain OFDM frame is constructedby combining: (a) One or more training symbols or preamblesthat are used for both time and frequency synchronizationat the receiver side. (b) The modulated data. (c) The BPSKmodulated pilots which are used for data-aided synchroniza-tion algorithms employed by the receiver. EachNs encodedcomplex data symbols generated by the frame builder areused to construct one OFDM symbol by employing the IDFTblock that is used to synthesize the OFDM symbol, whereNs

denotes the number of sub-carriers per one OFDM symbol.Thus, thenth time-domain sample of themth symbol can beexpressed as given by (1) whereC(k,m) is the modulateddata to be transmitted on themth OFDM symbol with thekth

sub-carrier.

s(n,m) =1√Ns

Ns/2−1∑

k=−Ns/2

C(k,m) ej2πkn/Ns (1)

To reduce the effect of Inter-Symbol Interference (ISI),the lastNg samples of the time domain OFDM symbol arecopied to the beginning of the symbol in order to forma guard time or cyclic prefix. Therefore, the OFDM blockhas a period ofTs = (Ns + Ng)/Fs where Fs is thesampling frequency. At the receiver, the inverse blocks are

2

Time

Fre

quen

cy

�r

Ns

Preamble OFDM Data symbols

DC sub-carrier

Data sub-carrier

Pilot sub-carrier

Null sub-carrier

Reserved tone

Figure 1. Time-Frequency allocation for one OFDM frame to exploredifferent sub-carrier types

applied. After timing synchronization (frame detection, startof symbol timing, and SFO estimation and compensation) andfrequency synchronization (CFO estimation and correction),the cyclic prefix is removed. Then, the received OFDM symbolis transformed again into the frequency domain through anNs

point DFT. The channel is then estimated and the received datais equalized. The complex data output is then mapped to bitsagain through the De-mapper. De-interleaving, decoding, andDe-randomization are applied later to the received block torecover the original source bits.

From the network point of view, we consider a cognitiveradio network ofK SUs and onePU . The PU occupies aspectrum of a certain bandwidth for its transmission, whilethesame spectrum is shared by the SUs. In fact, the spectrum istotally utilized by one SU (the master node or the fusion node)to send different data to the otherK−1 SUs (the slave nodes).This model was originally introduced for Frequency DivisionMultiple Access (FDMA) [11] but it has been modifiedlater to suite the OFDM environment. Currently, this modelparticularly matches two promising solutions, namely Ecma-392 and IEEE 802.11af, that employ OFDM as the underlyingphysical transmission technique [12]. The standards introducecognitive radio approach to the TV white space. Usually, asecondary user should get necessary information from TVwhite space database which maintains a list of the unusedTV channels geometrically. However, the standards specifychannel power management functionality in order to updatethe available channel lists.

The current Ecma-392 standard supports spectrum sensingfunctionality to periodically check the existence of incumbentsignals on the current operating channel. Ecma-392 has spec-ified the operation in only single TV channel which can beone of three channel bandwidths of 6 MHz, 7 MHz, or 8MHz according to regulatory domain. The objective is that the

secondary user can utilize the full band on which the primaryuser operates. The IEEE 802.11af standard is an extensionto the Wireless Local Area Network (WLAN). The channelbandwidths in this standard can be adaptively changed whenseveral adjacent TV channels are available. Again, the fusionnode (the access point) utilizes the whole primary user bandto broadcast the downlink signal to all slaves. In reality, ouralgorithm is demonstrated by a more general model whichdoes not perfectly match the implementation of either Ecma-392 or IEEE 802.11af. The main difference is that our modelhas no limitations on the channel bandwidth, the channelcharacteristics, or even the frequency tolerances.

In our model, the fusion node constructs OFDM frames inthe downlink path such that the same pilots are transmitted toall slaves but the data sub-carriers are allocated in time andfrequency for different users based on a predefined schedulingtechnique. For the return path, Orthogonal Frequency DivisionMultiple Access (OFDMA) is assumed to divide the spectrumand the time into distinct and non-overlapping channels fordifferent slaves, so that interferences between the slavesisavoided. The fusion node fully controls the timing of eachslave, possibly by letting the slave know the required timeadvance or delay, so that the combined signal from all slavesseem to be synchronized at the fusion node receiver. In thiscase, the fusion node can convert the signal back to thefrequency domain in order to extract the data and controlinformation from different slaves. A valid assumption is thatthe slaves can send important information such as spectrummonitoring decisions and channel state information over alogical control channel in the return path. The master node cansimply apply a majority rule based on the received monitoringdecisions to decide whether to stop transmission or not.

III. E NERGY RATIO ALGORITHM

On the time-frequency grid of the OFDM frame and beforethe IDFT, a number of tones,NRT , are reserved for thespectrum monitoring purposes. These tones are reserved forthe whole time except the time of the training symbol(s) inorder not to change the preamble waveform, which is used forsynchronization at the receiver. The proposed OFDM frame isshown in Fig. 1. Notice that we allocate the reserved tonesdynamically so that their indices span the whole band whensuccessive OFDM symbols are considered in time. The tonesare advanced by∆r positions every OFDM symbol. When thelast index of the available sub-carriers is reached, the spanningstarts again from the first sub-carrier. Hence, by consideringsmall values for∆r, the reserved tone sequence injected tothe energy ratio spans the whole band. The reasons for thisscheduling are: (1) The primary user may have some spectrumholes because of using OFDM as well. If the reserved tonesfrom the SU are synchronized with those spectrum holes inthe PU side, then the algorithm will fail. On the contrary, ifthe PU uses a traditional single carrier modulation techniquelike QAM, this issue does not have a harm effect on thealgorithm since the PU signal has a flat spectrum over theentire band. (2) The reserved tones typically occupy narrowband and the primary to secondary channel may introduce

3

Ts

Sensing Phase Monitoring Phase

Threshold

( 1 )

( 2 )

( 3 )

( 4 )

Primary user appearance

Figure 2. Energy Ratio processing details. (1) The time domain sequencefor the OFDM blocks. (2) Frequency domain samples. (3) Reserved tonesprocessing with two sliding windows forNRT = 2 andN = 4. (4) Decisionmaking variable,Xk.

notch characteristics to this narrow band resulting in detectinglower primary power level, which is referred to the narrowband problem. Therefore, it is recommended that the reservedtones are rescheduled by changing the value of∆r over time tomitigate the channel effect and to protect the reserved tonesfrom falling into primary holes. Of course, all SUs shouldknow the code for this scheduling in prior.

Based on the signal on the reserved tones at the receiver,the secondary user can monitor the band and test the pri-mary user appearance. In fact, the traditional radiometer maybe employed to measure the primary signal power and thesecondary noise power by accumulating the energy of thosereserved tones. As a consequence, the primary signal powercan be detected if this energy exceeds a predefined threshold.However, this approach does not necessary guarantee the pri-mary user detection as the spectral leakage of the neighbouringsub-carriers will affect the energy at the reserved tones evenfor no in-band primary signal [13]. Here, we propose anotherdecision making criterion that has a powerful immunity forthis power leakage. In fact, the power leakage, the ICI resultedfrom the residual CFO and SFO errors, and even the effect ofNBI can be overcome by our approach.

The overall algorithm is illustrated by Fig. 2. It is assumedthat the primary signal appears after some time during themonitoring phase. At the secondary receiver, after CP removaland frequency domain processing on the received signal, thereserved tones from different OFDM symbols are combinedto form one sequence of complex samples. Two consecutiveequal-sized sliding windows are passed over the reserved tonesequence in the time direction. The energy of the samplesthat fall in one window is evaluated and the ratio of the twoenergies is taken as the decision making variable and hencethe nameenergy ratio.

The algorithm aims to check the change in variance on thereserved tones over time. In a mathematical form, letZi bethe ith sample of the reserved tone sequence. The decisionmaking variable,Xk, can be defined as given by (2) whereNis the number of samples per window,Uk is the energy of thesecond window,Vk is the energy of the first window, andkis an integer such thatk = 1, 2, 3, ...

Xk =Uk

Vk=

∑2N+k−1i=N+k

∣

∣Zi

∣

∣

2

∑k+N−1i=k

∣

∣Zi

∣

∣

2 (2)

It should be mentioned that the reserved tones processingdone by theenergy ratioalgorithm starts from the beginningof the sensing phase. Meaning that, the decision makingvariable is evaluated during both sensing and monitoringphases. However, it provides decisions only during monitoringphase. During the sensing phase, if the decision from thespectrum sensing algorithm is that the PU is inactive, thenthe energy ratioalgorithm has been properly calibrated to beable to detect the appearance of the PU during monitoringphase. Calibration means that both sliding windows are filledwith pure unwanted signals. During the monitoring phase,the receiver monitors the reserved tones by evaluating theparameter,Xk. If it exceeds a certain threshold, then thesecondary user assumes that there is a power change onthe reserved tones which perhaps due to the primary userappearance and it is time to vacate the band. If not, thesecondary user can continue transmission. Indeed, if thereisno primary user in band, then the energy of each window stillinvolves only the strength of the unwanted signals includingthe noise, the leakage from the neighbouring sub-carriers,andthe effects of ICI produced by the residual synchronizationerrors. Therefore, ifN is large enough, the ratio will be veryclose to unity since the strength of the unwanted signals doesnot offer significant changes over time.

Once the primary user appears, the second window willhave two types of signalling which are the primary userinterference and the unwanted signals. Meanwhile, the firstwindow will only maintain the unwanted signals without theprimary user interference. The ratio of the two energies willresult in much higher values when compared to one. The valuewill of course depend on the primary user power. When thetwo windows slide again, the primary signal plus the unwantedsignals will be observed by the two windows and the decisionmaking variable returns to the initial state in which the ratio isclose to unity. Thus, we can expect that the decision variableproduces a spike when the primary user is detected. Otherwise,it changes very slowly maintaining theenergy ratioclose toone as shown in Fig. 2 part (4).

This approach can resist the different impairments involvedin the received signal on the account of reducing the through-put of the secondary user by the ratio of the number of reservedtones to the number of useful tones. However, this reductioncan be easily overcome since OFDM systems allow adaptivemodulation where good conditioned sub-carriers are loadedwith higher modulation order.

For the previous discussion, it is assumed that the primaryuser should appear at the boundaries of the OFDM blocks.Therefore, the reserved tones should have the full power,that is supposed to be for those sub-carrier indices, of theprimary user when it is active. In reality, the primary user mayappear any time within any OFDM block in the monitoringphase. In this case, we have to consider two effects. (1)The FFT window applied by the SU receiver will have atime-shifted version of the PU signal which involves a phase

4

rotation to the PU sub-carriers. Since the energy is the usefulparameter for our algorithm, the phase shift is acceptable tohappen with no effect on the algorithm. (2) The power on thereserved tones will not have the full power transmitted by theprimary user on those sub-carriers since part of the signal istruncated. However, the next OFDM symbol will have thatfull power. Similar to the near-far problem, if the PU poweris large enough, then the reserved tones form the first OFDMsymbol, in which PU signal appears, are considered to be full.Otherwise, the reserved tones from this OFDM symbol areconsidered as noise ifN ≫ NRT .

IV. ENERGY RATIO ANALYSIS FOR AWGN CHANNELS

To verify the algorithm, we first analyze theenergy ratiotechnique assuming perfect synchronization and neglecting theleakage power effect. However, these issues will be consideredand their effects will be studied in the next section. Throughoutthe analysis, we assume that the signal to be detected does nothave any known structure that could be exploited. Therefore,the reserved tone sequence is modelled via a zero-meancircularly symmetric complex Gaussian distribution (thisisalso true in case of frequency selective fading channels asdiscussed in section VI). The target of this analysis is to findthe receiver operating characteristics (ROC) representedby theprobability of detection,PD, and probability of false alarm,PFA. The detection probability is the probability of detectinga primary signal when it is truly present while the false alarmprobability is the probability that the test incorrectly decidesthat the primary user is present when it is actually not.

Since we are dealing with a two state model in which thechannel is assumed to be idle or busy by the primary user,then we wish to discriminate between the two hypothesesH0

and H1 where the first assumes that the primary signal isnot in band and the second assumes that the primary useris present. Using theenergy ratioalgorithm, one can definethese hypotheses as given by (3) where it is assumed thatthe samples contained in the first window have a variance ofσ2v and the samples enclosed by the second window have a

variance ofσ2u.

{

H0 : X = UV , σ2

u = σ2v

H1 : X = UV , σ2

u > σ2v

(3)

The performance of the detector is quantified in terms ofits ROC curve, which represents the probability of detectionas a function of the probability of false alarm. By varying acertain thresholdγ, the operating point of a detector can bechosen anywhere along the ROC curve.PFA andPD can bedefined as given by (4) and (5), respectively.

PFA = Prob[

X > γ | H0

]

(4)

PD = Prob[

X > γ | H1

]

(5)

Clearly, the fundamental problem of detector design is tochoose the detection criteria, and to set the decision thresholdγ to achieve good detection performance. Detection algorithmsare either designed in the framework of classical statistics,or in the framework of Bayesian statistics [14]. In the clas-sical case, eitherH0 or H1 is deterministically true, and

the objective is to maximizePD subject to a constraint onPFA; this is known as the Neyman-Pearson (NP) criterion.In the Bayesian framework, by contrast, it is assumed thatthe source selects the true hypothesis at random, accordingto some priori probabilities. The objective is to minimize theso-called Bayesian cost. In this work, the former approach isfollowed. First, the Probability Density Function (PDF) andthe Cumulative Distribution Function (CDF) of the decisionvariable are derived. Next, both the detection and the falsealarm probabilities are evaluated in closed-forms.

A. Energy Ratio PDF and CDF Evaluation

Since the samples of the reserved tone sequence follow azero-mean circularly symmetric complex Gaussian distribu-tion, then the energy contained in one window will follow aChi-Square distribution and the PDFs for the random variablesU and V can be written as given by (6) and (7), respec-tively [15].

fU (u) =1

2N σ2Nu Γ(N)

uN−1 e−u/(2σ2u) , u > 0 (6)

fV (v) =1

2N σ2Nv Γ(N)

vN−1 e−v/(2σ2v) , v > 0 (7)

The CDF for the random variableX and hence the PDF, canbe evaluated as given by (8) and (9), respectively, where thetwo random variablesU andV are assumed to be independent.It is obvious that the PDF forX follows a scaled F-distributionwith meanmX =

(

Γ(N − 1) Γ(N + 1)/Γ2(N))

×(

σ2u/σ

2v

)

and varianceV ar(X) =(

Γ(N − 2) Γ(N + 2)/Γ2(N))

×(

σ2u/σ

2v

)2. The CDF forX can be derived in a closed-form

as given by (10), whereIb(N,N) is the regularized incompletebeta function with the parametersb andN .

B. PFA andPD Evaluation

To obtain the ROC, we develop the classical NP criterion inwhich the detection probability is maximized while the falsealarm probability is maintained at a fixed value. Since theprobability of false alarm for theenergy ratioalgorithm isgiven by (11), one can obtain the thresholdγ subjected to aconstantPFA as given by (12) whereI−1

b (N,N) is the inverseincomplete beta function with parametersb andN .

PFA = Prob[

X > γ | H0

]

= 1− I (γ)(1+γ)

(N,N) (11)

γ =I−11−PFA

(N,N)

1− I−11−PFA

(N,N)(12)

Once the primary user becomes available in the band, thesecond window will contain the power of the primary userin addition to the power of the noise whereas the first windowwill contain only noise and hence, the receiver noise varianceis represented byσ2

v . Therefore,σ2u = σ2

v +PNR×σ2v where

PNR is the ratio of the primary user power to the secondaryuser noise power at the secondary user receiver. Hence, thedetection probability can be expressed in terms of PNR as,

PD = Prob[

X > γ | H1

]

= 1− I (σ2v γ/σ2

u)

(1+σ2v γ/σ2

u)

(N,N)

= 1− I (γ/(1+PNR))(1+γ/(1+PNR))

(N,N) (13)

5

FX(x) = Prob[

U ≤ xV]

=

ˆ ∞

0

ˆ xv

0

fUV (u, v) du dv

=

ˆ ∞

0

ˆ xv

0

1

22N σ2Nv σ2N

u Γ(N) Γ(N)uN−1 e−u/(2σ2

u) vN−1 e−v/(2σ2v) du dv

=1

22N Γ2(N)

ˆ ∞

0

[

ˆ xv σ2v/σ

2u

0

uN−1 e−u du

]

vN−1 e−v dv (8)

fX(x) =d

dxFX(x) =

1

22N Γ2(N)

ˆ ∞

0

d

dx

[

ˆ xv σ2v/σ

2u

0

uN−1 e−u du

]

vN−1 e−v dv

=1

22N Γ2(N)

ˆ ∞

0

[

(

v σ2v

σ2u

)(

xv σ2v

σ2u

)N−1

e−xv σ2v/σ

2u

]

vN−1 e−v dv

=xN−1

Γ2(N)

(

σ2v

σ2u

)NΓ(2N)

(

1 + σ2v x/σ

2u

)2N

[

ˆ ∞

0

(

v(

1 + σ2v x/σ

2u

)

)2N

22N Γ(2N)e−v

(

1+σ2v x/σ2

u

)

dv

v

]

=σ2v

σ2u

Γ(2N)

Γ2(N)

(

σ2v x/σ

2u

)N−1

(

1 + σ2v x/σ

2u

)2N, x ≥ 0 (9)

FX(x) = Prob[

X ≤ x]

=

ˆ x

−∞

fX(t) dt =σ2v

σ2u

Γ(2N)

Γ2(N)

ˆ x

0

(

σ2v t/σ

2u

)N−1

(

1 + σ2v t/σ

2u

)2Ndt

=Γ(2N)

Γ2(N)

ˆ (σ2v x/σ2

u)/(1+σ2v x/σ2

u)

0

(

u

1− u

)N−1(

1 +u

1− u

)−2Ndu

(

1− u)2

=Γ(2N)

Γ2(N)

ˆ (σ21 x/σ2

u)/(1+σ2v x/σ2

u)

0

uN−1 (1− u)N−1 du = I (σ2v x/σ2

u)

(1+σ2v x/σ2

u)

(N,N) (10)

V. OFDM CHALLENGES ON ENERGY RATIO ALGORITHM

In this section we first present an overview of the currentchallenges faced by conventional OFDM systems and pos-sible techniques that have been introduced to address thesechallenges. Finally, we show that by adopting any of thesetechniques, ourenergy ratio detector does not require anyadditional complexity to the OFDM system with efficientdetection capabilities.

A. NBI and Power Leakage

By definition, the power of a NBI is concentrated in asmall frequency band compared to the overall system band-width [16]. Although the total power of the interference maybe substantially lower than the total received signal power,these disturbances can reach a noise level which exceedsthe received signal level by orders of magnitude inside theinterference band. Therefore, the system performance willbe severely degraded. Aside from NBI, the side-lobes ofmodulated OFDM sub-carriers even in case of having no NBIare known to be large. As a result, there is power leakagefrom sub-carriers to adjacent sub-carriers. It is known that themost efficient solution to NBI is to disable the sub-carrierscorresponding to this interference. This will eliminate theeffect of NBI at those sub-carriers, however, the signal to noiseratio at the other sub-carriers will be slightly reduced.

For the power leakage, recent research has carefully ad-dressed this problem. For example, the out of band leakagescan be reduced by including special cancelling carriers atthe edge of the band [17]. These sub-carriers are modulatedwith complex weighting factors which are optimized suchthat the side-lobes of the those carriers cancel the side-lobesof the original transmitted signal in a certain optimizationrange. Another solution is proposed in [18] where the powerleakage is totally suppressed by a pre-coding technique. Thispre-coding is applied to the frequency domain OFDM signalbefore IDFT block at the transmitter side. At the receiver,a decoder is applied to omit the spectral distortion to theOFDM signal caused by pre-coding. This technique can totallyeliminate the effect of spectral leakage but of course it needsfull revision for all synchronization algorithms applied totraditional OFDM system.

By utilizing the fact thatenergy ratiocan perfectly counterany consistent noise like signals, windowing can be appliedtothe time domain OFDM symbols [19] to limit the leakages andto reduce the influence of NBI. Thus, if a windowing function(e.g., Nyquist window) is carefully chosen to only affect theinterference while leaving the OFDM signal unchanged, thenspectral leakage can be avoided. In [19], a folding techniqueis proposed in order not to use a double length DFT. In thiscase, the samples preceding the OFDM symbol to the end of

6

the symbol are added to the samples following the symbol toits beginning. To evaluate the performance of ourenergy ratiodetector in the presence of NBI and power leakage, we turn offthe sub-carriers corresponding to the NBI. Moreover, the timedomain windowing technique with folding is applied at thereceiver side, as it offers the lowest computational complexitywith sufficiently good performance.

B. Inter-carrier Interference Effect

In addition to the NBI and power leakage problems dis-cussed earlier, OFDM systems also suffer from ICI effects.The main sources for ICI in OFDM-based systems are thephase noise (PN), the carrier frequency offset (CFO), and thesampling frequency offset (SFO) [20].

The phase noise is due to the instability of carrier signalgenerators used at the transmitter and receiver. In fact, theeffect of PN can be greatly reduced by increasing the sub-carrier spacing,∆f . We will (optimistically) assume that∆fis large enough such that the ICI introduced by the PN isneglected with respect to the ICI generated by either CFOor SFO. On the other hand, the carrier frequency offset isdue to the difference between the carrier frequencies generatedby the transmitter and receiver oscillators, or by the Dopplerfrequency shift. It is commonly represented by the normalizedCFO which is the ratio of the frequency offset to the sub-carrier spacing, defined asε = εi + εf where εi is theinteger part of the normalized CFO whileεf is the fractionalpart. Even after estimating and compensating both integerand fractional CFO, a residual CFO,εr, which represents theremaining uncompensated fractional CFO always exists.

For the sampling frequency offset, it is mainly caused bythe mismatch between the transmitter and receiver oscillatorssuch that the received continuous-time waveform is sampledat an interval of(1+ δ)Ts instead ofTs whereTs is the idealsampling period andδ (usually expressed in part per millionor ppm) is the normalized difference between the periods ofthe two clocks. In [21],δ is estimated by the receiver wherecompensation is carried out by feeding the clock generatorwith the amount of time shift in order to adjust the clockor by interpolating the received time domain samples with afractional delay.

It is known that the residual CFO and SFO results in ICIwhich degrades the Signal-to-Noise Ratio (SNR) over all sub-carriers. The SNR degradation,SNRDCFO, due to the residualCFO is analytically analyzed in [22]. The analysis shows thatin the Additive White Gaussian Noise (AWGN) channel andwhen the number of sub-carriers is large, the SNR degradationis given by,

SNRDCFO

∣

∣

∣

∣

dB

=10

3 ln(10)

(

π εr)2

SNR (18)

Similarly, the SNR degradation due to the residual SFO,δr,in the kth sub-carrier,SNRDSFO(k), is analyzed in [23] andis given by,

SNRDSFO(k)

∣

∣

∣

∣

dB

= 10 log10

(

1 +1

3

(

π δr k)2

SNR

)

(19)

Since CFO and SFO estimation and compensation is a mustfor traditional OFDM systems, we have to consider theseissues when theenergy ratio algorithm is evaluated in thepresence of ICI. Our goal here is to emphasize that theenergyratio technique does not require any new solutions for theOFDM synchronization problems. Indeed, theenergy ratiocan provide a very good performance even with the existingalgorithms for the OFDM synchronization engine.

1) CFO Estimation and Compensation:Any practicalsystem assumes a maximum acceptable frequency offset,CFOmax, between the transmitter and receiver. Therefore, theinteger CFO range is known by the maximum integer CFO,εimax = ⌊CFOmax/∆f⌋. Hence, the integer CFO range willbeL =

[

−εimax −εimax+1 ... −1 0 1 ... εimax−1 εimax

]

.In [24], a two step time domain estimation technique isintroduced for CFO. This approach depends on the trainingsymbols that are transmitted at the front of the OFDMframe. Actually, a good compromise between performanceand complexity is achieved by this technique. The idea is tofirst estimate the fractional CFO by a maximum likelihoodestimator as given by (20) wherey(n) is the received timedomain signal andD = Ns +Ng.

εf =1

2πD∠

{

n=Ns−1∑

n=0

y(n) y∗(n+D)

}

(20)

It applies an autocorrelation to the time domain waveformwith the condition that two or more training symbols areinserted at the beginning of the frame. The time domainsignal is compensated for the fractional CFO resulting in thesignalycomp(n). This signal is then cross-correlated with thetransmitted time domain waveform for the training symbols,yt, after applying a progressive phase shift that depends onthe desired integer CFO as given by (21).

εi = maxm∈L

∣

∣

∣

∣

∣

n=Ns−1∑

n=0

ycomp(n) y∗t (n) e

−2πjmn/D

∣

∣

∣

∣

∣

(21)

This cross-correlation is repeated for each integer CFO inL and the maximum is searched for. The integer CFO thatcorresponds to the maximum correlation is selected as theestimated integer CFO. Once the normalized CFO is estimated,the OFDM signal can be compensated by rotating the phaseof the time domain signal by−2π(εf + εi)n wheren is thetime index.

2) SFO Estimation and Compensation:In [21], the carrier-frequency and timing offsets are jointly estimated by applyinga weighted least-squares (WLS) algorithm where a weightingmatrix,W, is designed to improve the estimation accuracy ofthe least-squares. The analytical results in [21] show thatthismatrix should be a function of the noise variance. In fact, ifanincorrect (estimated) value of the noise variance is used, thenthe resulting estimation accuracy may perform rather poorly.Since theenergy ratio is strong enough to compact ICI, wecan simply apply the WLS algorithm by replacingW withan identity matrix. This reduces the WLS algorithm into thewell-known least-squares estimation. First, we compute theaveraged phase difference between the pilots contained in twoconsecutive OFDM training symbols in the frequency domain

7

fRe{Y (rkj )}|Xp(rkj )=a+jb(w) = fIm{Y (rkj )}|Xp(rkj )=a+jb(w) =1

√

2π(σ2n + Eabσ2

H)exp

( −w2

2(σ2n + Eabσ2

H)

)

(21)

Primary

User Tx

Secondary

User Tx

CP

removal+

OFDM

Synchronization

blocks

FFT

Energy

Ratio

Channel

Estimation

Channel

EqualizationBit chain

hps

hss

nsr

Secondary User Rx

Figure 3. Communication model for SISO system where primaryuser channel and secondary user channel are considered

to obtain y =[

y0 y1 ... yJ−1

]Twhere J is the number

of pilots inserted in one preamble symbol. Second, the pilotsub-carrier indices denoted byxj , j = 0, 1, 2, ... J − 1 arearranged to construct the matrixX which is given by (22).Finally, the estimated carrier-frequency offsetε and timingoffset δ can be obtained by (23).

X =

[

x0 x1 x2 . . . xJ−1

1 1 1 . . . 1

]T

(22)

[

δ ε]T

=Ns

2π(Ns +Ng)

(

X∗ X)−1

X∗ y (23)

VI. FREQUENCYSELECTIVE CHANNEL AND

MULTI -ANTENNA SYSTEM

To study the effect of the frequency selective fading channelon the energy ratioalgorithm, we first consider the single-input single output (SISO) model shown in Fig. 3 where thesecondary transmitter communicates with one SU slave overthe channelhss. During the transmission, the primary usermay attempt transmission which is received by the secondaryreceiver across the channelhps. Both signals are combinedat the receiver antenna and then processed as one receivedstream. The receiver noise is added to the combined signalsand the result is converted to the frequency domain by theDFT block. The reserved tone sequence is then organized inorder to be processed by the monitoring algorithm.

If rki , i = 0, 1, ..., NRT−1 denotes the reserved tone indicesfor the kth OFDM symbol, then thejth reserved tone can bemodelled as given by (24) whereXs(r

kj ), Xp(r

kj ), Hss(r

kj ),

Hsp(rkj ), andn(rkj ) are the secondary user transmitted symbol,

the primary user transmitted symbol, the frequency domainresponse for the secondary channel, the frequency domainresponse for the primary channel, and the noise sample,respectively, where all are observed at sub-carrierrkj . Indeed,this is one of the most important properties for OFDMtechnique in which the frequency selective fading can beconverted into flat fading over each sub-carrier. Since thesecondary transmitter forces the reserved tones to be null,then Xs(r

kj ) = 0, ∀j and hence the received reserved

tones include the effect of the primary user and the noise

of the secondary receiver under perfect synchronization andneglecting the power leakage effect.

Y (rkj ) = Hps(rkj )Xp(r

kj ) +Hss(r

kj )Xs(r

kj ) + n(rkj )

= Hps(rkj )Xp(r

kj ) + n(rkj ) (24)

Now, suppose that the primary-to-secondary channel im-pulse response,hps, is modelled by a finite impulse response(FIR) filter with Ng taps where each tapl has the channelgain hps(l) for l = 0, 1, ..., Ng − 1. Here, we assumethat the maximum delay of the multi-path fading channelis fully characterized by the cyclic prefix length. If wedenoteσ2

H as the sum of the channel tap powers such thatσ2H =

∑Ng−1l=0 E

[

|hps(l)|2]

, then the conditional probabilitydensity function for either the real part or the imaginary partof the received symbol at indexrkj given that the transmittedsymbol isXp(r

kj ) = a + jb can be obtained by (21) where

σ2n is the noise variance andEab = (a2 + b2) [25].If the PU uses any Phase Shift Keying (PSK) modula-

tion like QPSK, then the average symbol energy is simplyEs = Eab = a2 + b2 and the received signal is modelledby a circularly symmetric Gaussian distribution with zero-mean and varianceσ2

n +Esσ2H . In this case, theenergy ratio

algorithm can still detect the reappearance of the primary userwhen the first window is filled with unwanted signals (i.e:σ2v = σ2

n) and the second window includes both the unwantedsignals and the primary user signal (i.e:σ2

u = σ2n + Esσ

2H ).

The same performance as the AWGN case can be obtained.However, the primary to secondary power ratio is definedas PNR = Es/σ

2n and hence the probability of detection

will depend on the channel profile as given by (22) whereσ2u = σ2

v (1 + PNR × σ2H). The conclusion is that the

energy ratioalgorithm can behave as in AWGN channel evenwhen the channel is frequency-selective for both primary andsecondary users.

PD = Prob[

X > γ | H1

]

= 1− I (σ2v γ/σ2

u)

(1+σ2v γ/σ2

u)

(N,N)

= 1− I (γ/(1+σ2H

PNR))

(1+γ/(1+σ2H

PNR))

(N,N) (22)

8

FIFO| | 2 FIFO

x

++ - ++ -

NN

Threshold

Decision

Spectrum

Monitoring

Samples

Comparator

Figure 4. Proposed architecture for the energy ratio algorithm

To enhance the detector performance in fading chan-nels, multiple-antennas at the receiver side can be utilized.For Single-Input Multiple-Output (SIMO) or Multiple-InputMultiple-Output (MIMO) systems, if the number of receiveantennas isNRx, there will beNRx available sets of reservedtones at the receiver for each OFDM symbol or equivalentlyNRx×NRT reserved tones every OFDM symbol. Theenergyratio monitoring technique will combine all these sets to formthe reserved tone sequence. In this case, the confidence ofprimary user presence is increased by the diversity gain offeredby the system. This allows for more robust decision comparedto the SISO case. Effectively, applying SIMO or MIMO isequivalent to increasing the window size by a factor ofNRx.If the same performance is required, the window size can bereduced byNRx which implies that the primary user poweris sensed in less time when compared to the SISO case.Otherwise, increasing the window size directly increases themean of the decision making variable underH1 which allowsfor higher detection probability and less false alarm.

VII. C OMPLEXITY OVERHEAD FOR ENERGY RATIO

ALGORITHM

To evaluate theenergy ratiofrom complexity point of view,we propose an architecture for the algorithm and then analyzethe corresponding complexity and compare it to the traditionalenergy detectors. The proposed architecture is shown in Fig. 4.First, the reserved tone sequence is injected to be squared.Next, two First-In First-Out (FIFO) memories are used to storethe squared outputs in order to manage the energy evaluationfor the two windows. The idea depends on the sliding conceptfor the windows where the total energy enclosed by onewindow can be evaluated by only adding the absolute squaredof the new sample and subtracting the absolute squared of thelast sample in the previous window as given by,

V (k) =

N+k−1∑

i=k

∣

∣Zi

∣

∣

2

= V (k − 1) +∣

∣ZN+k−1

∣

∣

2 −∣

∣Zk−1

∣

∣

2(23)

The ratio may not be evaluated directly, instead we canmultiply the energy of the first window by the threshold

0 2 4 6 8 100

0.05

0.1

0.15

0.2

0.25

0.3

0.35

0.4

x

f X(x

)

pdf from theoretical

pdf from simulation

Figure 5. Simulated PDF versus analytical PDF for the energyratio decisionmaking variable withN =32 and10 log10(σ2

u/σ2v) = 5dB

and the multiplication output is then compared to the en-ergy of the second window. We conclude that the proposedarchitecture typically uses double the components appliedforthe traditional energy detector. Moreover, traditional spectrumsensing which is applied prior to spectrum monitoring surelyinvolve multipliers and accumulators. To further reduce thecomplexity, these modules can be reused and shared with theenergy ratioalgorithm during spectrum monitoring as sensingand monitoring are non-overlapped in time.

VIII. S IMULATION RESULTS

In the simulation, we used an OFDM system that employsa total ofNs = 1024 sub-carriers, 224 of which are used asguard bands on both ends of the signal band. There are 32pilot sub-carriers andNRT = 4 reserved tones, distributedacross the entire 800 sub-carriers. Therefore, the throughputreduction due to reserved tones is only0.5% which is aninconsiderable amount for high data rates. The cyclic prefixisNg = 64 samples long and the sampling frequency is 16MHz.The sub-carrier spacing is then∆f = 15.625 KHz which islarge enough to neglect the phase noise distortion and thetime domain windowing effect. Unless otherwise specified,the frame has two consecutive training symbols, 256 OFDMdata symbols, and the reserved tone spacing∆r = 2. Thedata for both primary and secondary transmitters is modulatedby 16-PSK mapper and the secondary power to noise ratioin the absence of primary signal is assumed 9dB. Whenthe system operates under non-perfect synchronization, themaximum acceptable CFO is assumed to be 400KHz, the CFOis 320KHz, and the sampling clock offset is assumed to be 100ppm.

A. Analytical Verification

Fig. 5 shows a comparison between the PDF given by (9)and the one obtained from simulation where we have used10 log10(σ

2u/σ

2v) = 5dB and an energy ratio windowN =

32. To obtain the simulated PDF,107 circularly symmetricGaussian distributed samples are generated and scaled properlyfor both windows. The samples are then applied to theenergy

9

0 1 2 3 4 5 6 70

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

1.8

x

f X(x

)

pdf under H0

pdf under H1 − PNR=−2 dB

pdf under H1 − PNR=0 dB

pdf under H1 − PNR=2 dB

pdf under H1 − PNR=4 dB

Figure 6. Conditional PDF underH0 and conditional PDF underH1 forPNR=-2, 0, 2, and 4 dB

ratio algorithm and the PDF is obtained by considering thehistogram of the decision making variable. It is obvious thatthe analytical results are in excellent agreement with thesimulated ones.

Next, the hypothesis test is to be verified by exploring theconditional PDF under bothH0 andH1. In fact, when there isno primary user in band, the decision variable follows only oneunique PDF that is shown in Fig. 6. UnderH1, the conditionalPDF depends on the PNR ratio. Four additional curves are alsoshown in Fig. 6 for the conditional PDF underH1 with fourdifferent PNR values (-2, 0, 2, and 4 dB). It is clear that thedecision variable can distinguish between no primary user caseand primary user presence based on the PNR.

B. Receiver Characteristics

The detection probability for four different false alarmprobabilities is shown in Fig. 7. The horizontal axis denotesthe secondary to primary power ratio (SPR) which is related tothe primary to secondary noise ratio (PNR) such that PNR

∣

∣

dB= SNR

∣

∣

dB- SPR

∣

∣

dB, where SNR is the secondary power to

noise power ratio. It is to be noticed that, PNR is the ratiothat determines the performance of theenergy ratioalgorithmwhereas SPR is assumed to be the main parameter by whicha monitoring algorithm is evaluated.

The ROC for theenergy ratiofor different values of SPRis shown in Fig. 8. These results are obtained by simulatingthe OFDM system twice, one when primary signal is presentand the second when it is absent. The system is run over106

realizations and the probability of detection or false alarmis evaluated. The threshold is set based on the theoreticalvalue given by (12). In order to compare the proposedmonitoring algorithm with the receiver statistics techniquefound in [9], the OFDM system is simulated such that thesystem parameters match the simulation environment followedby [9]. The simulation is run for 4-QAM under SNR= 6dB,PFA =0.04, andN=128. Fig. 9 shows the simulation resultsfor the detection probability of theenergy ratioalgorithm incomparison with the results obtained in [9]. In addition ofhaving fast detection, it is noted that theenergy ratioshowsa better performance than the receiver statistics algorithm.

5 6 7 8 9 10 11 12 13 14 150.4

0.5

0.6

0.7

0.8

0.9

1

Secondary to Primary Power Ratio, SPR, in dB

Dete

ction p

robabili

ty, P

D

PFA

=0.025

PFA

=0.05

PFA

=0.075

PFA

=0.1

Figure 7. The detection probability at fixed false alarm probability underperfect synchronization and neglecting the power leakage effect

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

Probability of false alarm, PFA

De

tectio

n p

rob

ab

ility

, P

D

SPR=11 dB

SPR=12 dB

SPR=13 dB

SPR=14 dB

SPR=15 dB

Figure 8. Receiver operating characteristics for different SPR values underperfect synchronization and neglecting the power leakage effect

C. OFDM Challenges

The power leakage is modelled by applying oversamplingto the frequency domain signal, where the number of pointsat the receiver DFT is four times the number of points used atthe transmitter. Time domain Hanning window with folding isapplied at the receiver to limit the NBI and power leakage.Also the phase of the time domain samples is rotated by2πεn to model the receiver CFO wheren is the time index.Moreover, the received signal is re-sampled at time instancesthat are multiple of(1+ δ)Ts to model the receiver SFO. Thepreamble detection and the exact frame timing are assumed tobe perfect. Here the time domain preamble is used to estimateand compensate for the CFO. The CFO compensated signalis converted to the frequency domain via DFT. The SFO,δ, and the residual CFO are further estimated by applyingthe least squares algorithm discussed in V-B2. Moreover, thetime domain signal is re-sampled according to the delayδ tocompensate for the SFO.

Fig. 10 shows the mean square error for the estimated CFO

10

6 8 10 12 140.7

0.75

0.8

0.85

0.9

0.95

1

Secondary to Primary Power Ratio, SPR, in dB

Dete

ction p

robabili

ty, P

D

Energy Ratio

Receiver Statistics [9]

Figure 9. Comparison between energy ratio and receiver statistics algorithmsin case of QPSK, SNR= 6 dB, PFA = 0.04, andN =128

5 10 15 2010

−8

10−6

10−4

10−2

100

102

Signal to Noise Ratio in dB

Me

an

Sq

ua

re E

rro

r

AWGN CFO

Rayleigh CFO

AWGN SFO − in samples

Rayleigh SFO − in samples

Figure 10. MSE for both CFO and SFO estimation under AWGN andfrequency selective fading channels. The MSE for SFO is measured insamples.

and SFO. From these results, we can see that the residual frac-tional CFO and SFO at 9dB are9×10−3 and5×10−6, respec-tively. This implies SNR degradation ofSNRDCFO = 0.0092dB for CFO, andSNRDSFO(1023) = 0.003 dB for SFO atthe last sub-carrier, based on (18) and (19), respectively.Thisshows the advantages of the powerful estimation techniqueswe have chosen for the OFDM synchronization engine.

To examine the combined effects of OFDM impairments,the detection probability for theenergy ratiois simulated inthe presence of power leakage, CFO, and SFO as shown inFig. 11. The signal is oversampled four times by applying 4096points DFT at the receiver in order to allow the emulation ofthe continuous spectrum. The sub-carriers are then selectedby sampling this spectrum every four samples. Since thesub-carrier sinc shape becomes more narrow because of theHanning window, the introduced ICI by the residual CFO andSFO errors has a very small noticed degradation. Therefore,if windowing, CFO and SFO estimations and compensations

8 9 10 11 12 13 140.5

0.55

0.6

0.65

0.7

0.75

0.8

0.85

0.9

0.95

1

Secondary to Primary Power Ratio, SPR, in dB

De

tectio

n p

rob

ab

ility

, P

D

Perfect System

Power Leakage effect

CFO effect

SFO effect

Power leakage + CFO + SFO

Figure 11. Power leakage, CFO, and SFO effects on the energy ratioalgorithm atPFA = 0.025

4 6 8 10 12 140.4

0.5

0.6

0.7

0.8

0.9

1

Secondary to Primary Power Ratio, SPR, in dB

De

tectio

n p

rob

ab

ility

, P

D

AWGN

SISO

MIMO 2×2

MIMO 4×4

Figure 12. Frequency selective fading channel effect on energy ratio forSISO and MIMO systems taking power leakage and ICI into consideration,PFA = 0.025 andN = 128

are applied, the power leakage to neighbouring sub-carriersdoes not introduce severe degradation to the PU detection.As we claimed earlier, theenergy ratio is shown to berobust to OFDM challenges as only minor degradation indetection performance is noted compared to the perfect case.For instance, the overall loss due to all impairments is only0.4 dB at a detection probabilityPD = 0.9.

D. Effect of Frequency-Selective Fading

To study the effect of frequency-selectivity on the proposedenergy ratio technique, the channel is modelled as a lineartime-varying filter whose impulse response,h(n), is obtainedby: (1) Ng circularly symmetric Gaussian samples with unitvariance. The number of channel taps is defined by the cyclicprefix length as we assume that the cyclic prefix fully definesthe channel maximum excess delay. (2) The samples are scaledto fit the required power delay profile which is assumed to be

11

exponentially decaying [26]. Thus, the channel tapl is scaledby exp(−l) for l = 0, 1, 2, ..., Ng − 1.

The OFDM system is simulated in frequency selectivechannel for different SPR. In Fig. 12, we show the effectof frequency selective fading channel on theenergy ratioperformance for SISO,2 × 2 MIMO, and 4 × 4 MIMOsystems. The fading channel effect is compared with theAWGN channel where a minor degradation is noticed due tothe narrow band problem. From these results, it is clear thathaving more receive antennas will offer great enhancement tothe detection accuracy of theenergy ratiodetector.

IX. CONCLUSION

We proposed a spectrum monitoring algorithm that cansense the reappearance of the primary user during the sec-ondary user transmission. This algorithm, named "energyratio" is designed for OFDM systems such as Ecma-392 andIEEE 802.11af systems. We also derived the detection proba-bility and the probability of false alarm for AWGN channelsin order to analyze the performance of the proposed algorithm.Simulation results indicate that the detection performance issuperior than the receiver statistics method. For computationalcomplexity, theenergy ratioarchitecture is investigated whereit was shown that it requires only about double the complexityof the conventional energy detector. When frequency-selectivefading is studied, theenergy ratio algorithm is shown toachieve good performance that is enhanced by involvingSIMO or MIMO systems. We have proven that the multiplereceive antenna system will further result in a better detectionaccuracy by emulating the increase in sliding window size.Therefore, our proposed spectrum monitoring algorithm cangreatly enhance the performance of OFDM-based cognitivenetworks by improving the detection performance with a verylimited reduction in the secondary network throughput.

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