Performance Comparison of Cooperative and Distributed Spectrum Sensing in Cognitive Radio

1 Performance Comparison of Cooperative and Distributed Spectrum Sensing in Cognitive Radio Zheng SUN, Wenjun XU, Zhiqiang HE and Kai NIU School of Informati on Engineering, Beijing Universi ty of Posts and Telecom municat ions, Beijing, Chi na zhengs.bupt@gmail .com Abstract —In this paper, we compare the performances of cooperative and dis tributed sp ectrum sensing in wireless sensor networks. Afte r introducing the basic proble m, we de scribe tw o strategies: 1) a cooperative sensing strategy, w hich takes advantage of cooperation diversity gain to increase p robability of detection and 2) a distributed sensing strategy, which by passing the results in an inter-node man ner increases energy efficien cy and fairness among no des. Then, we compare the performances of the strategies in terms of three cri teria: agility, en ergy efficiency, and robustness against SNR changes, and summarize the comparison. It shows that: 1) the non-cooperative strategy has the best fairness of energy con sumption, 2) the cooperative strategy leads to the best agility, and 3) th e distributed strategy leads to the lowest energy consumption and the best robustness against SNR changes. Index Terms — cooperative sensing, distributed sensing, cognitive radio networks. I. I NTRODUCTION Recently the field of cognitive radio (CR ) has drawn great interest, since this novel technology provides prom ising solution to enhance the spectrum efficiency of today’s wireless network. Studies have shown that spectrum is extremely underutilized [1] . One way to increase the utilization is to design CR networks, where wireless equipm ents use sm art radio to detect tem poral and sp atial “holes” in the spectrum, thus learn from t he environment and perform further functions to serve the users. A significant feature of CR networks is to allow users to operate in licensed bands without a license. However, since CR has to limit its interference to the primary network , CR users using a licensed band must vacate the band due to the presence of the primary user. Thus it is significant to detect the presence of licensed (prim ary) users by spectrum sensing in a very short time. Recent work considers how to take advantage of the local oscillator leakage power emitted from RF receivers to allow cognitive radios to sense and lo cate the primary users [2] . Some physical lay er issues of spect rum sensing are discussed i n [3] . For radio sensitivity of the se nsing function through processing gain, the authors of [4] study three digit al signal processing techniques. In this paper, we are going to discuss how to deal with spectrum sensing i n wireless sensor networks (WSN). Related work includes [2] , which gives a physi cal layer and MAC lay er solution of sensor nodes but lacks further designing on net work architecture. Rather, we will discuss two strategies for efficient spectrum sensing in WSN. The first is cooperati ve sensing. Cooperative techniques are wi dely studied recently ( [5] - [8] ) to achieve a new form of spati al diversity vi a the cooperation of users [5] . In [6] , the authors study two-user cooperative spectrum sensing in cogn itive radio and sho w that, by allowing the cognitive users operating in the same band to cooperate, the detection time reduces and thus the overall agility in creases. In [7] , light-weight cooperation in sensing based on hard decision is proposed to mitigate the sensitivity requirem ents on individual radi os. And in [8] , the cooperative situations are considered by using gam e theory, and the authors show how the lack of cooperation affects t he performance. In this paper, the cooperative sensing is describe d in a multi-node WSN network, in which multi-user diversity gain is further achieved . The second strategy being discussed i s distributed spectrum sensing, which is speciali zed from distri buted learning and estimation theory [10] . To our best knowledge, dist ributed spectrum sensi ng is a rather fresh topic. The reason of adopt ing distributed spectrum sensing in WSN is twofold. Firstl y, traditional cooperati on in WSN needs node fusion center transmissi ons with length of → ( ) 1 O , while distribut ed sensing strategy adopts int er-node transmissi ons with lengt h of only ( ) 2 log n n O [9] , which therefore reduces energy costs and increases overall network longevity. Secondly , in this paper we show that by using distribut ed sensing strategy, the probability of detectio n at the fusion cen ter is greatly increased comparing wit h both non-coopera tive and cooperati ve sensing strategy. The main purpose of this paper i s to present strategies of cooperative and distributed spect rum sensing in WSN, and to compare their performances in terms of agility, energy efficiency, and robust ness against SNR changes. The results drawn here may act as a refe rence for further researches. The rest of the paper is organized as follows. In Section II, we describe the basic problem and a non-cooperative spectrum sensing strategy as a baseline. In Section III, a cooperative strategy utilizing inter-node info rmation is discussed. And in Section IV we use distributed est imati on theory to develop a distributed spect rum sensing strategy. Then in Sect ion V, we discuss and compare the performan ces of the three strategies. And Section VI gives a sum mary and concludes t he work. This research is sponsored by Project 60772108 supported by National N atural Science Foundation of China and National Basic Research Program of China (973 Program ), 2007CB310604 2 II. N ON -C OOPERATIVE S PECTRUM S ENSING In this section, we describe the basic spectrum sensing problem in WSN and a spectrum sensing strategy wit hout utilizing cooperation among sensor nodes. This strategy will be used as a baseline of the other two strategies throughout the paper. A. Basic Detection Problem Let us consider a W SN with nodes operating in a TDMA mode. Assum e that t he nodes are uniformly distributed over a square with side of unit length as illustrated in Figure 1. Each node measures and therefore senses the presence of the primary user independ ently, and then transmits its detection results to the fusion center. The signal received by every sensor node is given by N ip i yP h w i θ =⋅ ⋅ + , (1) where P is the transmit power of the pr imary user, denotes the instantaneous channel gain between the prim ary user and the i th node, and denotes the additive Gaussian no ise. We assume that and are independent zero-mean com plex Gaussian random variabl es with variances pi h i w pi h i w 2 h σ and 2 w σ , respectively. Also, θ is the primary user indicator, i.e. 1 θ = implies the presence of the prim ary user and 0 θ = implies the absence. Given that the p rimary user transmit with unit power, i.e. 1 P = , 2 h σ also represents the received signal power at node i from the prim ary user. When th e signal is received, sensor nodes will do following detection: Given the observation in (1) , the detector decides on 1 :1 H θ = or 0 :0 H θ = . B. Non-cooperative Spectrum Sensing Strat egy Now we describe the baseline non-cooperati ve strategy. In this strate gy, every node conducts an energy det ection based on the statistics 2 () ii Ty y = [6] . Let ( ) 0 F t and ( ) 1 F t denote the cumulati ve density function of t he random variable Ty under hypothesis () i 0 H and 1 H . Since and are both independent complex Gaussian, Ty is exponential di stributed wit h variance of pi h i w () i 22 2 hw θ σσ + . Therefore () () () () 2 2 00 /2 () | w i t i F tP T y t H P w t e σ − => = = > , (2) and () () () () () 22 2 11 /2 () | hw ip i t i F tP T y t H P h w t e σσ −+ => = + = > . (3) Suppose the predefined maxi m um false alarm probability is α , then from (2) , the correspondi ng detection threshold λ is given by () 2 2l o g w λ σα =− . (4) And the probability of detection of every sensor node is () ( ) () 22 2 11 1 wh w SNR F σσ σ λα α + + == , (5) Fig. 1. Spectrum sensing str ategi es discussed in this paper. where is defined as the ratio of the received useful signal power to noise power. At the fusion cent er, a majorit y vote is conducted to decide the presence of t he primary user. For sensors, the pro bability of detection at the fusion center is SNR N () () () /2 11 0 11 N Nk k fc k N pF F k λλ − = ⎛⎞ =− − ⎜⎟ ⎝⎠ ∑ . (6) III. C OOPERATIVE S PECTRUM S ENSING The baseline non-cooperative stra tegy given above has two main disadvantages: 1) Sensor nodes are required to transmit their detection results to the fusion center in every tim e slot. However, this is unnecessary, since the nodes who fail to detect actually need not to transmit thei r results. 2) The strategy fails to take advantage of cooperativ e diversity gain among sensor nodes, which would further increas e the detection probability at the fusion center. Taking account of these aspects, we present the following cooperative strategy. Suppose every two nodes in the sensor network are grouped to form a one-hop relay pair. In the first tim e slot (T1) of every two consecutive slots, every sensor node ma kes the sam e energy detection as in the non-c ooperative strategy. If the first node (Node1) in every relay pair fails to detect the prim ary node, it would amplify and forward (AF) the signal it receives in T1 to the second node (Node2) in its own relay pair in the second time slot (T2). And in T2, Node2 would m ake the same energy detection as in non-coope rative strategy but with the difference that the signal being observed is the one it received from the prim ary user plus the one received from Node1. Thus, from [6] , the signal received by Node2 in T2 is () () 22 2 1 1 2 1 22 1 1 2 1 1 21 1 2 1 21 1 2 p pp pp yh w h y hw h h w hh h w h θβ θβ θ βθ β =+ + =+ + + =+ + + 1 w , (7) where ( ) 22 1 1 h P βθ σ +   is the scaling factor of Node1 in AF, is the instantaneous channel gain between Node1 and Node2 within a relay pair, and is the signal received by Node1 in T1. The probability of det ection by Node2 is given by 12 h 1 y [6] 3 {} () ( ) ( ) ( 2 22 2 12 ;1 , 1 1 ch h h pP E h ϕλ σ σ θ σ =+ + +  ) 2 , (8) where () () t 0 ;, ha b h ta b e d h ϕ ∞ −− + = ∫ , P  is th e ma xi mum r el ay power constrain, { } 2 12 Eh is the channel gain between the two sensor nodes in a relay pair and λ is given by solving equation {} ( ) 2 12 ;1 , PE h ϕ λα =  . At the fusion center, majority votes are conducted in both T1 and T2. So the probabilities of detection in T1 and T2 are () () () /2 _1 1 1 0 11 N Nk k fc T k N pF F k λλ − = ⎛⎞ =− − ⎜⎟ ⎝⎠ ∑ , (9) and () () ' ' /2 ' _2 _ 1 0 11 1 N Nk k fc T fc T c c k N pp p p k − = ⎛⎞ ⎛⎞ =− ⋅− − ⎜⎟ ⎜⎟ ⎜⎟ ⎝⎠ ⎝ ⎠ ∑ ) N , (10) where is the number of nodes who fail to detect in T1. In all, the probab ility of detection at the fusion center in both two consecutive time slots is () ( ' 1 c NF λ =− _1 _ 2 f cf c T f c T pp p =+ . (11) IV. P RIMARY U SER D ETECTION U SING D ISTRIBUTED S TRATEGY The strategy proposed above involves cooperation in spectrum sensing am ong nodes, and accordingly increases the probability of detection. Howeve r, the drawback of it also exists. Since both Node1 and Node2 in every relay pair have to transmit their detection results over a node fusion center distance of → ( ) 1 O , the energy efficiency is not optimal. To this end, we consider a distributed spectrum sensing strategy in sensor network, which reduces the average distance to only ( 2 log On ) n [9] . Notice that estim ating the presence of the primary user is like the problem of estimating a series of variables in a sensor network, which can be solved by distributed learning a nd estimation theory [9][10] . To be specific, build a path through the network which passes through all nodes and visits each node just once. The sequence of nodes can be constructed so that the path hops from neighbor to neighbor. The global detection re sult can be computed by a single detection process from start node to end node, with each node contributing its own local detection result to the total along the way. Suppose every sensor node receives its own local signal from the primary user as in (1) . Let {} () ( 2 2 1... 1 1 ,, N ii i i iN i fy T y T N ) θ θ ∈ = − ∑  , (12) where is the detection thres hold. A maximum likelihood estimate for the presence of the primary user is found by solving i T {} ( 1... ˆ arg m in , , ii iN fy T θ where ˆ θ is the estimation of θ at the fusion center after iterative computation among nodes. This non-linear least square problem fits well into the gene ral increm ental subgradient framework [11] . Taking () ( ) 2 2 ii i fy T θ θ =− , (14) the gradient of ( ) i f θ is () ( ) 2 2 ii i i f yT T θ θ ∇= − . (15) The theory of increm ental subgradient methods shows that given ( ) i f θ ∇ is bounded, ˆ θ converges to θ . We assume every sensor node uses the same detection threshold , i TT i = ∀ , thus the gradient is bounded by observing that () 2 2 ii ) θ θ ∈ = , (13) f Ty T c θθ ∇ ≤− < , (16) where comes from the assum ption on limitation of sensor detection range: c 2 2 i c yT T θ −< , i ∀ . (17) Now we calculate the probability of detection of this strategy. With , i TT i = ∀ , let { } ( ) 1... ,, / ii iN fy T θθ ∈ 0 ∂ ∂= , we get 2 1 ˆ N i i yN T θ = = ∑ . (18) Since is a complex Gaussian, i w 2 i w and 2 1 N i i w = ∑ are chi-square distributed variables with 2 and degrees of freedom, respectively. Therefore the false alarm probability at the fusion center is given by 2 N () 1 2 2 2 0 2 10 1 ˆ | !2 NTt k NN w i ik w NTt Pt H P w N T t e k σ θ σ − − == ⎛⎞ ⎛⎞ >= > = ⎜ ⎜⎟ ⎝⎠ ⎝⎠ ∑∑ ⎟ .(19) With a predefined false alarm probability α , the product in Tt (19) is uniquely determined by solving ( ) 0 ˆ | Pt H θ α >= since (19) is strictly decreasing in . Denote as t Tt ( ) ' P α , the probability of detection at the fusion center is () () () () () () () 1 22 2 1 22 0 ' ' 1 22 2 22 0 1 ˆ | ! 2 1 ! 2 NTt k N hw d k hw NP k N hw k hw NTt pP t H e k NP e k σσ α σσ θ σσ α σσ − − + = ⋅ − − + = ⎛⎞ => = ⎜⎟ ⎜⎟ + ⎝⎠ ⎛⎞ ⋅ = ⎜⎟ ⎜⎟ + ⎝⎠ ∑ ∑ .(20) V. P ERFORMANCE A NALYSIS AND D ISCUSSION In this section, to compare the non-cooperative, cooperative, and distributed spectru m sensing strategies, three criteria are considered: ¾ Agility ¾ Energy efficiency ¾ Robustness against SNR change 4 1) Agility When cognitive users are using the licensed band, they must be able to detect the presence of primary users in a very short time and vacate the band for the prim ary users as soon as possible. This calls a great agility of detection of the primary users. In this paper, the agility is m easured as the number of slots taken by the fusion center to detect the prima ry user. Firstly, let us consider the baseline non-cooperative strategy. Let τ denote the num ber of slots taken by the fusion center to detect the presence of the prim ary user, so τ can be modeled by geometric random distribution as {} () 1 Pr 1 k f cf kp τ − == − c p , (21) where f c p is the probability of detec tion by the fusion center from (6) . Let T be the detection time by the non-cooperative strategy, then nc {} () 1 1 1 k nc fc fc k TE k p p τ +∞ − = == − ∑ . (22) Secondly, in the cooperative strategy, the average detection can be calculated by (22) similarly. But since every detection at the fusion center under the coopera tive strategy takes one or two time slots, the result should be m ultiplied by 1 or 2, i.e., {} () () 1 _1 _1 1 1 _2 _2 1 1 21 k cf c T f c k k T f cT f cT k TE k p p kp p τ +∞ − = +∞ − = == − +⋅ − ∑ ∑ , (23) where _1 f cT p and _2 f cT p are given by (9) and (10) . Notice that in this strategy, agility is co m pensated to involve cooperation among nodes. That is, if the detection at the fusion center in T1 fails, the information of this failed detection would be acquired by the fusion center and be utilized to enhance the detection in T2 by allowing to amplify-and- forward the signal within every relay pair. Finally, let us consider th e distributed strategy. In [12] the authors propose the in-cluster di stributed estimation for sensor networks, which greatly reduces latency by a factor of cluster number . Specifically, suppose the whole network is divided into clusters, and each cluster has c N c N / s c NN N  sensors. The detections and transmissions in different clusters are conducted simultaneously. In a single iterati on, the detection results are transmitted over 1 s N − inter-node hops, and the last cluster head transmits the results to the fusion center. Therefore a single iteration of the distri buted strategy takes totally s N slots. And the total iteration needed to achieve an estimation error smaller than is given by 2 c [12] 20 25 30 35 40 1 1. 2 1. 4 1. 6 1. 8 2 2. 2 2. 4 2. 6 2. 8 Number of nodes Av erage dete c t ion t i m e (s lo t s ) α = 0. 2, S NR = 2dB α = 0. 2, S NR = 3dB α = 0. 2, S NR = 4dB α = 0. 3, S NR = 2dB α = 0. 3, S NR = 3dB α = 0. 3, S NR = 4dB 20 22 24 26 28 30 32 34 36 38 40 1 1.05 1. 1 1.15 1. 2 1.25 1. 3 1.35 Number of nodes Av erage detec tion t im e (slot s ) α = 0. 2, S NR = 2dB α = 0. 2, S NR = 3dB α = 0. 2, S NR = 4dB α = 0. 3, S NR = 2dB α = 0. 3, S NR = 3dB α = 0. 3, S NR = 4dB 20 22 24 26 28 30 32 34 36 38 40 4 4.2 4.4 4.6 4.8 5 5.2 5.4 5.6 5.8 6 Number of nodes Av erage de tect ion time (slots) α = 0. 2, SNR = 2dB α = 0. 2, SNR = 3dB α = 0. 2, SNR = 4dB α = 0. 3, SNR = 2dB α = 0. 3, SNR = 3dB α = 0. 3, SNR = 4dB (a) Non-cooperative strategy (b) Coopera tive strategy (c) Distributed strategy ( K 2 = , 2 s N = ) Fig. 2. Comparison of Average detection tim e. () 0 2 ˆ K θθ c ⎢ ⎥ =− ⎣ ⎦ , (24) where is the gradient limitation from c (16) , and ( ) 0 ˆ θ is the arbitrary iteration starting poi nt. Therefore, the average detection time in the distribut ed strategy is given by () 1 1 1 k ds d k TN K k p p +∞ − = =⋅ ⋅ − ∑ d , (25) where is given by d p (20) . The comparison of average det ection tim e is in Figure 2, which shows that under the sam e false alarm probability and SNR, the cooperative strategy achieves the least detection time and the distributed strategy achie ves the most. Notice that since the distributed strategy uses at least K N × time slots, the agility can not be improved further by increasing the node num ber. 2) Energy Efficiency Powered by batteries, sensor nodes in a WSN are very energy-limited, and the m ain e xpenditure of energy in a WSN is in the cost of communication. Thus energy efficiency is a critical factor in designing spect rum sensing strategy. In this paper, we mainly focus on two as pects of energy: 1) the total energy consumption needed for a single successful detection at the fusion center and 2) the fairness of energy consumption among sensor nodes. Because the whole longevity of a wireless sensor network is highly affected by the least life time of sensor nodes, fairness of energy consumption is crucial to increase network life time. When considering fairness, we define the fairness degree as the ratio of maxim um and m inimum energy consumed by nodes in a single time slot, i.e., . Recall that we assume nodes are uniformly deployed over a square meter, and that the energy cost of every transmission is positive proportional to the tran smission distance by a fixed factor max min / EE μ  N η . Therefore the average en ergy consumption of an inter-node transmission is , and of a transmission from node to the fusion center is 1/ 2 n η − η . The total energy used for a single successful detection at th e fusion center as a function of 5 the number of nodes is given by , where n is the number of nodes, and is the average amount of energy required to transmit over one hop. () n En e n =⋅ n e Firstly, in the non-cooperative strategy, every node needs to transmit its detection result to the fusion center in every slot, therefore n e η = and . Since () EN N η =⋅ max min E E = , we have 1 μ = . Secondly, in the cooperative strategy, the energy cost by the first node in every relay pair is 1/ 2 N ηη − + and η by the second node. So the average total energy consumption is given by ( ) () () () ( ) () () () 1/ 2 11 1/ 2 1 11 1 EN F N N F N F N FN N ηλ η λ η λ λη η − =+ − + − =− + 1 .(26) Since 1/ 2 max EN ηη − =+ , and min E η = , so . 1/ 2 1 N μ − =+ Lastly, in the distributed strategy, with a path through which all nodes are visited only once, the distance between neighbor nodes is reduced to ( 2 log / ) N N O [9] . So in every cluster, except the last cluster head, every node costs 2 log / NN η , and the cluster head costs 2 log / NN ηη + . Therefore () () () ( ) 22 2 log / log / log / cc c EN K N N N N N N N KN N N KN ηη η ηη =− + + =+ ,(27) where K is given by (24) . Since 2 max log / EN N ηη =+ , and 2 min log / E η = N N , we have () () 22 l o g/ l o g/ 1/ l o g NN NN NN μη η η =+ =+ . (28) The performances of the total energy consumption and the fairness are shown in Figure 3 and 4, respectively. It shows that under lower SNRs (such as 0dB), the relation of total energy consumption roughly is: CS DS CS > NCS. The performance com parison is summ arized in Table 1. VI. C ONCLUSIONS In this paper, we focus on the performances of cooperative and distributed spectru m sensing in wireless sensor networks. After introducing a baseline non-c ooperative strategy, we have described two strategies: 1) the cooperative strategy, which takes advantage of cooperation diversity gain to increase probability of detection and 2) the distributed strategy, which by passing the results in an inter-node m anner increases energy efficiency and fairness among nodes. Analysis shows that the distributed strategy leads to a higher probability of detection at the fusion center than the other tw o strategies. Furthermore, we have compared the performances of the three strategies based on the criteria of agility, energy efficiency, and the robustness against SNR changes. To sum up, perform ance comparison shows that: 1) the non-cooperative strategy has the best fairness of energy consumption, 2) the cooperative strategy leads to the best agility, and 3) the distributed strategy leads to the lowest energy consumption and the best robustness against SNR changes. 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