ofdm cognative

7/27/2019 OFDM Cognative

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Primary user detection in OFDM based MIMOCognitive Radio

Vijaykumar Kuppusamy and Rajarshi Mahapatra Member, IEEE Applied Research Group

Satyam Computers Services Ltd.,Bangalore, India,

Email: {vijaykumar kuppusamy, rajarshi mahapatra }@satyam.com

Abstract In order to detect the presence of the primary usersignal with high probability, spectrum sensing is a fundamentalrequirement to achieve the goal of cognitive radio (CR). Thisensures efcient utilization of the spectrum. Energy detectionis one of the technique to detect the primary users that arereceiving data within the communication range of a CR user.In this work, detection performance of the primary user (PU)signal on CR receiver is investigated. In particularly, the OFDMbased CR receiver detect the primary user OFDM signal, whereCR receiver is equipped with multiple antennas based energydetector. We observe signicant improvement in primary userdetection with SLC based energy detection at the MIMO CRs incomparison to single antenna CRs.

Index Terms Cognitive radio, Spectrum sensing, OFDM,MIMO

I. INTRODUCTION

The demand of radio-frequency spectrum is increasing tosupport the user needs in wireless communication. FCC report[1] suggests that many portion of radio spectrum are not in

use for signicant period of time and use of these spectrumholes can be increased signicantly. Cognitive radio (CR)[2], inclusive of software-dened radio, has been proposedas a means to promote the efcient use of the spectrum byexploiting the existence of spectrum holes. The intelligenceof cognitive radio lies on three basic functions: the ability tosense the outside environment; the capacity to learn, ideally inboth supervised and unsupervised modes; and nally, the ca-pability to adapt within any layer of the radio communicationsystem [3].

Cognitive radio transmits on a piece of spectrum found notutilized by the primary user (PU). Subsequent transmissionfrom CR should not cause interference to primary user when

PU starts using previously unused spectrum. To achieve thisgoal of CR, it is a fundamental requirement that the cogni-tive radio performs spectrum sensing from time to time todetect the presence of the PU signal. The sensing of radioenvironment to determine the presence of primary user isa challenging problem as the signal is attenuated by fadingwireless channel. This results in low signal-to-noise ratio(SNR) condition at the CR input, and makes CR susceptible tohidden node problem, wherein CR fails to detect primary userand begins transmission, thereby causing potential interferenceto the primary user. To minimize the occurrence of thisproblem, detection technique has to achieve probability of

detection close to unity for a specied probability of falsealarm and a given SNR.

Many signal detection techniques has been proposed inthe literature, such as matched ltering, energy detection,and cyclo-stationary feature detection [4]. The matched ltertechnique requires accurate prior knowledge about the primary

user signal, e.g. modulation type, pulse shaping, channelequalization and timing and frequency synchronization. Thesub-optimum, non-coherent energy detection technique is usedonly when the power spectral density of the Gaussian noise isknown to the receiver. Susceptibility of threshold to changingnoise statistics, inability to distinguish between PU signal andin-band interference are the major drawbacks of energy de-tector. The computationally complex cyclo-stationary featuredetector exploits the build-in periodicity of modulated signal toperform better than energy detector in discriminating againstnoise. However, in this work, we consider that the cognitiveradio uses energy detection technique to keep the complexityof the receiver low. However, use of energy detector in a single

antenna CR results in poor detection performance at low SNRregion, thereby causing interference to the PU signal. It hasbeen shown that CR equipped with multiples antennas andsquare-law-combining (SLC) based energy detector schemeoffer potential improvement in detection performance [5], [6].

OFDM has been proposed as the best physical layer can-didate for a CR system since it allows easy generation of spectrally shaped signal waveform that can t into discontin-uous and arbitrary sized spectrum segments [7], [8]. OFDMis also optimum from a capacity point of view since it allowsachieving the Shannon channel capacity in a segmented spec-trum. Hence, in this paper, we consider the performance of anOFDM based CR equipped with multiple antennas to receive

the signal from primary user and uses SLC based energydetector to detect the presence of PU. In a recent study in [9],the detection performance of OFDM based CR is addressedfor three different cases of primary user signal: a GaussianPU signal with known probability-density-function (PDF) andfrequency band PU signal resides; with only known frequencyband PU signal resides; and nally, no prior knowledge of PU signal. In this work, we provide an alternative approachof spectral sensing in OFDM based CR. We demonstrate thetheoretical detection performance gains that can be obtainedthrough appropriate signal processing with multiple antennaCRs in comparison to single antenna CRs.


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The rest of the paper is organized as follows. Section IIdescribes the system model for OFDM based MIMO cognitiveradio and provides detailed analysis of detection probabilities.The simulation results are presented in Sec. III. Finally, Sec.IV concludes the work.

II. PU SIGNAL DETECTION IN OFDM BASED MIMOC OGNITIVE R ADIO

In this section, we derive the detection probabilities of OFDM based MIMO cognitive radio using energy detector todetect the presence of PU in a Rayleigh fading channel. Weconsider PU transmitting OFDM signal with K -subcarriers ona bandwidth B . The transmission parameters, such as symbolperiod, carrier frequency and sub-carrier spacing of PU-OFDMsignal are dened as T i , f i and ( f ) i = 1T i , respectively. TheCR-OFDM system consists of Q number of sub-carriers withsymbol period T s , carrier frequency f s , sub-carrier spacing( f )s = 1T s and occupies bandwidth W . The carrier fre-quencies f s , f i and T iT s ratio determines the mapping of PUspectrum onto the CR spectrum window. With the assumption

f s = f i , the value n = ( T s (K + 1) /T i ) 1 is the numberof CR-OFDM sub-carriers overlapping with the PU spectrum.In the following, we derive the detection probabilities of PUsignal on CR receiver with multiple antennas.

In OFDM transmission, the symbols of PU are passedthough K -point IDFT block and cyclic prex (CP) is added.The resulting signal is up-converted to carrier frequency (f i )and then transmitted through wireless channel. The lth trans-mitted PU-OFDM symbol is given by

x (t lT i ) =K 1

k=0

X l,k ej 2 k ( t lT i )

T i ej 2f i ( t lT i ) (1)

where, X l,k is PU symbol modulated on kth

sub-carrier,generating lth PU-OFDM symbol.

A. Single Antenna (SA) Scheme

The received signal on CR is down converted, sampledat T d = T sQ and passed through Q-point DFT system. Weconsider the n th CR-OFDM symbol to fall within the spanof PU signals lth symbol, such as nT s t < (n + 1) T s . Indetection of the n th OFDM symbol, the contribution of PUsignal in a frequency selective fading channel at the down-converter output of the receiver is given by

s (t nT s ) = e j 2fs ( t nT s )

L 1

m =0 hm x(t lT i mTs ) (2)where, hm are coefcients of frequency selective fading chan-nel. Substituting (1) in (2) yields

s (t nT s ) =L 1

m =0hm

K 1

k=0

X l,k ej 2 k ( t lT i mT s )

T i

ej 2f i ( t lT i mT s ) e j 2f s ( t nT s )=

K 1

k=0

X l,k H k ej 2 k ( t lT i )

T i

ej 2f i ( t lT i ) e j 2f s ( t nT s ) (3)

where, H k =L 1

m =0hm e

j 2m (f i T s + k T sT i ) . The resulting signal

is then sampled at every T d = T sQ seconds, and the corre-sponding sampled signal is given as

s p =K 1

k =0

X l,k H k ej 2 pT sQ (

kT i

+ f i f s ) ej 2 ( lf i T i + nT s f s ) , (4)

The discrete time signal {s p} is passed through a Q-pointDFT, which provides the signal component on q th sub-carrieras follows

S q(n) =Q 1

p=0s pe

j 2 pqQ

=K 1

k=0

X l,k H k ej 2 ( lf i T i + nf s T s ) ej k,q (Q 1)

sin ( k,q Q)sin ( k,q )

0 q Q 1 (5)where, k,q = ( kT i + f i

f s )T d

qQ . Therefore, the received

signal at the CR post DFT operation can be written as,

Rq(n) = S q(n) + W q(n) (6)

where, W q(n) is DFT of complex noise sequence with vari-ance 2w . The primary objective is to determine the presence(Hypothesis H 1 ) or absence (Hypothesis H 0) of PU signal.Under these two hypothesis, received signal is denoted as

Rq(n) =S q(n) + W q(n) H 1W q(n) H 0

n = 1 , . . . , N (7)

The energy detector forms the decision statistics ( E q ) collect-ing N samples from the output of DFT block corresponding to

q th

sub-carrier. The decision statistics ( E q) will be comparedwith threshold calculated for a given probability of false alarm(P f ) to detect the presence of PU signal. The decision makingblock marks the sub-carrier as unused when the decision statis-tics is less than threshold value. This procedure is repeatedfor all the Q sub-carriers and subsequently, the number of sub-carriers free for use by CR is determined. Under H 0 , thenormalized decision statistics is given as

E q =2

2w

N

n =1|W q(n)|2

=2

2w

N

n =1

(|W qr (n)|2 + |W qi (n)|2) (8)where, W qr (n) and W qi (n) are real and imaginary parts of W q(n) and they are zero mean gaussian random variable withvariance 2w / 2. Now, we dene Z qr (n) =

W qr (n ) 2w / 2 , and Z qr (n)is zero mean gaussian random noise with unit variance. Thedecision statistics is given as

E q =N

i=1

(|Z qr (n)|2 + |Z qi (n)|2) (9)Thus, E q under H 0 , can be viewed as the sum of square of the2N standard Gaussian i.i.d random variable with zero mean


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and unit variance. Therefore, E q follows a central chi-squaredistribution with 2N degree of freedom. The probability of false alarm is given as [6]

P f = (N,/ 2)

(N )(10)

where, (., .) is the incomplete gamma function, is the

threshold with which the decision statistics is compared todetect the presence of PU signal. Under H 1 , the decisionstatistics E q is given as

E q =2

2w

N

n =1|S q(n) + W q(n)|2

=2

2w

N

n =1(S qr (n) + W qr (n))

2 + ( S qi (n) + W qi (n))2

=2

2w[RT qr Rqr + R

T qi Rqi ]

=2

2wuT u (11)

where, u = [RT qr RT ri ]T , and Rqr = [Rqr (1) . . . Rqr (N )].The decision statistics E q under H 1 is sum of square of 2N correlated gaussian random variable. The correlation of Gaussian random sequence Rq(n) is due to signal componentS q(n) obtained considering small segment of oversampled PUOFDM symbol, assuming T i /T s > 1. The PDF of decisionstatistics can be written as (using (23) in Appendix I)

P E q /H 1 (E q) =1

2

()e jE q d (12)

where, () = N i =1 (1 j 2 i ) 1 =2N i =1 (1 j 2 i ) 0.5

is characteristic function of decision statistics, i are theeigenvalues of covariance matrix ( C E q ) of gaussian randomvariable constituting decision statistics, i are the eigenvaluesof covariance matrix R = [C E q 0N,N ; 0N,N C E q ]. ThePDF is evaluated numerically once eigenvalues of covariancematrix are computed. The covariance matrix of decision statis-tics is given as (using (28) in Appendix II)

C E q =1

2w {Cs + 2w I} (13)

where, (n, m )th elements of covariance matrix C s is as follows

C sn,m =1

| b|

K 1

k=0

ej 2 (b)T s f s

sin 2 ( k,q Q )sin 2 ( k,q ) |b| 1

0 Otherwise

(14)

where b = n m and = T iT s with x being the largestinteger not greater than x. The probability of detection is givenas

P d =

P E q /H 1 (E q)dE q (15)

The threshold is computed from (10) for a given probabilityof false alarm.

B. Square Law Combining (SLC) Scheme

In this section, we derive the detection probabilities of diversity-based energy detectors in a fading channel for MIMOcognitive radio. In this scheme, multiple antennas are used atthe cognitive radio receiver end for making efcient decisionon the detection of primary user signal. Received signal ispassed through energy detector, output of which is combined

to form the decision statistics. The received signal at the jth

antenna can be written as

R jq(n) = S jq (n) + W

jq (n), j = 1 . . . M (16)

where, M is the number of CR antennas. The normalizeddecision statistics for SLC scheme is equal to the sum of theenergy of all the received antennas which can written as

E q =2

2w

M

j =1

N

n =1S jq (n) + W

jq (n)

2(17)

Under H 0 ,

E q =2

2w

M

j =1

N

n =1W jq (n)

2

=2

2w

M

j =1

N

n =1W jqr (n)

2+ W jqi (n)

2

=M

j =1

N

n =1Z jqr (n)

2+ Z jqi (n)

2(18)

Thus, E q can be viewed as the sum of the squares of the2MN standard Gaussian i.i.d random variable with zero meanand unit variance. Therefore, decision statistics E q under H 0follows a central chi-square distribution ( 2) with 2MN degreeof freedom. The probability of false alarm ( P f ) of SLC schemeis given as [6]

P f = (MN,/ 2)

(MN )(19)

Under H 1 , the decision statistics E q is given as

E q =2

2w

N

n =1S 1q (n) + W

1q (n)

2+ . . .

+2

2w

N

n =1S M q (n) + W

M q (n)

2(20)

The characteristic function is () = N i =1 (1 j 2 i ) M , as-suming independence and same statistics for MIMO channels,where i are the eigenvalues of covariance matrix ( C E q ) of gaussian random variable constituting decision statistics. ThePDF and probability of detection is evaluated numerically onceeigenvalues of covariance matrix and threshold for a givenprobability of false alarm is computed.

III. S IMULATION RESULTS

In our simulation, we consider the PU-OFDM system con-sisting of K = 256 sub-carriers with symbol period T i = 26 .6s and carrier frequency f i = 3 .1 GHz. Subsequently, weconsider CR receiver with Q = 128 sub-carriers of symbol


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100

104

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102

101

100

Probability of False Alarm (Pf)

P r o

b a

b i l i t y o

f M i s s

( P m

)

SA SNR=0 dBSA SNR=2 dBSA SNR=5 dBSLC SNR=0 dBSLC SNR=2 dBSLC SNR=5 dB

Fig. 1. Complementary ROC curves for different diversity schemes basedenergy detector ( T i = 26 .6 s , T s = 2 .66 s , N =10, M = 2 ).

period T s = 2 .66 s and carrier frequency f s = 3 .1 GHz,and equipped with single antenna and two antennas for SA and

SLC scheme respectively. To show the detection performanceof MIMO cognitive radio, we use complementary receiveroperating characteristic (ROC) function.

Figure 1 shows the complementary ROC curves overRayleigh fading channel for different diversity scheme basedon energy detector for different SNR and N = 10 . Asexpected, the performance of SLC scheme is superior than nodiversity schemes for xed SNR, and N . Figure 2 illustratesthe effect of SNR on ROC curves for SA and SLC schemewhich shows that diversity based energy detector performsbetter at low SNR and the difference decreases as SNRincreases for a particular value of P f , N and T i /T s ratio.

The detection probability can also increases by consideringhigh number of CR-OFDM symbols ( N ) for forming decisionstatistics in both the cases, as shown in Fig. 3. However, con-sidering high number of N , increases the sensing time, wheresensing time is directly proportional to N . To achieve theprobability of detection 0.9 for P f = 0 .01, SA scheme requiresclose to 40 CR-OFDM symbols at SNR 5 dB and neededmore than 200 CR-OFDM symbols at SNR 2 dB. However,diversity-based detector requires only 20 CR-OFDM symbolsat SNR of 2 dB and 5 symbols at 5 dB SNR. Thus, diversity-based detector achieves the same performance with decreasedsensing time. Therefore, a trade-off is necessary between P d ,sensing time and number of antenna at a particular value of P f and T i /T s ratio.

Finally, Fig.4 shows the dependence of P d on T iT s ratio forSLC and SA scheme. The CR receiver with T iT s = 10 , N = 10considers single PU OFDM signal for decision statistics. SmallT iT s = 5 ratio implies that CR OFDM symbol takes into accounttwo PU OFDM signal for xed N = 10 . Hence a gain in thedetection performance. However, for T iT s = 20 , only half of the PU OFDM symbol is considered.

IV. C ONCLUSION

In this work, we considered sub-carrier level spectral sens-ing in OFDM based CR, where CR receiver is equipped

0 2 4 6 8 100

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

SNR (dB)

P o r b a

b i l i t y o

f D e

t e c

t i o n

( P d

)

SASLC

Fig. 2. Probability of detection versus SNR for different diversity schemesbased energy detector ( T i = 26 .6 s , T s = 2 .66 s , N =10, M = 2 , P f =0 .01 ).

0 20 40 60 80 1000

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

Number of CR OFDM symbols (N)

P r o

b a

b i l i t y o

f D e

t e c

t i o n

( P d

)

SA SNR=0 dBSA SNR=2 dBSA SNR=5 dBSLC SNR=0 dBSLC SNR=2 dBSLC SNR=5 dB

Fig. 3. Probability of detection versus N for different diversity schemesbased energy detector ( T i = 26 .6 s , T s = 2 .66 s , M = 2 , P f = 0 .01 ).

0 10 20 30 40 50 60 70 800

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

Number of CR OFDM symbols (N)

P r o

b a

b i l i t y o

f D e t e c

t i o n

( P d

)

SLC Ti /T

s= 5

SLC Ti /T

s= 10

SLC T i /Ts = 20

SA T i /Ts = 5

SA Ti /T

s= 10

SA Ti /T

s= 20

Fig. 4. Probability of detection versus N for different T iT s ratio ( T i=

26 .6 s , M = 2 , SN R = 2 dB ).


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with multiple antennas. The CR used SLC based energydetection to detect primary user signal. The SLC based energydetector provides high detection probabilities even at low tomoderate SNRs. Increasing number of CR-OFDM symbols isalso considered for decision statistics, leading to a increasedperformance, but at the expense of increased sensing time.The investigation also shows the impact of T i /T s ratio on thedetection performance.

R EFERENCES

[1] FCC, Spectrum Policy Task Force Report, ET Docket No. 02-135,Nov. 2002

[2] J. Mitola et al. , Cognitive radio: making software radios more per-sonal, IEEE Pers. Commun., vol 6, no. 4, pp. 13-18, Aug. 1999.

[3] S. Haykins, Cognitive radio: brain-empowered wireless communica-tions, IEEE J. Select. Areas Commun, vol. 23, no. 2, pp. 201-220, Feb.2005.

[4] I. F. Akyildiz et al. , Next generation/dynamic spectrum access/cognitiveradio wireless network: a survey, Computer Network , pp. 2127-2159,2006.

[5] F. F. Digham, M. S. Alouini, and M. K. Simon, On the energydetection of unknown signals over fading channels, Proc. IEEE Int.

Conf. Communications. (ICC03), vol. 5, pp. 3575-3579, May. 2003.[6] F. F. Digham, M. S. Alouini, and M. K. Simon, On the energy detection

of unknown signals over fading channels, IEEE Trans. Commun., vol.55, no. 1, pp. 21-24, Jan. 2007.

[7] H. Tang, Some physical layer issues of wide-band cognitive radiosystems, Proc. IEEE Int. Symp. on new frontiers in Dynamic Spectrum Access Networks (DySPAN05), pp. 151-159, Nov. 2005.

[8] T. A. Weiss, and F. K. Jondral, Spectrum pooling: an innovative strategyfor the enhancement of spectrum efciency, IEEE Commun. Mag., vol.42, no. 3, pp. S8-S14, Mar. 2004.

[9] C. H. Hwang, and S. C. Chen, Spectrum Sensing in wideband OFDMcognitive radios, submitted to IEEE Trans. Signal Processing., Aug.2007.

[10] W. Huan, W. Yajun and L. Maocang, CFAR performance analysis of a phase-coded pulse compression systemwith hard limiter, CIE Inter.Conf. of Radar, vol. 8, pp. 409-412, Oct. 1996.

[11] C. R. N. Athaudage and K. Sathananthan, Probability of error of space-time coded OFDM systems with frequency offset in frequency-selectiveRayleigh fading channels, The IEEE Inter. Conf. on Communications(ICC05), vol. 4, pp. 2593-2599, May. 2005.

A PPENDIX I

Theorem 1 : Let u = [ uT r uT i ]T be a 2N dimensional realGaussian random variable with positive denite covariancematrix R . Then the characteristic function of y = uT u isgiven by [10]

() =2N

i =1

(1 j 2 i )12 (21)

where, i are the eigenvalues of R . When R takes the specialform, (i.e) R = diag{R u , R u }, () can be written as

() =N

i =1

(1 j 2 i ) 1 (22)

where, R u = E {ur uT r }= E {u i uT i }, i are the eigenvalues of R u . The PDF of y is obtained by Fourier transform of (),that is

p y (y) =1

2

()e jy d (23)

A PPENDIX II

The received signal on q th subcarrier of CR-OFDM systemcan be written as (6)

Rq(n) =K 1

k =0

X l,k H k ej 2 ( lf i T i + nf s T s ) ej k,q (Q 1)

sin ( k,q Q)

sin ( k,q )+ W q(n) 0

q

Q

1 (24)

The received signal Rq(n) can be approximated by a Gaussianrandom sequence when the number of complex sinusoidal K is very large due to central limit theorem. The signal and noisecomponents are assumed to be independent. Let us denote theevent A that the n th and m th CR OFDM symbols both fallwithin the span of the lth PU symbol. Clearly, Rq(n) andRq(m) are zero-mean Gaussian random variable. Conditionedon the event A , the correlation of Rq(n) and Rq(m) is [11]

E {Rq(n)Rq (m)/ A} =K 1

k =0

E {|H k |2}E {|X l,k |2}

ej 2 (n m )T s f s sin 2( k,q Q)sin 2( k,q )+ 2w (25)

Assuming, E {|X l,k |2}= 1 and E {|H k |2}= 1 ,

E {Rq(n)Rq (m)/ A}=K 1

k=0

ej 2 (n m )T s f ssin 2( k,q Q)sin 2( k,q )

+ 2w

(26)On the contrary, if OFDM symbols n and m fall within the

span of distinct symbols of PU signal, then

E {Rq(n)Rq (m)/ A}= 0with A is the complement of A . Let = T iT s with x beingthe largest integer not greater than x. The probability P r {A}of event A is roughly equal to [9]

P r {A}= 1 | n m | , |n m| 10 Otherwise (27)Thus, the (n, m ) th element of the covariance matrix of

{Rq(n)}N 1n =0 is given byP r {A}.E {Rq(n)Rq (m)/ A} (28)

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