Cooperative spectrum sensing over unreliable reporting channel
aa r X i v : . [ s t a t . O T ] J un COOPERATIVE SPECTRUM SENSING OVER UNRELIABLE REPORTING CHANNEL
Amanda de Paula, Cristiano Panazio
University of S˜ao PauloEscola Polit´ecnicaEmail: { amanda,cpanazio } @lcs.poli.usp.br ABSTRACT
This article aims to analyze a cooperative spectrum sensingscheme using a centralized approach with unreliable reportingchannel. The spectrum sensing is applied to a cognitive radiosystem, where each cognitive radio performs a simple energydetection and send the decision to a fusion center through areporting channel. When the decisions are available at the fu-sion center, a n -out-of- K rule is applied. The impact of thechoice of the parameter n in the cognitive radio system per-formance is analyzed in the case where the reporting channelintroduces errors. Index Terms — cognitive radio, cooperation, spectrumsensing, data fusion.
1. INTRODUCTION
The increasing demand for communication resources is lead-ing to a scarcity in the spectral bands available to transmis-sion. Such scarcity is mainly due to the inflexible spectrumutilization regulamentation, where the bands are statically al-located. As shown in [1], this statical spectrum allocationleads to an inefficient spectral occupancy.Motivated by the necessity of implementing more effi-cient band allocation schemes, several papers have recentlyproposed systems based on cognitive radio (CR) [2], [3]. Insuch systems, secondary users (SU) are allowed to occupy theband licensed to primary users (PU), if the PU are not usingthe spectral band for that time.Therefore, the SU must be able to determine whether thespectral band is free or not. This task is accomplished byperforming spectral sensing, which can be implemented withseveral types of algorithms [4], [5], [6], where the simplestapproach is by the means of an energy detection. The mainadvantage of this spectrum sensing scheme is that it does notrequire a high a priori knowledge about the PU signal. Onthe other hand, it does not provide a good performance whencompared to other techniques, such as feature and coherentdetection [7]. An alternative to improve the energy detectorperformance is applying cooperative algorithms [7], [8], [9].These cooperative algorithms bring the possibility to combinethe measurements provided by the various cognitive radios in the system in order to generate a more reliable spectral sens-ing.The cooperative spectrum sensing can be performed bythe exchange of soft information [10] or quantized hard in-formation [9]. It is often interesting to implement coopera-tive cognitive radio system applying hard decision in order tosimplify the exchange of information between the cognitiveradios and the fusion center. Restricting our attention to thiscase, a problem that arises is how to merge the decisions pro-vided by the different cognitive radios in order to provide amore reliable sensing.In [9] and [11] is pointed out that the OR decision rule ismore suitable in many cases of practical interest. However,these analysis considered that the reporting channel betweenthe cognitive radio and the fusion center was perfect. Re-stricting the decision rule to the OR rule, [12] investigated theeffect of reporting errors introduced in the system.In this article, we will assume the same context in [12],but we will investigate the decision rules of the kind n -out-of- K , observing that, differently from the perfect reportingchannel situation, the decision rule which provides the bestsystem performance is not the OR, i.e. the 1-out-of- K rule.This article is organized as follows. In Section 2, the sys-tem model utilized throughout this paper is depicted. In Sec-tion 3, local and cooperative spectrum sensing are described.Section 4 presents theoretical and simulated results. Finally,in Section 5, the conclusions of the paper are stated.
2. SYSTEM MODEL
In this article, we consider a cooperative cognitive radio sys-tem with K SU. As depicted in Fig. 1, we assume that the i th cognitive radio receives the signal transmitted by the PUthrough a channel h i and that the signal is corrupted by ad-ditive white Gaussian noise (AWGN). Each cognitive radiosenses the spectrum using an energy detector and sends itsone-bit quantized decision to the fusion center. The signalreceived by the fusion center sent by each cognitive radio iscorrupted with AWGN noise with variance σ n i .Finally, the spectral sensing is performed in the fusioncenter, where a n -out-of- K rule is applied, i.e. , the fusion rimary UserCR h η CR h η CR K h K η K Fusion Center n n n K ... Fig. 1 . System Modelcenter states that the PU is active if the received decision issent by at least n out of the K cognitive radios.
3. PROBLEM FORMULATION3.1. Local Sensing
The received signal in the i th cognitive radio can be expressedas one of the following hypothesis: r ( n ) = ( h i x ( n ) + η i ( n ) , H η i ( n ) , H , ≤ n ≤ M (1)where h i is the channel coefficient, which is assumed to be acomplex Gaussian random variable, x ( n ) is the signal trans-mitted by the PU and η i ( n ) is AWGN signal with variance σ η i .Each cognitive radio will apply an energy detection rule inorder to decide between these two hypothesis. This decisionrule consists in the comparison of the estimated signal energyto a given threshold λ . The estimated received signal energy, i.e. the decision statistic, is given by: T ( r ) = 1 σ η i M X n =1 | r ( n ) | (2)The hypothesis test is them accomplished by: T ( r ) ≷ H H λ (3)This means that the i th cognitive radio will state that thespectrum is occupied by the PU if the metric T ( r ) is greaterthan λ .In the specification of spectrum sensing systems, two pa-rameters are extremely relevant. One of them is the falsealarm probability ( P f ), which is defined as the probabilityof the cognitive radio declares that the spectrum is occupiedunder H , i.e. : P f = Pr { T ( r ) ≥ λ | H } (4) This probability measures the efficiency of the cognitiveradio system radio, given that if the system presents a low P f it means that the spectrum holes are allowed to be occupiedby the CR more often.The second important parameter in the cognitive radiosystem is the miss detection probability ( P m ), that is definedas the probability of the cognitive radio states that the spec-trum is free given that the PU is transmitting: P m = Pr { T(r) < λ | H } (5)For a single cognitive radio in a fading scenario, theseprobabilities have been derived in [13] and can be expressedas: P f = Γ (cid:0) M, λ (cid:1) Γ ( M ) (6) P m = e − λ M − X l =0 (cid:0) λ (cid:1) l l ! + (cid:18) γγ (cid:19) M − × e − λ γ − e − λ M − X l =0 (cid:16) λγ γ (cid:17) l l ! (7)where Γ( x ) is the gamma function, Γ( x, y ) is the upper in-complete gamma function and γ is the average system signal-to-noise ratio (SNR) per sample under H .It is important to note that the P f and P m are parame-terized by the threshold λ . P f is a decreasing function of λ ,while P m is an increasing function of λ . Therefore, in order tospecify the threshold λ , one should analyze the compromisebetween low P f and high P m .In [8] the system parameters were optimized in order tominimize the total error, i.e. , P f + P m . Another common ap-proach to determine the system parameters is the following:for a given P m , determine what are the system parameters thatlead to the lower P f [7]. This approach provides the highestspectrum occupancy given the PU is protected under a speci-fied P m . Previously, we have analyzed the spectrum sensing performedin each cognitive radio. In this subsection, we deal with thedata processing in the fusion center.We will consider that the i th cognitive radio sends a one-bit decision to the fusion center and that the channel betweenthe cognitive radio and the fusion center is corrupted by anAWGN signal: s i = d i + n i (8)where d i = { , } is the decision sent by the i th cognitiveradio and n i ∼ N (cid:0) , σ n i (cid:1) .urthermore, the error in the i th cognitive radio is givenby: P ie = Q s σ i ! (9)where Q ( x ) is the complementary error function.In this article, in order to simplify the analysis, we willconsider that the cognitive radio’s reporting channel presentthe same SNR ( σ i = σ, i = 1 . . . K ).Applying the n -out-of- K rule, we have that the falsealarm and miss-detection probabilities after the decision pro-vided by the fusion center are given by: Q f = K − n X i =0 (cid:18) Ki (cid:19) [(1 − P f ) (1 − P e ) + P f P e ] i × [ P f (1 − P e ) + (1 − P f ) P e ] K − i (10) Q m = K X i = K − n +1 (cid:18) Ki (cid:19) [ P m (1 − P e ) + (1 − P m ) P e ] i × [(1 − P m ) (1 − P e ) + P m P e ] K − i (11)The results above were obtained from a direct generaliza-tion from [11], where a similar expression is derived for the n = 1 case, and from [8] where the overall false alarm andmiss-detection probabilities were obtained for the perfect re-porting channel case.Analyzing (10) and (11), one can note that if the individ-ual false alarm probability, P f , is not significant, the overallfalse alarm is given by: Q ∞ f ( n ) = lim P f → Q f = K − n X i =0 (cid:18) Ki (cid:19) (1 − P e ) i P K − ie (12)In a similar way, if the individual miss-detection probabil-ity, P m , approaches zero, the overall miss-detection probabil-ity is given by: Q ∞ m ( n ) = lim P m → Q m = K X i = K − n +1 (cid:18) Ki (cid:19) P ie (1 − P e ) K − i (13)We will refer to these probabilities as asymptotic falsealarm and miss-detection probabilities, which do not dependon the average SNR γ received in the cognitive radio and arecompletely due to the errors introduced by the report channel.These asymptotic probabilities, however, depend on theparameter n . Q ∞ f is a decreasing function of n , on the otherhand, Q ∞ m is a increasing function of n . In the next section,we will analyze the system performance dependence on theparameter n choice in some specific scenarios.
4. RESULTS
In this section we will describe how to choose the parameter n of a cognitive radio system applying a n -out-of- K rule inthe fusion center. When the reporting channel is perfect, the -out-of- K rule, i.e. , the OR rule, often provides better results[11], [9]. This fact is attested in the receiver operating char-acteristics (ROC) curves shown in Fig. 2. In this example, weconsiderer a cognitive radio system with K = 4 secondaryusers, M = 6 samples and an average SNR γ = 20 dB withperfect reporting channel. From Fig. 2, we can observe thesystem performance for different values of n and concludethat for this situation the performance of the system degradeswith increasing n .In the following, we will analyze how the errors intro-duced by the reporting channel influences the choice of theparameter n . We evaluate the same system with ROC de-picted in 2, but the SNR in the reporting channel is now givenby SN R r = 10 log (cid:0) σ (cid:1) = 10 dB.From Fig. 3, one can note that decision rule that mini-mizes the false alarm probability for a given miss-detectionprobability depends on the miss-detection probability. Thisis not unexpected since, from eq. (12), one can note thatthe asymptotic false alarm probability Q ∞ f is a function of n .Therefore, for different values of n , the minimum achievablefalse alarm probability is different.In this situation, the optimum decision rule should beadaptive, depending on the target miss-detection probability.Denoting the target miss-detection probability by Q tm , wehave that the following rule should be applied: n opt = , Q tm ≤ Q ∗ m (1) n + 1 , Q ∗ m ( n ) < Q tm ≤ Q ∗ m ( n + 1) K, Q tm > Q ∗ m ( K − (14)where Q ∗ m ( n ) corresponds to the minimum miss-detectionprobability that leads to Q ∞ f ( n ) , as indicated in Fig. 3.It is important to emphasize that the optimality criterionis to minimize the false alarm probability for a given targetmiss-detection probability.
5. CONCLUSIONS
It was pointed out throughout this paper that the analysis ofthe cooperative spectrum sensing system, applying the n -out-of- K in the fusion center, should be cautionary when the re-porting channel introduces errors. It was shown that, whenthe reporting errors are take into account, the changes intro-duced in the ROCs are such that the optimal parameter n ismodified. −6 −5 −4 −3 −2 −1 −6 −5 −4 −3 −2 −1 P f P m SimulatedTheoreticaln=1n=2n=3n=4
Fig. 2 . ROC - γ = 20 dB, K = 4 , perfect reporting channel
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