Multi-Antenna Spectrum Sensing for Cognitive Radio under Rayleigh Channel

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1 Multi-Antenna Spectrum Sensing for Cognitive Radio under Rayleigh Channel Alphan Salarvan, Güneş Karabulut Kurt Department of Electronics and Communications Engineering Istanbul Technical University Istanbul, Turkey {salarvan, Abstract This paper focuses on two different signal combining and detection methods for multi-antenna spectrum sensing in cognitive radio networks. These methods were previously introduced, and their performances are analyzed in the presence of additive white Gaussian noise (AWGN). Noting the severe fading conditions that may be encountered in cognitive radio networks, considering solely AWGN as channel impairment might not be realistic. Moreover the SNR gain obtained by receiver diversity using multiple antennas at the receiver may well be different than the single antenna case when Rayleigh fading is added to the channel model. Therefore, this paper evaluates the combining and detection methods in the presence of Rayleigh fading channel conditions and concludes that evaluating multi-antenna spectrum detection methods and algorithms with AWGN channels does not provide an accurate indication about their performances. As expected equal gain combining (EGC) method, which gives the best performance for the AWGN case, gives the worst performance with uncorrelated Rayleigh fading channels. Thus, we conclude that the performance comparison of the combining and detection algorithms may differ with different channel conditions. Keywords: multi-antenna, spectrum sensing, Rayleigh, cognitive radio I. INTRODUCTION Spectrum sensing is one of the most important tasks in cognitive radio as it vitally affects the whole performance of the system. Therefore, there are a significant number of studies focusing on efficient spectrum sensing [-4]. Efficiency in spectrum sensing may correspond to having low computational complexity in detection algorithms (such as blind estimation in case of unknown parameters) or reducing the sampling rate in order to make use of wideband spectrum (such as compressed sensing techniques). This paper focuses on the combining and detection methods of one of the works that employ compressed wideband spectrum sensing algorithm [5]. Since signal-to-noise ratio (SNR) is critical for spectrum detection, multiple antenna techniques are introduced in order to exploit receiver diversity and increase the SNR of the received signal. There are different signal combining methods such as EGC to benefit from the receiver diversity. These algorithms combine the received signals in order to boost the SNR of the signal to be processed by the detection algorithm. Most of these combining and detection algorithms are evaluated in with respect to SNR of the received signal in AWGN channel conditions [6-8]. The channel model used in the system becomes extremely important in the performance evaluation of detection algorithms since SNR of the signal depends on the channel characteristic [9]. It is obvious that the performance of single antenna detection algorithms under AWGN channel condition will be better than the performance under more complex or more realistic channel condition. However, in the case of multiple antennas, the performance comparison of the combining and detection algorithms may differ with different channel conditions. This paper evaluates one of the low complexity multiple antenna detection algorithms under a more realistic channel model. Authors in [5] propose an algorithm named Divided- Averaged (DA) algorithm to enhance the performance of the compressed sensing methods, with AWGN on the received signal. The theoretical probability of detection and false alarm are derived and numerical results are obtained for the performance of the algorithm. Moreover [5] uses EGC and square law combining (SLC) algorithms to combine the multiple antenna signals into one SNR boosted signal to perform the DA algorithm. As the AWGN channel model is not a realistic approach, we strongly believe that it might not reveal the true gain of using multiple antennas along with the combining and detection methods. In other words, SNR gain by adding multiple antennas may differ when fading is introduced into the system. Moreover, the performance comparison of different combining and detection algorithms may be different with a different channel model. Therefore in this work, in order to be able to simulate fading channel conditions, we added Rayleigh fading on top of the existing AWGN channel model. To the best of our knowledge, works in [, ] are the closest works in terms of system model and simulations. Authors in [] propose a new algorithm for spectrum sensing in OFDM based cognitive radio systems. Then the new algorithm is tested in a single input multiple output (SIMO) channel with both AWGN and Rayleigh fading models. Authors in [] also propose a new algorithm for spectrum sensing for cognitive radio systems and test their algorithms in /2/$3. 22 IEEE 78

2 the presence of Rayleigh channel model. However, both of these works do not focus on the hypothesis that with Rayleigh fading channels, the obtained gain by the spectrum sensing algorithms is better observed. In our work, we derived new probabilities for detection and false alarm and obtained new numerical results for the performance of different algorithms using Rayleigh channel model to compare the performance gains with sole AWGN channel model. The rest of this paper is organized as follows. Section II describes the system model of the spectrum sensing scheme. Section III summarizes the detection and combining algorithms, the detection and false alarm performances in both single antenna scenario and multiple antenna cases with different combining algorithms. Section IV reflects the changes in the system by the Rayleigh fading channel extension, and gives the theoretical derivations for single antenna and multiple antenna cases. Section V shows the simulation results and paper concludes with section VI. II. SYSTEM MODEL The system model of this work is illustrated in Fig.. The primary user transmitter sends a signal which has a predetermined spectrum usage ratio in the frequency domain. The signal goes through the SIMO channel which has different channel coefficients per receiver antenna. Transmitter s(k) h h N Thus, the received signal in any receiver antenna is composed of two components, one is the signal of the transmitter multiplied by the channel coefficient, and the other is noise which is AWGN y (k) = h s(k) + n, () where y i (k) is the signal received from antenna i, h i is the fading channel coefficient of the corresponding antenna and n i is the AWGN noise component. Authors in [5] does not include a fading model in their channel model, which would correspond to h i = for all i. We will be focusing our work on fading channels, i.e. small scale fading, as it is one of the defining characteristics of wireless channels [2]. The received signals are then fed into the combining and detection algorithm, which works as a pre-combining detector. First, the signals are combined to obtain one signal with an improved SNR. Then, the obtained signal is given to the detection algorithms. The details of the combining and detection process are explained in the algorithms section. III. y (k) y N(k) Figure. The overall system model. ALGORITHMS Combining & Detection Algorithm In this section the detection algorithm and multiple antenna combining methods used throughout this work is described and their performances are given in terms of probability of detection and false alarm. A. Divided-Averaged Algorithm The procedures of DA algorithm are illustrated in Fig. 2. At first, the received signal is transformed into its discrete Fourier transform by taking a fast Fourier transform (). After that, it is divided into non-overlapping sub-bands (with M points) and the average energy is calculated for every subband to be compared with a threshold to decide whether the sub-band is occupied or not. The threshold is the average energy of the wideband signal. y(k) y (k) y N(k) Y(k) Y (k) Y N(k) Sub-band Energy calculation Combining Algorithm Authors in [5] derive the probabilities of detection and false alarm of the DA algorithm for AWGN channel model as = F,2M( + γ), (2) = F (2M( + γ)), (3) where λ = 2Mγ/μ, and M denotes the number of points in one sub-band, γ denotes the SNR of the wideband signal, μ denotes the spectrum usage ratio of the spectrum signal. F, ( ) denotes the cumulative distributed function (CDF) of non-central chi-square distribution X,, F ( ) denotes the CDF of chi-square distribution X. B. Multiple Antenna Combining Methods The probabilities above of the DA algorithm were for single receiver antenna case. [5] proposes several combining methods to exploit multiple receiver antennas to achieve better performance for the DA algorithm. The combining of signals occur right after operation as illustrated in Fig. 3. ) Equal Gain Combining Algorithm: In the EGC algorithm the signals from multiple antennas are combined by addition after operation Y(k) Threshold Comparison Figure 2.The block diagram of the DA algorithm (single antenna case). Sub-band Energy Detection & Threshold Comparison Figure 3. The block diagram of the multiple antenna detector. Decision Y(k) = Y (k) / N. (4) where N R is the number of receiver antennas. Authors in [5] derive the detection and false alarm probabilities of DA-EGC method as, = F,2M( + N γ), (5), = F 2M( + N γ), (6) V i Decision /2/$3. 22 IEEE 78

3 where λ = 2MN γ/μ. 2) Square Law Combining Algorithm: In the SLC algorithm the signals from multiple antennas are combined by squared addition after operation. Y(k) = Y (k) / N (7) Authors in [5] derive the detection and false alarm probabilities of DA-SLC method as, = F,2MN ( + γ), (8), = F 2MN ( + γ), (9) where λ = 2MN γ/μ. EGC algorithm seems to achieve the best performance in the presence of AWGN channels among the algorithms proposed in [5]. IV. FADING CHANNEL EXTENSION We can derive the detection and false alarm probabilities of these algorithms under Rayleigh channel assumption using the fact that the probability of error in slow, flat fading channels can be obtained by averaging the error in AWGN channels over the fading probability density function [9]. In doing so, the probability of error in a slow, flat fading channel can be evaluated as = (X)p(X)dX, () where e (X) is the probability of error for an arbitrary modulation at a specific value of signal-to-noise ratio X, and p(x) is the probability density of X due to fading channel, and X = E /N where is the gain of the channel [9]. Under Rayleigh fading channel assumption, has a Rayleigh distribution, so and consequently X have a chisquare distribution with two degrees of freedom. Thus the distribution is p(x) = exp X, () where = α is the average value of the signal-to-noise ratio which depends on the mean power of the channel, α. For the Rayleigh case, the channel has unit mean power. A. Single Antenna Case The probability of detection of the DA algorithm for the Rayleigh channels can be derived by using = = ( F,(2M( + γ)) ) (γ)p(γ)dγ, (2) exp dγ, (3) which depends on value. The derivation for the d yields an integral which does not have a closed form: d = (-(MQ M 2M γ, - MQ M 2M γ,2m(+γ)))exp - dγ, (4) Where MQ M stands for the Marcum s Q function of the M th order. Integrals involving the Marcum s Q function are not trivial to evaluate. Hence we used numerical integration to evaluate the expression in Eq. 4. There s a similar case for the probability of false alarm which has a regularized incomplete gamma function = = = ( F (2M( + γ)) ) ( (Gamma(M( + γ), M)))) (γ)p(γ)dγ, (5) exp dγ, (6) exp γ dγ,(7) where Gamma stands for the regularized incomplete gamma function. B. Multiple Antenna Case For the multiple antenna case, following a derivation similar to explained above, the upper and lower bounds for the probability of detection and probability of false alarm of EGC method are found to be d,egc (-(MQ M 2MN γ, - MQ M 2MN γ,2m(+n γ)))exp - dγ, (8), ( (Gamma(M( + N γ), M))) exp γ dγ.(9) These upper and lower bounds for the EGC algorithm corresponds to the case of identical instantaneous SNR at the receiver antennas. As the correlation between channel coefficients of different antennas decrease, EGC method tends to decrease its detection performance. Similarly, the lower and upper bounds for probability of detection and probability of false alarm of SLC method are found to be d,slc (-(MQ M 2MN γ, - MQ M 2MN γ,2mn (+γ)))exp - dγ, (2), ( (Gamma(M( + N γ), M))) exp γ dγ.(2) We obtain a different case in SLC. Again the upper and lower bounds for the SLC algorithm corresponds to the case of identical instantaneous SNR at the receiver antennas. However for SLC method, as the correlation between channel coefficients of different antennas decrease, the detection performance increases. Since integrals in (8) to (2) are not trivial to evaluate, we used numerical integration to evaluate their expressions. The /2/$3. 22 IEEE 782

4 results of the numerical evaluation can be observed in Figs. 4, 5, 6 and 7. Note that for the case of single receiver antenna, since identical instantaneous SNR at the receiver antennas condition is satisfied, the upper and lower bounds in (8), (2) and (9), (2) converge to the equations in (4) and (7) respectively. V. SIMULATION RESULTS To compare and verify simulation and theoretical results with [5], some of their simulation parameters were used, which would include setting M as 82, spectrum occupancy ratio µ as % (.) and size is selected as To create the relevant spectrum usage data; the transmitted signal, SIMO Rayleigh channel exposure, the system in [3] was reused to fit the simulation parameters such as size of the simulation. The work in [3] is an MIMO OFDM downlink simulation environment which is developed in order to conform to the Long Term Evolution (LTE) physical and link-layer standardizations [4, 5]. The number of receiver antennas for the multiple antenna simulations was selected as 4. As expected, the single antenna case simulation results for the detection (see Fig. 4) and false alarm (see Fig. 5) probabilities fit well with the theoretical curves. For the multiple antenna case, the simulation results with uncorrelated Rayleigh channel coefficients verify that EGC performance decreases with decreasing correlation of the channel coefficients as the uncorrelated channel detection and false alarm probabilities coincide with single antenna performance (see Figs. 4 and 5).However for the SLC method, it is verified that the detection performance increases with decreasing correlation of the channel coefficients (see Figs. 6 and 7). The comparison of AWGN and Rayleigh channel conditions for 4 receiver antennas is illustrated in Figs. 8 and 9. We can observe that EGC has better performance in the case of AWGN channel, however SLC outperforms EGC in the case of Finally, the comparison of the SNR gain of adding multiple antennas to a receiver in case of AWGN and Rayleigh channel conditions can be observed in Figs. 6 and 7. Here we take SLC performance for comparison since it has the best performance. For d =.95, using 4 antennas at the receiver instead of a single antenna provides an SNR gain of 3.5 db for AWGN channel and 7.5 db for the Rayleigh channel. For fa =.5, using 4 antennas at the receiver instead of a single antenna provides an SNR gain of 3 db for AWGN channel and 9 db for the Therefore, we can conclude that the obtained gain by using multiple antennas at the receiver is better observed when a fading model such as Rayleigh is used in the channel model. Since Rayleigh fading channel model corresponds to multipath fading and does not include line of sight component, the detection performance observed in this work is close to the worst case performance for wireless channels. For the case of partial line of sight, the performance is expected to be between what is illustrated here with uncorrelated Rayleigh channels and the corresponding lower and upper bounds AWGN EGC Theory (N R Rayleigh EGC Upper Bnd (N R Rayleigh EGC Simulation (N R Figure 4. Comparison of probability of detection for single antenna DA algorithm and for multiple antenna case (N R with EGC method under robabilty of False Alarm AWGN EGC Theory (N R Rayleigh EGC Low er Bnd (N R Rayleigh EGC Simulation (N R Figure 5. Comparison of probability of false alarm for single antenna DA algorithm and for multiple antenna case (N R with EGC method under AWGN SLC Theory (N R Rayleigh SLC Low er Bnd (N R Rayleigh SLC Simulation (N R Figure 6. Comparison of probability of detection for single antenna DA algorithm and for multiple antenna case (N R with SLC method under /2/$3. 22 IEEE 783

5 robability of False Alarm Figure 7. Comparison of probability of false alarm for single antenna DA algorithm and for multiple antenna case (N R with SLC method under AWGN SLC Theory (N R Rayleigh SLC Upper Bnd (N R Rayleigh SLC Simulation (N R Rayleigh SLC Simulation Figure 8. Comparison of probability of detection for DA algorithm with EGC and SLC method under AWGN and Rayleigh channel (N R. robabilty of False Alarm AWGN EGC Theory AWGN SLC Theory Rayleigh EGC Simulation AWGN EGC Theory AWGN SLC Theory Rayleigh EGC Simulation Rayleigh SLC Simulation Figure 9. Comparison of probability of false alarm for DA algorithm with EGC and SLC method under AWGN and Rayleigh channel (N R. VI. CONCLUSIONS In this work two multiple-antenna spectrum detection methods were re-evaluated with Rayleigh channel conditions as it was evaluated considering solely the AWGN channel before. The argument that the performance comparison of the combining and detection algorithms may differ with different channel conditions is verified as EGC (which outperformed SLC in AWGN channel) was outperformed by SLC in Rayleigh fading channel. EGC algorithm does not yield increase in performance for Rayleigh channels with uncorrelated channel coefficients. Also we can verify that the detection performance for Rayleigh channels is worse than it is for AWGN channels. Moreover, for Rayleigh channels, using multiple antennas may or may not increase the sensing performance, as it is dependent on the selected combining algorithm. Finally, we can conclude that the obtained gain in spectrum detection methods by using multiple antennas at the receiver is better observed when a fading model such as Rayleigh is used in the channel model. REFERENCES [] Yucek, T.; Arslan, H.; "A survey of spectrum sensing algorithms for cognitive radio applications," Communications Surveys & Tutorials, IEEE, vol., no., pp.6-3, First Quarter 29 [2] Won-Yeol Lee; Akyildiz, I.F.; "Optimal spectrum sensing framework for cognitive radio networks," IEEE Transactions on Wireless Communications, vol.7, no., pp , October 28 [3] Chu-Hsiang Huang; Kwang-Cheng Chen; "Dual-Observation Time- Division Spectrum Sensing for Cognitive Radios," IEEE Transactions on Vehicular Technology, vol.6, no.8, pp , Oct. 2 [4] Zhi Quan; Shuguang Cui; Sayed, A.H.; oor, H.V.; "Optimal Multiband Joint Detection for Spectrum Sensing in Cognitive Radio Networks," IEEE Transactions on Signal rocessing, vol.57, no.3, pp.28-4, March 29 [5] Xianjun Yang, Qimei Cui, Rui Yang, Xiaofeng Taoa and Xin Guo; Multi-antenna compressed wideband spectrum sensing for cognitive radio IEEE Wireless Communications and Networking Conference (WCNC), 2 [6] Axell, E.; Larsson, E.G.; "Optimal and Sub-Optimal Spectrum Sensing of OFDM Signals in Known and Unknown Noise Variance", IEEE Journal on Selected Areas in Communications, vol.29, no.2, pp.29-34, February 2 [7] Alghamdi, O.A.; Ahmed, M.Z.; Abu-Rgheff, M.A.;, "robabilities of detection and false alarm in multitaper based spectrum sensing for cognitive radio systems in AWGN," 2 IEEE International Conference on Communication Systems (ICCS), 7-9 Nov. 2 [8] Hwang, S.-H.; Baek, J.-H.; Dobre, O.A.; "Spectrum sensing using multiple antenna-aided energy detectors for cognitive radio,". Canadian Conference on Electrical and Computer Engineering, 29. CCECE '9, 3-6 May 29 [9] Theodore S. Rappaport, Wireless Communications: rinciples & ractice, rentice Hall, 22. [] Alghamdi, O.A.; Abu-Rgheff, M.A.; "Local MTM-SVD based spectrum sensing in SIMO OFDM cognitive radio under bandwidth constraint," 2 roceedings of the Fifth International Conference on Cognitive Radio Oriented Wireless Networks & Communications (CROWNCOM). [] Tao Lin; Qun an; Xin Zhang; Dacheng Yang; "Novel multi-antenna spetrum sensing under Rayleigh fading in cognitive radio networks," 29 IEEE 2th International Symposium on ersonal, Indoor and Mobile Radio Communications, 3-6 Sept. 29 [2] David Tse, ramod Viswanath, Fundamentals of Wireless Communication, Cambridge, 25. [3] Alphan Salarvan, Future Cellular Systems: Long Term Evolution, MS Thesis, Ecole olitechnique Federale de Lausanne, 29. [4] 3G Std. TS 36.2 Release 8. Evolved universal terrestrial radio access (e-utra) physical channels and modulation. [5] 3G Std. TS Release 8. Evolved universal terrestrial radio access (e-utra) multiplexing and channel coding /2/$3. 22 IEEE 784