Cooperative spectrum sensing over unreliable reporting channel

COOPERA TIVE SPE CTR UM SENSING O VER UNRELIABLE REPOR TING CHANNEL Amanda de P aula, Cristiano P anazio Univ ersity of S ˜ ao Paulo Escola Polit ´ ecnica Email: { amanda,cpanazio } @lcs.poli .usp.br ABSTRA CT This article aims to an alyze a cooper ativ e spectrum sensing scheme using a centralized approac h with unreliable repo rting channel. The spectrum sensing is applied to a cognitive rad io system, where each cognitive rad io performs a simple energy detection and send the decision to a fusion center throu gh a reportin g cha nnel. When the decisions are available at the fu- sion center, a n -out- of- K rule is applied . The imp act of th e choice o f the parameter n in the cogn iti ve r adio system per- forman ce is analyze d in the case where the r eporting chann el introdu ces er rors. Index T erms — cognitive radio, cooper ation, spec trum sensing, data fusion. 1. INTR ODU CTION The increasing dem and for commun ication resources is lead- ing to a scar city in the spectral band s available to tr ansmis- sion. Such scarcity is main ly due to the in flexible spectrum utilization regulamenta tion, wh ere the ban ds are statically al- located. As shown in [1], this statical spectr um allocation leads to an ineffi cient spectral occupan cy . Motiv ated by the necessity of implementing more ef fi- cient b and allocatio n schemes, several papers h av e recen tly propo sed systems based on co gnitive radio (CR) [2], [ 3]. In such systems, secondary users (SU) are allo wed to o ccupy the band licensed to pr imary users ( PU), if the PU are n ot using the spectral band for that time. Therefo re, the SU must be ab le to deter mine whe ther the spectral ba nd is fre e o r not. This task is accom plished by perfor ming spectral sensing, which can be implemen ted with se veral typ es of a lgorithms [4], [5], [ 6], where the simp lest approa ch is by the mean s of an energy d etection. The main advantage of this sp ectrum sensing sch eme is that it does no t require a high a priori knowledge ab out the PU sign al. On the other han d, it do es not pr ovide a good per forman ce when compare d to other tech niques, such as f eature and coheren t detection [7]. An alternative to imp rove the energy detector perfor mance is applyin g c ooperative algorithms [7], [8] , [9]. These coop erative algorithms bring the possibility to combine the measurements provided by the various cognitive radios in the system in ord er to gener ate a m ore reliable sp ectral sen s- ing. The co operative spectr um sen sing can b e perfor med by the exchange of soft info rmation [10] or q uantized hard in- formation [9]. It is often intere sting to implement coop era- ti ve cogniti ve radio system applying hard decision in order to simplify the exchange of infor mation between the co gnitive radios and the fusion cen ter . Restricting our attention to th is case, a problem that arises is ho w to merge the decisions pro- vided b y th e d ifferent cog nitive radios in o rder to provid e a more reliable sensing. In [9] and [11] is poin ted out th at the OR decision ru le is more suitab le in many cases of pr actical interest. Ho wever , these analysis con sidered that the repo rting ch annel between the cognitive radio and the fusion ce nter was pe rfect. Re- stricting th e decision r ule to the OR rule, [12] inv estigated the effect o f reporting errors introd uced in the system. In this article, we will a ssume th e same co ntext in [12], but we will investigate the decision rules of the kind n -out- of- K , ob serving th at, differently from the perfe ct repo rting channel situation, th e decision rule which provid es the best system perform ance is not the OR, i.e. the 1-o ut-of- K rule. This article is organ ized as follows. In Section 2, th e sys- tem mod el utilized thr ougho ut this paper is depicted. In Sec - tion 3, local and c ooperative spectrum sensing ar e de scribed. Section 4 presents th eoretical and simulated results. Fina lly , in Section 5, the conclusions of the paper are stated. 2. SYSTEM MODEL In this article, we consider a co operative cogniti ve radio sys- tem with K SU. As depicted in Fig. 1, w e assume that the i th cognitive radio receives the signal transmitted by the PU throug h a channe l h i and that the sign al is co rrupted by ad- ditiv e white Gaussian n oise (A WGN). Each co gnitive radio senses the spe ctrum using an energy detector an d sends its one-bit quan tized d ecision to the fusion center . The signal received by the fusion c enter sent by each cogn iti ve r adio is corrup ted with A WGN noise with variance σ 2 n i . Finally , the spectral sensing is p erform ed in th e fusion center, where a n -out-of - K rule is applied , i.e. , the fusion Primary User CR 1 h 1 η 1 CR 1 h 2 η 2 CR K h K η K Fusion Center n 1 n 2 n K ... Fig. 1 . System Mod el center states that th e PU is active if the r eceived decision is sent by at least n o ut of the K cogn iti ve radios. 3. PR OBLEM FORMULA TION 3.1. Local Sensing The r eceived signal in the i th cognitive radio can be expr essed as one of the following hypoth esis: r ( n ) = ( h i x ( n ) + η i ( n ) , H 0 η i ( n ) , H 1 , 1 ≤ n ≤ M (1) where h i is th e ch annel coefficient, which is assumed to be a complex Gaussian rand om variable, x ( n ) is th e signal tr ans- mitted by the PU and η i ( n ) is A WGN signal with variance σ 2 η i . Each cog nitiv e radio will app ly an energy detection rule in order to decide betwee n these two hypo thesis. This decision rule consists in the comparison of t he estimated s ignal energy to a g iv en thresho ld λ . Th e estimated received s ignal energy , i.e. the decision statistic, is given b y: T ( r ) = 1 σ 2 η i M X n =1 | r ( n ) | 2 (2) The hypo thesis test is them accomplished by: T ( r ) ≷ H 1 H 0 λ (3) This mean s th at the i th cognitive radio will state th at the spectrum is oc cupied by the PU if the metric T ( r ) is greater than λ . In the specification of spectrum sensing systems, two pa- rameters are extremely r elev ant. One o f them is the false alarm probab ility ( P f ), which is defined as the prob ability of the cog nitive radio dec lares th at the spectrum is o ccupied under H 0 , i.e. : P f = Pr { T ( r ) ≥ λ | H 0 } (4) This pro bability m easures the efficiency of the cognitive radio system radio, gi ven that if the system presents a lo w P f it means that the spectrum holes are allowed to be occupied by the CR more often. The second imp ortant parameter in the cognitive radio system is th e miss detection probab ility ( P m ), that is defined as the pro bability of the cog nitiv e radio states that the spe c- trum is free giv en that the PU is transmitting: P m = Pr { T(r) < λ | H 1 } (5) For a sing le cognitive r adio in a fading scenario, these probab ilities have bee n derived in [1 3] and can be expr essed as: P f = Γ  M , λ 2  Γ ( M ) (6) P m = e − λ 2 M − 2 X l =0  λ 2  l l ! +  1 + γ γ  M − 1 ×    e − λ 2+2 γ − e − λ 2 M − 2 X l =0  λγ 2+2 γ  l l !    (7) where Γ( x ) is the gamm a func tion, Γ( x, y ) is the upp er in- complete gamma function and γ is th e a verage system signal- to-noise ratio (SNR) per sample under H 1 . It is imp ortant to note that the P f and P m are parame- terized by the thre shold λ . P f is a d ecreasing fu nction of λ , while P m is an incr easing fun ction of λ . Therefo re, in or der to specify th e th reshold λ , one should analyze the compr omise between low P f and high P m . In [8] the system parame ters were optimized in ord er to minimize the total error , i.e. , P f + P m . An other common ap- proach to deter mine the system parameters is the f ollowing: for a given P m , deter mine what ar e the system parameters that lead to the lower P f [7]. Th is appro ach provid es the highest spectrum occu pancy gi ven the PU is p rotected und er a speci- fied P m . 3.2. Cooperative sensing Previously , we have analyzed the sp ectrum sensing perfo rmed in e ach cognitive rad io. In this subsection , we d eal with the data processing in the fusion center . W e will co nsider that th e i th cognitive radio sends a o ne- bit decision to the fusion center an d that the channel between the cogn iti ve radio an d th e fusion cen ter is corru pted by an A WGN signal: s i = d i + n i (8) where d i = { 0 , 1 } is the decision sent by the i th cognitive radio and n i ∼ N  0 , σ 2 n i  . Furthermo re, the err or in the i th cognitive rad io is g iv en by: P i e = Q 1 2 s 1 σ 2 i ! (9) where Q ( x ) is the complemen tary e rror function. In this a rticle, in o rder to simplify the analysis, we will consider that the co gnitive radio’ s rep orting cha nnel present the same SNR ( σ i = σ , i = 1 . . . K ). Applying the n -ou t-of- K ru le, we have that th e false alarm and miss-detection pro babilities after the decision p ro- vided by the fusion center are giv en by: Q f = K − n X i =0  K i  [(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  K i  [ 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 fr om [11], whe re a similar expression is derived f or the n = 1 case, and from [8] whe re the overall false alarm an d miss-detection p robab ilities were obtain ed for the perf ect re - porting channel case. Analyzing (10) an d (11), on e can note th at if the individ- ual false a larm proba bility , P f , is not significant, the overall false alarm is gi ven by: Q ∞ f ( n ) = lim P f → 0 Q f = K − n X i =0  K i  (1 − P e ) i P K − i e (12) In a s imilar w ay , if the ind ividual miss-d etection pro babil- ity , P m , approaches z ero, the overall miss-detection probabil- ity is gi ven by: Q ∞ m ( n ) = lim P m → 0 Q m = K X i = K − n +1  K i  P i e (1 − P e ) K − i (13) W e will refer to th ese pro babilities as asym ptotic false alarm and miss-detec tion p robab ilities, w hich do not depen d on the average SNR γ received in the cogn iti ve radio an d are completely d ue to the errors introduce d by the report channel. These asympto tic probab ilities, howe ver , depen d on the parameter n . Q ∞ f is a decre asing fun ction of n , on th e other hand, Q ∞ m is a in creasing fun ction o f n . In the next section , we will analyze th e system perform ance depen dence on the parameter n choice in some specific scenarios. 4. RESUL TS In th is section we will describ e how to ch oose th e parameter n of a cognitive r adio system applyin g a n - out-of- K r ule in the fusio n center . When the r eporting chan nel is perf ect, the 1 -out- of- K rule, i.e. , the OR rule, o ften provides better results [11], [9]. This fact is attested in the r eceiv er operatin g ch ar- acteristics (R OC) c urves shown in Fig. 2 . I n this example, we considerer a co gnitive radio system with K = 4 seco ndary users, M = 6 samples and an average SNR γ = 20 d B with perfect repo rting c hannel. From Fig. 2, we can observe the system perf orman ce for different values o f n and con clude that for this situation the perfo rmance of the system degrades with increasing n . In the following, we will an alyze how the erro rs intro- duced by th e repor ting channel influenc es the choice o f the parameter n . W e ev aluate the same system with R OC de- picted in 2, but the SNR in the reporting c hannel is no w gi ven by S N R r = 10 log 10  1 σ 2  = 10 dB. From Fig. 3, one ca n no te that d ecision rule that mini- mizes the false alarm pr obability for a given miss-detection probab ility d epends on the miss-detectio n prob ability . This is not un expected sin ce, from eq. (12), one can note that the asymptotic false alarm prob ability Q ∞ f is a function of n . Therefo re, for different values of n , the minimu m achiev a ble false alarm probability is dif f erent. In this situation , the optim um decision rule shou ld be adaptive, d ependin g on the target miss-detection probab ility . Denoting the target miss-detection probability b y Q t m , we have that th e following ru le should be applied: n opt =      1 , Q t m ≤ Q ∗ m (1) n + 1 , Q ∗ m ( n ) < Q t m ≤ Q ∗ m ( n + 1 ) K, Q t m > Q ∗ m ( K − 1) (14) where Q ∗ m ( n ) correspond s to the minimum miss-detectio n probab ility that leads to Q ∞ f ( n ) , as indicated in Fig. 3 . It is importan t to emphasize that the o ptimality criterion is to minim ize th e false alar m prob ability for a g iv en target miss-detection probab ility . 5. CONCLUSIONS It was poin ted out throug hout this paper that the analy sis o f the cooperative spec trum sensing system, app lying the n -out- of- K in the fusion cen ter , should be cautionar y wh en the re- porting chan nel introduc es errors. 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