Effect of Time Bandwidth Product on Cooperative Communication

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1 Surendra Kumar Singh & Rekha Gupta Department of Electronics and communication Engineering, MITS Gwalior surendra886@gmail.com, rekha652003@yahoo.com Abstract Cognitive radios are proposed to be the technique that will ameliorate the problem of spectrum deficiency by using the underutilized radio frequency spectrum opportunistically on non-interfering basis. In this paper, we have analyzed the effect of time bandwidth product in spectrum sensing in AWGN (non fading) and Rayleigh fading environment under cooperative environment. For decision statics hard combining rule (k out of n) is considered. Simulation results are also given to confirm the analytical results. Keywords Cognitive radio, energy detection, spectrum sensing, time bandwidth product, cooperative communication, hard combining I. INTRODUCTION In recent years, due to high demand of wireless systems, the problem of spectrum utilization increases. Cognitive radio (CR) provides the solution to handle this situation to a large extant. Any secondary user (unlicensed user) may be allowed to use spectrum band in such away, it does not cause any interference to primary user (Licensed user ).In CR network this interference is defined by a limit called interference temperature[1]. The initial phase of cognitive Radio is defined as spectrum sensing which means detecting the presence and absence of transmitted signal ( or Primary user)[1], [3]. The existing spectrum sensing technique can be categorized as Energy Detection, Matched filter detection, Eigen value detection and cyclosationary detection[2]. Among all these, energy detection has been widely used as it does not require any prior knowledge of primary signals and has much lower complexity. Spectrum sensing is although a complex task as it includes the effect of shadowing, fading and time varying nature of wireless channels. In real propagating environment of wireless communication, the signal received by mobile may consist of a large no. of multipath component due to scattering, diffraction and reflection between transmitter and receiver. Each path has randomly distributed amplitude and phase which combined at receiver and gives resultant signal. The strength of this received signal may vary as the channel is varying in nature. When there is no LOS component between mobile and base station, the received signal will follow a Rayleigh distribution and if LOS component exist, distribution will be Rician. Rayleigh fading models are generally used in simulation for high frequency signals propagating in ionosphere. To mitigate the adverse effect of this fading, cooperative sensing [5], [6] is proposed which utilizes spatial diversity in multiuser CR networks. In cooperative sensing all CR user sense the PU individually a transmit the sensed information to fusion center, which combine all these results and give a final result to all CR, regarding the presence or absence of primary signal. The rest of this paper is organized as follows. Section II describes the energy detection model. Section III describes the probability of detection and false alarm probability in AWGN and Rayleigh fading environment. Section IV describes the effect of cooperative communication. Section V describes simulation result followed by concluding remarks. II. SYSTEM MODEL Energy detection as it doesn t require the knowledge of type of signal, so it is appropriate to consider the signal a sample function. Fig. 1: Energy Detection The detection of primary signal include two hypothesis as (1) 53

2 where is received signal by secondary user, is transmitted signal by Primary User, is the additive white Gaussian noise(awgn) with mean zero and variance and h is the amplitude gain of channel. For a particular time interval the T decision statistic Y (at the output of integrator) can written as [3] (2) It is well known by sampling theorem that a sample function of duration T, of a process which has a bandwidth W is described approximately by a set of sample values 2TW in number. Assume TW = m, where T and W is chosen in such way that m is an integer. Here the case for low pass process will be considered in which each sample is is apart. Energy in the noise sample signal of duration T may be represented as (approximation applied) [3] (7) Where is SNR and i is the mean of received signal. Now energy of transmitted signal may be written as (8) Now consider the case for hypothesis H1 (both noise and signal are present), the energy of x(t) in time interval T may be given as (9) Now detection hypothesis for H1 may be written as (3) Where n i is the amplitude noise sample. Now normalize this noise sample as (10) Thus Y is the sum of square of 2m random variable with mean i and unit variance. Therefore Y follows a noncentral chi square distribution with 2m degree of freedom and non-centrality parameter p[3]. Where So decision statics corresponding to hypothesis H0 will be (4) Thus Y is the sum of square of 2m Gaussian random variables, each with zero mean and unit variance. Therefore Y follows a central chi square distribution with 2m degree of freedom. Similarly consider the case when signal s(t) is present in received signal. Now energy of transmitted signal for a time interval T (apply approximation) may be given as [3] (5) Where i is the amplitude of transmitted signal. Now normalize this sample value by noise variance as (6) Where E s is the received sample. And i may be written as (11) III. DETECTION AND FALSE ALARM PROBABILITIES A. Non fading environment (AWGN channel) In non fading environment probability of detection, probability of false alarm and probability of missed detection may be formulated as [4] (12) (13) (14) Where Q m (.,.) is the generalized Macrum Q function. To calculate the probability of detection as given in equation (12), first set the value of false alarm probability P f to a specific value. Then from equation (13), detection threshold may be calculated. Put this value in the equation (12) for the fix value of m to calculate P d. 54

3 B. Rayleigh fading channel When the received signal consist of a large number of multipath component (there is no LOS), signal will follow a Rayleigh distribution. In case of Rayleigh fading, detection probability will be the function of instantaneous SNR. So average value of detection for Rayleigh fading in closed form may be written as [4] alarm for cooperative scheme in this case may be written as follows, (16) (17) Where P d and P f are the individual CR probabilities of detection and false alarm. AND Rule: In this rule, if all of the local decisions sent to fusion centre are one, the final decision made by fusion centre will be one. Probabilities of detection and false alarm for cooperative scheme in this case may be written as follows, (18) (15) IV. COOPERATIVE COMMUNICATION In co-operative spectrum sensing, all the local sensing decisions are forwarded to fusion center, where all these individual data are combined according to the defined rule [5], [6]. In general, the sensing results forwarded to fusion center or shared with neighboring CR may be combined in three different way. (i) Soft Combining: All CR users transmit the total spectrum sensing data to fusion center. This technique requires large bandwidth and higher data overhead. (ii) Quantized Soft Combining: All CR users only transmit total spectrum sensing the in quantized form, which reduces the data overhead a little. (iii) Hard Combining: All CR users perform their individual spectrum sensing and transmit only one bit (Hard decision) as an individual decision to fusion centre. This technique reduces data overhead to a great extent. Here we only discuss hard combing rule. Consider the case for N CR users which perform their individual sensing and forward the binary decision (1or 0) to fusion centre regarding PU is present or not. The distance between all CR users are considered negligible as compare to distance between PU and CR Users. So all the CR users receives the signal of same power. For simplicity fading scenario between PU and all CR users are considered as same. As for hard combining assume k out of n rule. This rule may be quantified in three conditions: OR Rule: In this rule, if any of the local decisions sent to fusion centre is one, the final decision made by fusion centre will be one. Probabilities of detection and false (19) Majority Rule: In this rule, if half or more than half local decisions sent to fusion centre are one, then combined decision made by FC (Fusion Centre) will be one. V. SIMULATION RESULT AND DISCUSSION (20) (21) All simulation was done on MATLAB version R2009a over non-fading and Rayleigh fading channel. For simulation BPSK signal is assumed as an Input signal. All the probabilities are taken as an average for total no of samples. The Fig. 2 shows ROC curves for AWGN channel for different value m of (Time bandwidth Product), which shows as the value of m increases, detection probability decreases. The reason for this may be given as for the large value of m, incoherency of noise increases which dilute the signal energy [3] and another reason is clear by simulation as mean of the signal is taken as. So as the value of m increase SNR decreases. Hence to achieve the original detection probability, SNR have to increase which is explained in Fig. 3. Fig. 4 compares the ROC curves for AWGN (non fading) and Rayleigh fading at different value of m. From this figure it is clear that as the value of m increases the probability of missing increases more for AWGN channel compare to Rayleigh channel. Thus in fading environment, increasing m is less effective as shown in Fig

4 Now consider cooperative communication for hard combining. Fig. 6 shows the ROC curve for all three Rules OR, AND and Majority. Now by comparing these, it is clear that OR rule gives higher value of probability of detection for the same value of m. Fig. 7 compare the ROC curves for the AND rule at different values of m. From this it is clear that at AND rule there is slightly degradation in probability of detection as m increases. Fig. 8 and Fig. 9 compare the ROC curves for OR rule and Majority rule at different values of m which shows as the value of m increases, probability of missing increases largely as compare to AND rule. From this comparison it is clear that out of all these three rule OR rule gives better probability of detection but only for some specific value m and this advantage of higher value of P d will be diminish as m Increases. So it keeps a limit on the value of m. Fig. 10 shows that as the value of SNR increases probability of detection also increases. If we count the effect of cooperative communication, there is large improvement in the value of P d for the low value of SNR. From Fig. 11 it is clear that as the number of CR users increases, probability of detection also increases. VI. CONCLUDING REMARKS In this paper we have compared the performances of CR users in cooperative environment using hard combining technique. Among all these rules (AND, OR and Majority) OR provides better probability of detection for the same value of time bandwidth product. But as we increase the value of time bandwidth product this improvement goes on detract. So there is a maximum limit of considering the value of time bandwidth product. It is also clear as the number of cooperative user increases, detection probability improves. Fig. 3: Required Signal Energy in AWGN (curve between m and required SNR (non-db) Fig. 4: Complimentary ROC curves for AWGN and Rayleigh for m =5, 10 at SNR=10 db Fig. 2: Complimentary ROC curves for AWGN for m=5, 10, 15 at SNR=10 db Fig. 5 : Complimentary ROC curves for Rayleigh fading for m =5, 10, 15 at SNR=10 db 56

5 Fig. 6: Complimentary ROC curves for Rayleigh fading for OR, AND and Majority for m =5 at SNR=10 Db Fig. 9 : Complimentary ROC curves for Majority rule for m =5, 10, 15 at SNR =10 db Fig. 7 : Complimentary ROC curves for AND rule for m =5, 10, 15 at SNR =10 db Fig. 10: Curve between SNR and P d at m=5 and P d =.1 Fig. 8 : Complimentary ROC curves for AND rule for m=5, 10, 15 at SNR =10 db Fig. 11 : Curve between number of secondary user and Probability of detection (P d ) at SNR =10 db (assume m=5). 57

6 VII. REFRENCES [1] S. Haykin, Cognitive radio: brain-empowered wireless communications, IEEE J. Select. Areas Commun, vol. 23, pp ,Feb [2] T. Y ucek and H. Arslan, A Survey of Spectrum Sensing Algorithms for Cognitive Radio Applications, IEEE COMMUNICATIONS SURVEYS TUTORIALS, VOL. 11, NO. 1,pp , FIRST QUARTER [3] H.Urkowitz, Energy detection of unknown deterministic signals." Proc.IEEE, vol.55, pp , apr [4] F.F.Digham, M.alouini and M.K.Simon, On the Energy Detection of Unknown Signals over Fading Channels, IEEE International Conference on Communications (ICC 03), vol. 5, pp , May [5] A Ghasemi and E. S. Sousa, Opportunistic spectrum access in fading channels through collaborative sensing, IEEE Journal on selected Areas in Communications, vol. 2, no. 2, pp , March, [6] A.Ghasemi and E. S. Sousa, Collaborative spectrum sensing for opportunistic access in fading environments, in Proc. of 1st IEEE Symp.New Frontiers in Dynamic Spectrum Access Networks, Baltimore, USA, Nov. 8-11, 2005, pp [7] N. Armi, N.M. Saad & M. Arshad, Hard Decision Fusion based Cooperative Spectrum Sensing in Cognitive Radio System, ITB J. ICT Vol. 3, No. 2, pp , [8] J.G.prokis, Digital communication. McGraw- Hill, fourth ed,