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Email: {ala.abu.alkheir, mohamed.ibnkahla}@queensu.ca. Abstract—This article proposes a novel Cooperative Spectrum. Sensing (CSS) scheme for Cognitive ...
This full text paper was peer reviewed at the direction of IEEE Communications Society subject matter experts for publication in the IEEE Globecom 2011 proceedings.

Selective Cooperative Spectrum Sensing In Cognitive Radio Networks Ala Abu Alkheir and Mohamed Ibnkahla Department of Electrical and Computer Engineering (ECE), Queen’s University, Kingston, Ontario, Canada Email: {ala.abu.alkheir, mohamed.ibnkahla}@queensu.ca

Abstract—This article proposes a novel Cooperative Spectrum Sensing (CSS) scheme for Cognitive Radio Networks (CRN). The proposed scheme, referred to as the Selective Cooperative Spectrum Sensing (SCSS) scheme, is capable of jointly reducing the reporting overhead and mitigating faulty reporters at the Base Station (BS). These goals are achieved by exclusively using reliably taken and delivered reports from the individual nodes to the BS. Two conditions are used to guarantee this, one on the detection reliability while the other is on the reporting reliability. These two conditions are designed to offer flexible performance, complexity and overhead tradeoff. The performance of SCSS is studied analytically and using simulations. Results show performance enhancements compared to conventional CSS schemes.

I. I NTRODUCTION Since the dawn of Cognitive Radio (CR) technology, CSS was marked as a powerful tool for a reliable detection of unoccupied spectrum bands, referred to as Spectrum Holes (SH) [1], [2]. In CSS, a group of CR nodes collaboratively detect a particular spectrum band for opportunistic access. This collaboration helps mitigating the wireless channel impairments, like shadowing and deep fading, as well as mitigating the hidden terminal problem. There are two possible scenarios for CSS, namely centralized and distributed. In centralized CSS, all nodes in the network forward their local reports (or measurements) to the BS to make the final decision. This scenario is suitable for infrastructure based networks like the Wireless Regional Area Networks (WRAN). On the other hand, distributed CSS allows nodes to exchange their local decisions such that every node makes its own final decision as in ad hoc CR networks. In both scenarios, every CR terminal in the network performs local Spectrum Sensing (SS) and report either its local decision or its decision metric itself. The former option is referred to as the decision-based CSS, while the latter is known as the data-based CSS. When the amount of the reporting overhead is a critical issue, decision-based CSS is preferred [3]. An example of this is the WRAN standard, the IEEE 802.22, [4]. In fact, since this standard does not specify any control channel for the sensing overhead, sensing information will share the available resources with the actual data. Consequently, it is fundamentally important that sensing throughput be reduced as much as possible while maintaining an acceptable level of performance. In addition, CSS faces another challenge when the nodes report

to the BS. Since the reporting channels are imperfect wireless channels prone to various channel impairments, like deep fading, shadowing, and path loss, some of the reports maybe lost or erroneously decoded at the BS. Hence, the accuracy of the BS decision is affected. This affect is referred to as the faulty reporter effect. Over the past few years, tens of SS methods have been proposed and studied. In general, a SS method models the sensing problem as a binary hypothesis testing problem where a decision is to be made in favor of one of the two hypotheses based on some decision metric. A widely used, and in fact attractive, SS method is the Energy Detection (ED). This method uses an estimate of the energy in the examined spectrum band to make its decision. A. Literature Review There have already been some attempts to reduce the reporting overhead of the decision-based CSS. These extend the conventional binary hypothesis testing by injecting a second decision threshold. Consequently, nodes with decision metrics falling between the two decision thresholds are not allowed to report to the BS. This scheme appeared first in [5]. It was shown that the number of reporting nodes has been reduced compared to the conventional decision-based CSS. A similar technique was also used in [6]. However, unlike [5], the authors allowed the nodes that did not report the first time to repeat their measurements and report. Hence, they achieved better performance at the cost of increasing the processing and the number of reporting nodes. An additional decision threshold was injected in [7], [8]. However, the objective was not to reduce the reporting overhead but rather to bridge the performance gap between data-based CSS and decision-based CSS through quantization. Instead of reporting the local decision metrics to the BS, the authors used a 2bit quantized version of these decisions. Consequently, the number of reporting nodes was double that of the decisionbased CSS. The effect of the faulty reporters problem on the performance of the decision-based CSS was analyzed in [9]. Next, the authors proposed three options to mitigate it, namely clustering [10], transmit diversity, and relaying [11]. In the clustering approach, the nodes are grouped into small clusters. Cluster heads are chosen based on the quality of their node-BS links. These heads collect the local decisions from the cluster

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This full text paper was peer reviewed at the direction of IEEE Communications Society subject matter experts for publication in the IEEE Globecom 2011 proceedings.

members and forward it to the BS. Hence, eliminating the faulty reporters effect or at least reducing it. On the other hand, transmit diversity using space-time coding allows the nodes to utilize time and space diversity to enhance the reporting quality. Obviously, this is achieved at the cost of considerable increase in the sensing time. The same also applies to the relaying option. B. Paper Contributions In this article, we design a CSS scheme, known as the SCSS scheme, that can jointly reduce the reporting overhead (and time) and mitigate the faulty reporters. The SCSS can solve both problems efficiently by restricting the reporting nodes as well as the acceptable reports. In this scheme, the decision region is divided into three subregions using a single control parameter. Unlike previous proposals, the width of the ”No Decision” region can be easily controlled to minimize the probability of fail to sense. Furthermore, the performance of the proposed scheme in terms of the detection and false alarm probabilities is studied. Additionally, to mitigate the faulty reporters problem, a condition is imposed on the participating nodes at the BS such that only reliably received reports are considered. II. S YSTEM M ODEL Consider a CR network consisting of K CRs collaboratively detecting a particular spectrum band licensed to some PU as shown in Figure 1 below. Every CR uses ED to estimate the energy in that band. The energy estimate of CRi is denoted φi .

CR h1

h p ,1

CR h p ,2

h2

PU

BS hK 1

h p ,K 1

CR

hK

h p ,K

CR Fig. 1. K CRs perform local spectrum sensing and report their decisions to the BS.

Every CR makes a local decision, denoted di , according to the following rule ⎧ ⎪ φi < λ − Δ; ⎨0, (1) di = 1, φi > λ + Δ; ⎪ ⎩ ”No Decision”, |φi − λ| ≤ Δ

where λ is a decision threshold calculated according to the Neyman-Pearson (NP) criterion [12], and Δ is a design parameter chosen to control the performance of the proposed scheme. Unlike the conventional two-level ED, SCSS divides the decision area into three regions, [0, λ−Δ), [λ−Δ, λ+Δ], and (λ + Δ, ∞). The first region corresponds to the ”Band Empty” region, denoted by the hypothesis H0CR , while the third region correspond to the ”Band Busy” region, denoted by the hypothesis H1CR . If φi falls in the intermediate region, the CR makes no decision. Hence, this region is denoted by the ”No Decision” region. As shall be shortly demonstrated, the width of this region, 2Δ, is used to control the performance of the proposed scheme. The statistical characteristics of φi depend on the status of the PU. In particular, the Probability Density Function (PDF) of φi when the PU is absent, denoted by H0PU , and when it is present, denoted by H1PU , was shown in [13] to be as follows  H0PU ; χ22ui , (2) fφi (φi ) = 2 χ2ui (2γp,i ), H1PU where χ22u is the central chi-square distribution with 2u = 2W T degrees of freedom, W is the detected channel bandwidth and T is the observation time, while χ22u (2γp,i ) is the noncentral chi-square distribution with noncentrality parameter of 2γp,i . In addition, γp,i  SNRp |hp,i |2 is the received Signal E to Noise Ratio (SNR) at CRi , while SNRp  Np0 is the transmit SNR at the PU side, Ep being the PU transmit energy, while N0 is the noise variance at CRi side (assumed identical for all terminals). hp,i is the channel coefficient of the PU-CRi link modeled as a zero mean complex valued Gaussian variable corresponding to a flat Rayleigh fading. Hence |hp,i |2 has an exponential PDF with mean value of μp,i . Since some of the nodes will not make local decisions, only a subset of the available nodes will report to the BS. This subset is denoted Cr , where the number of its elements ranges from 1 to K, i.e. 1 ≤ |Cr | ≤ K. Every CRi ∈ Cr sends its local decision, di , to the BS through its CRi -BS link experiencing flat Rayleigh fading. However, due to the many channel impairments like fading, shadowing, path loss etc., some of the local decisions may get corrupted when decoded by the BS. Despite the difficulty of identifying the corrupted ones, simple tests can be made to eliminate the reports that cannot be successfully decoded. In particular, we require that reports that undergo an event of outage be eliminated from the decision-making process. Mathematically, we require the instantaneous SNR of the CRi -BS link, γi = SNRc |hi |2 , where SNRc is the transmit SNR of CRi (assumed equal for all CRs), exceed a certain threshold, i.e., γi ≥ γth , where γth = 2Q − 1, Q being the spectral efficiency in bits per second per Hertz. Once again, a subset of Cr will satisfy this condition. This set is referred to as the decision set, denoted by Cd . Obviously, the number of elements in Cd is upper bounded by |Cr |, hence 1 ≤ |Cd | ≤ |Cr | ≤ K. Using the local decisions of the nodes in Cd , the BS computes the decision metric D by summing up all the local decisions of CRi ∈ Cd , i.e., D = d1 + d2 + . . . , d|Cd | .

This full text paper was peer reviewed at the direction of IEEE Communications Society subject matter experts for publication in the IEEE Globecom 2011 proceedings.

D is then compared to a decision threshold η, 1 ≤ η ≤ K. If D ≥ η, the BS decides that the band is busy, i.e., chooses H1BS , otherwise it decides that its empty through choosing H0BS . III. P ERFORMANCE A NALYSIS Let us now analyze the performance of the SCSS. In particular, we are interested in four performance measures. First, the performance, in terms of the detection and false alarm probabilities, at the node level. Second, the average number of reporting nodes. Third, the detection and false alarm probabilities at the BS side. Finally, the probability of failing to sense. These performance metrics will be defined and derived in the following subsections. A. Probability of Detection and False Alarm at the node level The detection probability, Pd,i , is a statistical measure of the CR’s ability to detect the PU when it is using the band. Mathematically, Pd,i is defined as Pd,i  Pr[φi > λ+Δ|H1PU ]. On the other hand, the probability of false alarm, Pf a,i , is a statistical measure of the CR’s ability to claim that the PU is using the band when it is actually not. Pf a,i is defined as Pf a,i  Pr[φi > λ + Δ|H0PU ]. With the aid of the statistical characteristics given in Eqn.(2), Pd,i and Pf a,i were found to be [13] √  Pd,i = Qu ( 2γp,i , λ + Δ), (3a) Γ(u, (λ + Δ)/2) , (3b) Pf a,i = Γ(u) where Qu(a, b) is the generalized Marcum Q-function, ∞ Γ(a, x)  x ta−1 e−t dt is the incomplete Gamma function. Since Pf a,i is not a function of γp,i , the subscript i can be dropped. Hence, all nodes will have the same Pf a . However, the situation is different for Pd,i since it depends on γp,i . In fact, this dependence makes Pd,i fluctuate with the instantaneous variations of γp,i . Thus, it needs to be averaged over the PDF of γp,i . Since we assumed a flat Rayleigh fading, γp,i has an exponential PDF with average value of γ¯p,i . The resulting averaged detection probability, denoted P¯d,i , was shown in [13] to be P¯d,i

=

e−

λ+Δ 2

1 λ + Δ n 1 + γ¯p,i u−1 + n! 2 γ¯p,i n=0 u−2

u−2

(λ + Δ)¯ − λ+Δ λ+Δ 1 γp,i n . × e 2(1+¯γp,i ) − e− 2 n! 2(1 + γ¯p,i ) n=0

(4) B. Average Number of Reporting Bits The number of reporting bits in the conventional two-level ED is simply the number of nodes in the network, K. In the SCSS, this number is reduced to |Cr |. However, since this varies with φi , i = 1, 2, . . . , K and with the state of nature of the PU, i.e., H0PU or H1PU , it can be best written using the Total Probability Theorem as follows ¯ = N

Pr[H0PU ]

¯0 + ×N

Pr[H1PU ]

¯1 , ×N

(5)

where Pr[H0PU ] and Pr[H1PU ] are the probabilities of occurrence ¯0 and N ¯1 are the of H0PU and H1PU , respectively, while N average numbers of reporting bits under the two hypotheses. In practice, CR networks attempt to utilize spectrum bands with Pr[H1PU ] < 50%, referred to as under-utilized bands. However, the actual percent of time a spectrum band is utilized, i.e., the probability of utilization, depends on so many factors even within the same licensed network or technology. ¯1 . If the probability that CRi ∈ Cr ¯0 and N Next, let us study N PU under H0 is denoted by β0,i , and under H1PU is denoted by ¯0 and N ¯1 can simply be written as N ¯0 = K β0,i β1,i , then N i=1  ¯1 = K β1,i , respectively. and N i=1 Since the event CRi ∈ Cr only happens when φi < λ − Δ or φi > λ + Δ happens, i.e., when |φi − λ| > Δ, βj,i , j = 0, 1 can be written as  λ+Δ fφi (φi |HjPU ) · dφi , (6) βj,i = 1 − λ−Δ

fφi (φi |HjPU )

is as given in (2) under the two hypotheses. where Upon solving the two integrals, one can readily find that Γ(u, (λ + Δ)/2) Γ(u, (λ − Δ)/2) − , (7a) Γ(u) Γ(u) √ √   = 1 + Qu ( 2γp,i , λ + Δ) − Qu ( 2γp,i , λ − Δ). (7b)

β0,i = 1 + β1,i

Finally, (5) becomes ¯ = Pr[H0PU ] N

K

β0,i + Pr[H1PU ] ×

i=1

K

β1,i .

(8)

i=1

¯j → K, and hence N ¯ → K, which Observe that as Δ → 0, N corresponds to the two-level ED case. Similarly, as Δ → ∞, ¯ → 0. Consequently, 0 ≤ N ¯ ≤ K, ¯j → 0, and hence N N which is a controlled reduction to the reporting overhead and the sensing time. However, does this reduction affect the performance at the BS side? The answer is in the next subsection. C. Detection and False Alarm Probabilities at the BS Side Due to the constraints on the identity of the reporting terminals, a decision attempt is only made when |Cd | ≥ η. Hence, the detection and false alarm probabilities can be defined as Qd  Pr[D ≥ η|H1PU , |Cd | ≥ η] and Qf a  Pr[D ≥ η|H0PU , |Cd | ≥ η], respectively. However, a deeper look at the condition |Cd | ≥ η reveals that it is automatically satisfied in the definition D ≥ η. Hence, the condition can be dropped, and Qd and Qf a can be redefined as Qd  Pr[D ≥ η|H1PU ] and Qf a  Pr[D ≥ η|H0PU ]. These can be written as Qd =

K

Pr[D = l|H1PU ],

(9a)

Pr[D = l|H0PU ].

(9b)

l=η

Qf a =

K l=η

The probability terms Pr[D = l|HjPU ], j = 0, 1 depend on the probability that CRi , successfully reports a 1 to the BS. This

This full text paper was peer reviewed at the direction of IEEE Communications Society subject matter experts for publication in the IEEE Globecom 2011 proceedings.

in turn depends on two independent probabilities i) probability that it successfully detected the PU, and ii) probability that its report was successfully decoded. Hence, the probability that CRi successfully reported a 1 to the BS under HjPU , P1,i,j , can be written as P1,i,j  Pr[φi > λ + Δ|HjPU ] × Pr[γi ≥ γth ],

where γ¯i = SNRs μi , μi being the average value of the channel gain |hi |2 . Since Pr[φi > λ + Δ|H0PU ] = Pf a,i and Pr[φi > λ + Δ|H1PU ] = P¯d,i , P1,i,j can be rewritten as P1,i,0 = Pf a,i e−γth /¯γi and P1,i,1 = P¯d,i e−γth /¯γi for j = 0 and 1, respectively. Finally, the probability terms Pr[D = l|HjPU ], j = 0, 1, become Pr[D =

=

bl

Uj,v Vj,v ,

(12)

v=1

where bl = K!/[(K − l)!l!] is the number of possible permutations of K elements taken l at a time. Uj,v is the v th permutation consisting of the product of l out of the K possible P1,i,j terms while Vj,v is the v th permutation forming the complements’ product of the remaining K − l terms, i.e., (1 − P1,i,j ). Substituting (12) in (9), Qd and Qf a can be rewritten as Qd =

bl K

U1,v V1,v ,

(13a)

U0,v V0,v .

(13b)

l=η v=1

Qf a =

bl K l=η v=1

D. Probability of Fail to Sense The detection and false alarm probabilities were defined when |Cd | ≥ η. When this condition is not met, a fail to sense event happens. In this case, the network repeats the sensing process. Obviously the occurrence of this event significantly increases the sensing time. Hence, the probability of failing to sense, Qf s should be as small as possible. Unlike Qd and Qf a , Qf s is defined under the two hypotheses, HjPU , j = 0, 1. Thus, with the aid of the Total Probability Theorem, Qf s can be written as Qf s = Pr[|Cd | < η|H0PU ]·Pr[H0PU ]+Pr[|Cd | < η|H1PU ]·Pr[H1PU ] (14) where the probabilities Pr[|Cd | < η|HjPU ], j = 0, 1, can be written as Pr[|Cd | < η|HjPU ] =

η−1

Pr[|Cd | = l|HjPU ].

Pr[CRi ∈ Cd |HjPU ] = Pr[|φi − λ| > Δ|HjPU ] × Pr[γi ≥ γth ] =

(10)

for i = 1, 2, . . . , K, and j = 0, 1. The probability Pr[γi ≥ γth ], which is identical under the two hypotheses, can be calculated using the Rayleigh fading assumption as  ∞ 1 −γ/¯γi e · dγ = e−γth /¯γi . (11) Pr[γi ≥ γth ] = γ ¯ i γth

l|HjPU ]

As mentioned earlier, for CRi ∈ Cd to hold, two independent conditions should hold, namely, |φi − λ| > Δ and γi ≥ γth . Hence, we can readily write

(15)

l=0

To find the probabilities Pr[|Cd | = l|HjPU ], j = 0, 1, we need to calculate Pr[CRi ∈ Cd |HjPU ], j = 0, 1, i = 1, 2, . . . , K.

βj,i · e−γth /¯γi ,

(16)

for i = 1, 2, . . . , K and j = 0, 1. With the aid of this result, Pr[|Cd | = l|HjPU ] becomes Pr[|Cd | = l|HjPU ] =

bl

Pj,k Sj,k ,

(17)

k=1

where bl = K!/[(K − l)!l!] is the number of possible permutations of K elements taken k at a time, Pj,k is the k th permutation consisting of the product of l out of the Pr[CRi ∈ Cd |HjPU ], i = 1, 2, . . . , K terms while Sj,k is the k th permutation forming the complements’ product of the remaining K − l terms, i.e., (1 − Pr[CRi ∈ Cd |HjPU ]). Substituting (17) in (14) yields Qf s =

Pr[H0PU ]

η−1 bl

P0,k S0,k +

Pr[H1PU ]

l=0 k=1

η−1 bl l=0 k=1

P1,k S1,k , (18)

IV. S IMULATION R ESULTS Let us start with the average number of reporting bits. In particular, consider a network with the following parameters: K = 10, u = 10, Q = 1, SNRs = 10dB, SNRp = 10dB, η = 1, Pr[H1PU ] = 20%, μp,i and μi , i = 1, 2, . . . , K are uniformly distributed over [0.5, 1.5] and [1, 2], respectively. Figure 2 below illustrates the reduction in the average number of reporting bits (same as number of reporting nodes) as the width of the ”No Decision” region, 2Δ, increases. In fact, if we allows as low as 2×0.3λ for the ”No Decision” region, then we can save more than 40% of the sensing throughput, and hence the sensing time, while complying to the IEEE 802.22 specifications. Next, let us study the complementary Receiver Operating Characteristics (ROC) of this network as a function of Δ. Figure 3 illustrates this performance. It clearly shows that a marginal performance loss is incurred for increasing Δ. It also shows that detection probabilities larger than 90% are achievable at a false alarm probability of around 10% or even lower. Finally, let us look at the probability of failing to sense. In Figure 4 below, we can see that higher Δ increases Qf s . However, this increase remains marginal if we recall that a practical system will be operating at Qf a of as high as 10%, at which Qf s is around 10−3 . V. C ONCLUSIONS This article proposed a novel CSS scheme capable of jointly reducing the reporting overhead and mitigating the faulty reporters problem. A reduction of as much as 40% can be achieved by proper control of the ”No Decision” region. We also demonstrated that this reduction is achieved with marginal loss in the detection performance. These gains have been

This full text paper was peer reviewed at the direction of IEEE Communications Society subject matter experts for publication in the IEEE Globecom 2011 proceedings.

0

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10 Analytical Simulation fs

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Analytical Simulation

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Average Number of Reporting Bits

11

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Probability of False Alarm QFA

Fig. 3. (1−Qd ) versus Qf a for different values of Δ relative to the decision threshold λ.

achieved at the cost of having a non-zero probability of failing to sense. The capabilities of this scheme can be optimized through proper selection of Δ and Q. However, this optimization process is not a trivial one as there are multiple objectives involved. In addition, the average sensing time in the presence of a non-zero probability of failing to sense needs to be investigated. These issues will be our future directions. R EFERENCES [1] A. Ghasemi and E. Sousa, “Collaborative spectrum sensing for opportunistic access in fading environments,” in First IEEE International Symposium on New Frontiers in Dynamic Spectrum Access Networks (DySPAN), 8-11 Nov. 2005, pp. 131 –136.

Fig. 4. Qf s versus Qf a for different values of Δ relative to the decision threshold λ.

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