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Primary user detection in OFDM based MIMO Cognitive 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 user signal with high probability, spectrum sensing is a fundamental requirement to achieve the goal of cognitive radio (CR). This ensures efficient utilization of the spectrum. Energy detection is one of the technique to detect the primary users that are receiving 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 OFDM based CR receiver detect the primary user OFDM signal, where CR receiver is equipped with multiple antennas based energy detector. We observe significant improvement in primary user detection with SLC based energy detection at the MIMO CRs in comparison to single antenna CRs. Index Terms—Cognitive radio, Spectrum sensing, OFDM, MIMO

I. I NTRODUCTION The demand of radio-frequency spectrum is increasing to support the user needs in wireless communication. FCC report [1] suggests that many portion of radio spectrum are not in use for significant period of time and use of these “spectrum holes” can be increased significantly. Cognitive radio (CR) [2], inclusive of software-defined radio, has been proposed as a means to promote the efficient use of the spectrum by exploiting the existence of spectrum holes. The intelligence of cognitive radio lies on three basic functions: the ability to sense the outside environment; the capacity to learn, ideally in both supervised and unsupervised modes; and finally, the capability to adapt within any layer of the radio communication system [3]. Cognitive radio transmits on a piece of spectrum found not utilized by the primary user (PU). Subsequent transmission from CR should not cause interference to primary user when PU starts using previously unused spectrum. To achieve this goal of CR, it is a fundamental requirement that the cognitive radio performs spectrum sensing from time to time to detect the presence of the PU signal. The sensing of radio environment to determine the presence of primary user is a challenging problem as the signal is attenuated by fading wireless channel. This results in low signal-to-noise ratio (SNR) condition at the CR input, and makes CR susceptible to hidden node problem, wherein CR fails to detect primary user and begins transmission, thereby causing potential interference to the primary user. To minimize the occurrence of this problem, detection technique has to achieve probability of

detection close to unity for a specified probability of false alarm and a given SNR. Many signal detection techniques has been proposed in the literature, such as matched filtering, energy detection, and cyclo-stationary feature detection [4]. The matched filter technique requires accurate prior knowledge about the primary user signal, e.g. modulation type, pulse shaping, channel equalization and timing and frequency synchronization. The sub-optimum, non-coherent energy detection technique is used only when the power spectral density of the Gaussian noise is known to the receiver. Susceptibility of threshold to changing noise statistics, inability to distinguish between PU signal and in-band interference are the major drawbacks of energy detector. The computationally complex cyclo-stationary feature detector exploits the build-in periodicity of modulated signal to perform better than energy detector in discriminating against noise. However, in this work, we consider that the cognitive radio uses energy detection technique to keep the complexity of the receiver low. However, use of energy detector in a single antenna CR results in poor detection performance at low SNR region, thereby causing interference to the PU signal. It has been shown that CR equipped with multiples antennas and square-law-combining (SLC) based energy detector scheme offer potential improvement in detection performance [5], [6]. OFDM has been proposed as the best physical layer candidate for a CR system since it allows easy generation of spectrally shaped signal waveform that can fit into discontinuous and arbitrary sized spectrum segments [7], [8]. OFDM is also optimum from a capacity point of view since it allows achieving the Shannon channel capacity in a segmented spectrum. Hence, in this paper, we consider the performance of an OFDM based CR equipped with multiple antennas to receive the signal from primary user and uses SLC based energy detector to detect the presence of PU. In a recent study in [9], the detection performance of OFDM based CR is addressed for three different cases of primary user signal: a Gaussian PU signal with known probability-density-function (PDF) and frequency band PU signal resides; with only known frequency band PU signal resides; and finally, no prior knowledge of PU signal. In this work, we provide an alternative approach of spectral sensing in OFDM based CR. We demonstrate the theoretical detection performance gains that can be obtained through appropriate signal processing with multiple antenna CRs in comparison to single antenna CRs.

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

Xl,k e

j2πk(t−lTi ) Ti

ej2πfi (t−lTi )

(1)

k=0

where, Xl,k is PU symbol modulated on k th sub-carrier, generating lth PU-OFDM symbol. A. Single Antenna (SA) Scheme The received signal on CR is down converted, sampled at Td = TQs and passed through Q-point DFT system. We consider the nth CR-OFDM symbol to fall within the span of PU signal’s lth symbol, such as nTs ≤ t < (n + 1)Ts . In detection of the nth OFDM symbol, the contribution of PU signal in a frequency selective fading channel at the downconverter output of the receiver is given by s (t − nTs ) = e−j2πf s(t−nT s)

L−1


hm x(t − lT i − mT s) (2)

m=0

where, hm are coefficients of frequency selective fading channel. Substituting (1) in (2) yields s (t − nTs ) =

L−1


K−1


i

. The resulting signal

is then sampled at every Td = TQs seconds, and the corresponding sampled signal is given as K−1


k s j2π pT Q ( Ti +fi −fs ) j2π(−lfi Ti +nTs fs )

Xl,k Hk e

e

, (4)

The discrete time signal {sp } is passed through a Q-point DFT, which provides the signal component on q th sub-carrier as follows Sq (n)

=

Q−1


sp e−

j2πpq Q

p=0

=

K−1


Xl,k Hk ej2π(−lfi Ti +nfs Ts ) ejπβk,q (Q−1)

k=0

×

sin(πβk,q Q) sin(πβk,q )

0≤q ≤Q−1

(5)

q where, βk,q = ( Tki + fi − fs )Td − Q . Therefore, the received signal at the CR post DFT operation can be written as,

Rq (n) = Sq (n) + Wq (n)

(6)

where, Wq (n) is DFT of complex noise sequence with vari2 . The primary objective is to determine the presence ance σw (Hypothesis H1 ) or absence (Hypothesis H0 ) of PU signal. Under these two hypothesis, received signal is denoted as  Sq (n) + Wq (n) H1 Rq (n) = n = 1, . . . , N (7) Wq (n) H0 The energy detector forms the decision statistics (Eq ) collecting N samples from the output of DFT block corresponding to q th sub-carrier. The decision statistics (Eq ) will be compared with threshold calculated for a given probability of false alarm (Pf ) to detect the presence of PU signal. The decision making block marks the sub-carrier as unused when the decision statistics is less than threshold value. This procedure is repeated for all the Q sub-carriers and subsequently, the number of sub-carriers free for use by CR is determined. Under H0 , the normalized decision statistics is given as Eq

=

N 2
|Wq (n)|2 2 σw n=1

=

N 2
(|Wqr (n)|2 + |Wqi (n)|2 ) 2 σw n=1

(8)

where, Wqr (n) and Wqi (n) are real and imaginary parts of Wq (n) and they are zero mean gaussian random variable with W (n) 2 variance σw /2. Now, we define Zqr (n) = √ qr2 , and Zqr (n) σw /2

j2πk(t−lTi −mTs ) Ti

is zero mean gaussian random noise with unit variance. The decision statistics is given as

hm Xl,k e m=0 k=0 j2πfi (t−lTi −mTs ) −j2πfs (t−nT s)

× e e K−1
j2πk(t−lTi ) Ti = Xl,k Hk e

Eq =

N


(|Zqr (n)|2 + |Zqi (n)|2 )

(9)

i=1

k=0

× ej2πfi (t−lTi ) e−j2πfs (t−nTs )

s −j2πm(fi Ts +k T T )

hm e

k=0

In this section, we derive the detection probabilities of OFDM based MIMO cognitive radio using energy detector to detect the presence of PU in a Rayleigh fading channel. We consider PU transmitting OFDM signal with K-subcarriers on a bandwidth B. The transmission parameters, such as symbol period, carrier frequency and sub-carrier spacing of PU-OFDM signal are defined as Ti , fi and (∆f )i = T1i , respectively. The CR-OFDM system consists of Q number of sub-carriers with symbol period Ts , carrier frequency fs , sub-carrier spacing (∆f )s = T1s and occupies bandwidth W . The carrier frequencies fs , fi and TTsi ratio determines the mapping of PU spectrum onto the CR spectrum window. With the assumption fs = fi , the value n = (Ts (K + 1)/Ti ) − 1 is the number of CR-OFDM sub-carriers overlapping with the PU spectrum. In the following, we derive the detection probabilities of PU signal on CR receiver with multiple antennas. In OFDM transmission, the symbols of PU are passed though K-point IDFT block and cyclic prefix (CP) is added. The resulting signal is up-converted to carrier frequency (fi ) and then transmitted through wireless channel. The lth transmitted PU-OFDM symbol is given by K−1


L−1
m=0

sp =

II. PU SIGNAL DETECTION IN OFDM BASED MIMO C OGNITIVE R ADIO

x (t − lTi ) =

where, Hk =

(3)

Thus, Eq under H0 , can be viewed as the sum of square of the 2N standard Gaussian i.i.d random variable with zero mean

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and unit variance. Therefore, Eq follows a central chi-square distribution with 2N degree of freedom. The probability of false alarm is given as [6] Pf =

Γ (N, η/2) Γ (N )

(10)

where, Γ(., .) is the incomplete gamma function, η is the threshold with which the decision statistics is compared to detect the presence of PU signal. Under H1 , the decision statistics Eq is given as Eq

=

N 2
|Sq (n) + Wq (n)|2 2 σw n=1

=

N 2
2 2 (Sqr (n) + Wqr (n)) + (Sqi (n) + Wqi (n)) 2 σw n=1

= =

2 T T [Rqr Rqr + Rqi Rqi ] 2 σw 2 T u u 2 σw

1 2 {Cs + σw I} 2 σw

In this section, we derive the detection probabilities of diversity-based energy detectors in a fading channel for MIMO cognitive radio. In this scheme, multiple antennas are used at the cognitive radio receiver end for making efficient decision on the detection of primary user signal. Received signal is passed through energy detector, output of which is combined to form the decision statistics. The received signal at the j th antenna can be written as Rqj (n) = Sqj (n) + Wqj (n),

j = 1...M

(16)

where, M is the number of CR antennas. The normalized decision statistics for SLC scheme is equal to the sum of the energy of all the received antennas which can written as Eq =

M N

2 2



j Sq (n) + Wqj (n) 2 σw j=1 n=1

(17)

Under H0 , (11)

T T T Rri ] , and Rqr = [Rqr (1) . . . Rqr (N )]. where, u = [Rqr The decision statistics Eq under H1 is sum of square of 2N correlated gaussian random variable. The correlation of Gaussian random sequence Rq (n) is due to signal component Sq (n) obtained considering small segment of oversampled PU OFDM symbol, assuming Ti /Ts > 1. The PDF of decision statistics can be written as (using (23) in Appendix I)  ∞ 1 PEq /H1 (Eq ) = φ(ω)e−jωEq dω (12) 2π −∞ N 2N where, φ(ω) = i=1 (1 − j2ωξi )−1 = i=1 (1 − j2ωλi )−0.5 is characteristic function of decision statistics, ξi are the eigenvalues of covariance matrix (CEq ) of gaussian random variable constituting decision statistics, λi are the eigenvalues of covariance matrix R = [CEq 0N,N ; 0N,N CEq ]. The PDF is evaluated numerically once eigenvalues of covariance matrix are computed. The covariance matrix of decision statistics is given as (using (28) in Appendix II)

CEq =

B. Square Law Combining (SLC) Scheme

Eq

M N 2



j

2 Wq (n) = 2 σw j=1 n=1 M N  2  2 j 2

 j W = (n) + W (n) qr qi 2 σw j=1 n=1 M
N  2 
 j 2 j Zqr (n) + Zqi = (n) (18) j=1 n=1

Thus, Eq can be viewed as the sum of the squares of the 2M N standard Gaussian i.i.d random variable with zero mean and unit variance. Therefore, decision statistics Eq under H0 follows a central chi-square distribution (χ2 ) with 2MN degree of freedom. The probability of false alarm (Pf ) of SLC scheme is given as [6] Γ (M N, η/2) (19) Pf = Γ (M N ) Under H1 , the decision statistics Eq is given as Eq

=

N

2 2


1 Sq (n) + Wq1 (n) + . . . 2 σw n=1

+

N

2 2


M M

S (n) + W (n) q q 2 σw n=1

(13)

where, (n, m)th elements of covariance matrix Cs is as follows 

 K−1
  |b|  1− η ej2π(b)Ts fs   s k=0 (14) Cn,m = sin2 (πβ Q)   |b| ≤ η − 1 × sin2 (πβk,q  k,q )   0 Otherwise where b = n − m and η =  TTsi  with x being the largest integer not greater than x. The probability of detection is given as  ∞ PEq /H1 (Eq )dEq (15) Pd = η

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

(20)

N The characteristic function is φ(ω) = i=1 (1−j2ωξi )−M , assuming independence and same statistics for MIMO channels, where ξi are the eigenvalues of covariance matrix (CEq ) of gaussian random variable constituting decision statistics. The PDF and probability of detection is evaluated numerically once eigenvalues of covariance matrix and threshold for a given probability of false alarm is computed. III. S IMULATION RESULTS In our simulation, we consider the PU-OFDM system consisting of K = 256 sub-carriers with symbol period Ti = 26.6 µs and carrier frequency fi = 3.1 GHz. Subsequently, we consider CR receiver with Q = 128 sub-carriers of symbol

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4

0

10

1 0.9 −1

0.8 d

Porbability of Detection (P )

m

Probability of Miss (P )

10

−2

10

SA SNR=0 dB SA SNR=2 dB SA SNR=5 dB SLC SNR=0 dB SLC SNR=2 dB SLC SNR=5 dB

−3

10

0.6 0.5 0.4 0.3 0.2

SA SLC

0.1

−4

10

0.7

−4

10

−3

10

−2

−1

10 10 Probability of False Alarm (Pf)

0

10

0

0

2

4

6

8

10

SNR (dB)

IV. C ONCLUSION In this work, we considered sub-carrier level spectral sensing in OFDM based CR, where CR receiver is equipped

1 0.9

d

Probability of Detection (P )

0.8 0.7 0.6 SA SNR=0 dB SA SNR=2 dB SA SNR=5 dB SLC SNR=0 dB SLC SNR=2 dB SLC SNR=5 dB

0.5 0.4 0.3 0.2 0.1 0

0

20

40 60 Number of CR OFDM symbols (N)

80

100

Fig. 3. Probability of detection versus N for different diversity schemes based energy detector (Ti = 26.6µs, Ts = 2.66µs, M = 2, Pf = 0.01).

1 0.9 0.8 d

period Ts = 2.66 µs and carrier frequency fs = 3.1 GHz, and equipped with single antenna and two antennas for SA and SLC scheme respectively. To show the detection performance of MIMO cognitive radio, we use complementary receiver operating characteristic (ROC) function. Figure 1 shows the complementary ROC curves over Rayleigh fading channel for different diversity scheme based on energy detector for different SNR and N = 10. As expected, the performance of SLC scheme is superior than no diversity schemes for fixed SNR, and N . Figure 2 illustrates the effect of SNR on ROC curves for SA and SLC scheme which shows that diversity based energy detector performs better at low SNR and the difference decreases as SNR increases for a particular value of Pf , N and Ti /Ts ratio. The detection probability can also increases by considering high number of CR-OFDM symbols (N ) for forming decision statistics in both the cases, as shown in Fig. 3. However, considering high number of N , increases the sensing time, where sensing time is directly proportional to N . To achieve the probability of detection 0.9 for Pf = 0.01, SA scheme requires close to 40 CR-OFDM symbols at SNR 5 dB and needed more than 200 CR-OFDM symbols at SNR 2 dB. However, diversity-based detector requires only 20 CR-OFDM symbols at SNR of 2 dB and 5 symbols at 5 dB SNR. Thus, diversitybased detector achieves the same performance with decreased sensing time. Therefore, a trade-off is necessary between Pd , sensing time and number of antenna at a particular value of Pf and Ti /Ts ratio. Finally, Fig.4 shows the dependence of Pd on TTsi ratio for SLC and SA scheme. The CR receiver with TTsi = 10, N = 10 considers single PU OFDM signal for decision statistics. Small Ti Ts = 5 ratio implies that CR OFDM symbol takes into account two PU OFDM signal for fixed N = 10. Hence a gain in the detection performance. However, for TTsi = 20, only half of the PU OFDM symbol is considered.

Fig. 2. Probability of detection versus SNR for different diversity schemes based energy detector (Ti = 26.6µs, Ts = 2.66µs, N =10, M = 2, Pf = 0.01).

Probability of Detection (P )

Fig. 1. Complementary ROC curves for different diversity schemes based energy detector (Ti = 26.6µs, Ts = 2.66µs, N =10, M = 2).

0.7 0.6 0.5 SLC T /T = 5

0.4

i

s

SLC Ti/Ts = 10

0.3

SLC Ti/Ts = 20

0.2

SA T /T = 5

0.1

SA Ti/Ts = 10

i

s

SA T /T = 20 0

i

0

10

20

30 40 50 60 Number of CR OFDM symbols (N)

Fig. 4. Probability of detection versus N for different 26.6µs, M = 2, SN R = 2dB).

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s

70

Ti Ts

80

ratio (Ti =

5

with multiple antennas. The CR used SLC based energy detection to detect primary user signal. The SLC based energy detector provides high detection probabilities even at low to moderate SNRs. Increasing number of CR-OFDM symbols is also considered for decision statistics, leading to a increased performance, but at the expense of increased sensing time. The investigation also shows the impact of Ti /Ts ratio on the detection 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 personal,” IEEE Pers. Commun., vol 6, no. 4, pp. 13-18, Aug. 1999. [3] S. Haykins, “Cognitive radio: brain-empowered wireless communications,” 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/cognitive radio wireless network: a survey,” Computer Network, pp. 2127-2159, 2006. [5] F. F. Digham, M. S. Alouini, and M. K. Simon, “On the energy detection of unknown signals over fading channels,” Proc. IEEE Int. Conf. Communications. (ICC’03), 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 radio systems,” Proc. IEEE Int. Symp. on new frontiers in Dynamic Spectrum Access Networks (DySPAN’05), pp. 151-159, Nov. 2005. [8] T. A. Weiss, and F. K. Jondral, “Spectrum pooling: an innovative strategy for the enhancement of spectrum efficiency,” IEEE Commun. Mag., vol. 42, no. 3, pp. S8-S14, Mar. 2004. [9] C. H. Hwang, and S. C. Chen, “Spectrum Sensing in wideband OFDM cognitive 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 spacetime coded OFDM systems with frequency offset in frequency-selective Rayleigh fading channels,” The IEEE Inter. Conf. on Communications (ICC‘05), vol. 4, pp. 2593-2599, May. 2005.

A PPENDIX I Theorem 1 : Let u = [uTr uTi ]T be a 2N dimensional real Gaussian random variable with positive definite covariance matrix R. Then the characteristic function of y = uT u is given by [10] φ(ω) =

2N 

− 12

(1 − j2ωλi )

A PPENDIX II The received signal on q th subcarrier of CR-OFDM system can be written as (6) Rq (n)

=

K−1


Xl,k Hk ej2π(−lfi Ti +nfs Ts ) ejπβk,q (Q−1)

k=0

×

sin(πβk,q Q) + Wq (n) sin(πβk,q )

The received signal Rq (n) can be approximated by a Gaussian random sequence when the number of complex sinusoidal K is very large due to central limit theorem. The signal and noise components are assumed to be independent. Let us denote the event A that the nth and mth CR OFDM symbols both fall within the span of the lth PU symbol. Clearly, Rq (n) and Rq (m) are zero-mean Gaussian random variable. Conditioned on the event A, the correlation of Rq (n) and Rq (m) is [11] E{Rq (n)Rq∗ (m)/A}

K−1


=

× ej2π(n−m)Ts fs 2 + σw

(1 − j2ωξi )−1

sin2 (πβk,q Q) sin2 (πβk,q ) (25)

Assuming, E{|Xl,k |2 } = 1 and E{|Hk |2 } = 1, K−1


sin2 (πβk,q Q) 2 +σw sin2 (πβk,q ) k=0 (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} =

ej2π(n−m)Ts fs

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

 1 − |n−m| , |n − m| ≤ η − 1 η (27) P r{A} = 0 Otherwise Thus, the (n, m)th element of the covariance matrix of −1 {Rq (n)}N n=0 is given by P r{A}.E{Rq (n)Rq∗ (m)/A}

(21)

where, λi are the eigenvalues of R. When R takes the special form, (i.e) R = diag{Ru , Ru }, φ(ω) can be written as N 

E{|Hk |2 }E{|Xl,k |2 }

k=0

i=1

φ(ω) =

0 ≤ q ≤ Q − 1 (24)

(22)

i=1

where, Ru = E{ur uTr } = E{ui uTi }, ξi are the eigenvalues of Ru . The PDF of y is obtained by Fourier transform of φ(ω), that is  ∞ 1 py (y) = φ(ω)e−jωy dω (23) 2π −∞

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(28)