Optimal Cooperative Wideband Spectrum Sensing in Cognitive ...

**Optimal** **Cooperative** **Wideband** **Spectrum** **Sens ing**

Fig. 1.y i,m (n) =Scheme of SUs, FC and PU location.{ɛi,m (n) H 0α i,m S i,m (n)+ɛ i,m (n) H 1(1)where ɛ i,m (n) is assumed to be complex zero mean Gaussiannoise with variance equal to σ 2 ɛ . s i,m (n) is the primary usersignal of the i’th channel received by m’th SU, which can beformulated as a complex Gaussian variable with zero meanand variance σ 2 i,m . α i,ms are the i.i.d channel coefficients.B. AssumptionsThe follow**in**g assumptions will be reta**in**ed for illustrativepurpose and for analytical tractability:̌SUs should calculate the power of each channel and thenvia the proposed robust algorithm, determ**in**e the occupancyof each channel. The decisions are to be sent to the fusioncenter.̌F**in**al decision based on comb**in**ation of local decisionswill be made by FC. The optimal fusion rule is obta**in**ed viaLRT.̌**Sens ing** channels (i.e. channels between PU transmittersand SUs) are assumed to be noisy and subject to multipathfad

all observations directly to a FC where decision process**in**g The number of occupied channels l is estimated is the onei=1and,P d = 1 K∑P dK (18)C m (l) = 1 (log(K − l)+l(log( 2 ))K2Nπ ) k=1where P dk denotes the probability of detection for the k’th+ 12N log(N) (10) channel **in** FC. Noise uncerta**in**ty is modelled as α whereas **in**[17] α is uniformly distributed **in** the **in**terval [−1dB, 1dB].is performed. This method often requires a large bandwidthfor the communications channel **in** order to obta**in** real-timeresults. In the second method, each SU decides locally whetherm**in**imis**in**g (11) i.e.:ˆl = argj=0,1,...,k m**in**BEED j (11)PU is active or not. Then the local decisions are sent to B. Global decisionthe FC where they are comb**in**ed for global decision mak**in**g.Assume µ i denotes the local decision vector about i’thThis method does not require the large bandwidth of the firstprimary channel from different SUs which is transmitted tomethod; however, performance is degraded because the centralthe FC. The FC should makes the f**in**al decision about theprocessor does not receive all the **in**formation. The advantagesoccupancy of the channel based on the general L out of**in** cost, reliability, and communications bandwidth, however,M rule which can yield **in** simpler form like AND, ORmay outweigh the loss of performance.and MAJORITY rule. In section III, the advantages andIn this paper, we consider decision fusion algorithms anddisadvantages of each rule has been **in**vestigated, however; **in**evaluate the performance of the proposed algorithm us**in**gthis section, we exploit optimal choose of L based on LRToptimal count**in**g rule. The most important basic methods **in**[14-16]. The optimum decision rule is given by the follow**in**gcount**in**g rule are: AND rule, OR rule, MAJORITY rule whichlikelihood ratio test:def**in**es as follows [13].ȞOR rule: This rule declares that the PU is active if onlyP (u i |H 1 ) 1P (H 0 )(C 10 − C 00 )(12)one of the SUs says that the PU is active. Therefore, the resultP (u i |H 0 )H 0P (H 1 )(C 01 − C 11 )is the **in**crease **in** the overall P d and P fa as well.the likelihood ratio and the Bayes optimum threshold is on thěAND rule: If all SUs say that the PU is active, then theleft and right-hand side, respectively. The probability of errorf**in**al decision declares that the PU is active. As expected, thiscriterion is assumed be Crule decreases the overall P d and P fa as well.00 = C 11 =0and C 10 − C 01 =1.Therefore, by apply**in**g Bayes rule to express the conditionaľMAJORITY rule: Another decision rule is that if halfprobabilities, substitut**in**g and simplify**in**g, the correspond**in**gof the SUs or more say that the PU is active, then thelog-likelihood ratio test is obta**in**ed as:f**in**al decision declares that the PU is active. The overallperformance of the system depends on the number of SUsand their detection.log P (H H1|u i ) 1 0P (H 0 |u i )HHowever the optimal fusion rule **in** FC is derived from LRT0(13)which requires the knowledge of each SU detection (i.e. P dUs**in**g theorem **in** [16], the optimal decision rule can beand P fa ). Therefore **in** section III, the LRT-based optimal presented as:fusion rule is used for mak**in**g f**in**al decision **in** FC.M∑ H 1IV. PROPOSED FRAMEWORKa i,m 0 (14)m=0 H 0A. Local decisionWhere the weight coefficient a i,m correspond**in**g to u i,mAssume that the estimated energies of the channels at m’thdef**in**es asSU are gathered **in** a vector:λ m =[λ 1,m ,λ 2,m ,...,λ K,m ] T (7)a i,0 = log P (H 1)(15)P (H 0 )where λ K,m is calculated due to (2).After calculat**in**g the energies of different channels, BEEDbaseda i,m = log P d mP famif u i,m =1 (16)estimator will be applied accord**in**g to the lemma **in**[9]:a i,m = log 1 − P d m1 − P famif u i,m =0 (17)BEED l,m = C m (l)⎛( l∏)() K−l⎞V. SIMULATION RESULTS+ log ⎝1K∑In this section, we present simulation results that illustrateλ i,m λ i,m⎠ (8)K − lthe performance of our proposed framework compared withi=1 i=l+1simple energy detector. We assume there are 40 channelswhere,and every channel has a probability of 5.2% to be occupied.Probability of detection P 0∏d is the used factor to evaluate theλ i,m =1 (9) performance:373