Cooperative Energy Detection using Dempster-Shafer Theory under Noise Uncertainties

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1 Cooperative Energy Detection using Dempster-Shafer Theory under Noise Uncertainties by Prakash Gohain, Sachin Chaudhari in IEEE COMSNET 017 Report No: IIIT/TR/017/-1 Centre for Communications International Institute of Information Technology Hyderabad , INDIA January 017

2 017 9th International Conference on Communication Systems and Networks (COMSNETS) Cooperative Energy Detection using Dempster-Shafer Theory under Noise Uncertainties Prakash B. Gohain, Sachin Chaudhari Signal Processing and Communications Research Center, Center of Excellence in Signal Processing International Institute of Information Technology Hyderabad ids: Abstract Cooperative spectrum sensing (CSS) is one of the efficient scheme that helps in improving the spectrum sensing performance of a cognitive radio network. In this paper we propose a Dempster-Shafer theory (DST) based CSS for cognitive radio network. The fusion rule is the D-S combination rule which is well known for its ability to handle uncertainty and has been used in quite a different number of fields. Noise uncertainty, which is unavoidable in practical field, can gravely limit the detection performance of CSS. In this paper we specially investigate sensor nodes undergoing uncertainty in noise power when the detection scheme is based on energy of the received signal and use DS theory to minimize such effects. Simulation results reveal significant improvement in CSS gain as compared to previous traditional methods. Index Terms Cognitive radio, cooperative spectrum sensing, data fusion, Dempster-Shafer theory, noise uncertainty. I. INTRODUCTION Cognitive radio (CR) has been considered as one of the pillars for next generation communication technologies that is yet to become a reality. CR systems have the ability to increase the spectrum utilization through dynamic spectrum access provided that there are policies and legal rules allowing them to function within a specific paradigm [1]. Spectrum sensing is a key enabler for cognitive radios as it provides spectrum awareness to the cognitive radios. Several spectrum sensing techniques have been proposed in the existing literature such as energy detection, autocorrelation detection, and cyclostationary feature detection []. In this paper we have considered energy detection which is widely used for its simplicity and ability to detect any signal. On the other hand, in presence of uncertainty in the noise statistics, its performance degrades significantly and may also result in performance limitation in the form of the SNR wall phenomenon [3]. To overcome the degradation and issues caused by uncertainty, cooperative spectrum sensing (CSS) has been shown to be an effective method to improve detection performance by exploiting spatial diversity [4], [5]. In CSS, all the secondary users (SUs), which are basically local sensing nodes, transmit their sensing information to the fusion center (FC). At the FC, a suitable fusion rule is applied to combine these data and make a global decision. One of the commonly used fusion rule is the sum of energies from each SU. However under Neyman- Pearson criteria, the threshold for the fusion rule is designed assuming worst case noise variance leading to significant loss in detection performance as compared to no noise-uncertainty case [6]. The use of Dempster-Shafer theory (DST) in such case can improve the performance and the focus of this paper is to demonstrate it. A CSS scheme based on credibility and evidence (i.e., DST) for cognitive radios was first proposed in [7]. However the paper did not present the method to evaluate the credibility of different nodes before they are combined at the fusion center. In [8], a DST based CSS with double threshold spectrum sensing method was proposed. However such schemes heavily rely on the accuracy of threshold being used. Therefore such methods may fail drastically under noise power fluctuation. In [9] and [10], a CSS scheme based on DST is proposed where energy of the received signal is used to determine the basic probability assignment. The paper also proposed a method to utilize the credibility factor to measure the reliability of each spectrum sensors. However the optimality of scheme is not discussed. Note that none of the papers in spectrum sensing literature have addressed noise uncertainty using DST which is the focus of this paper. In this paper we propose a novel DST based cooperative energy detection (CED) in the presence of noise uncertainty. First a novel method is proposed to evaluate basic probability assignment (BPA) for each sensor using the conditional likelihood functions of the energies evaluated from the received observations. Next, a technique to discount the credibility of each node is proposed such that the discount factor depends on the range of uncertainty in the noise variance. These discounted beliefs are then fused using DST fusion rule at the FC. It is shown that under no uncertainty, the DST fusion rule based on the proposed BPA boils down to the optimal fusion rule of likelihood ratio. Later, performance of this scheme is compared with the traditional sum fusion rule, i.e., sum of energies from SUs assuming Neyman-Pearson detection criteria. The paper is organized as follows: In Section II we discuss the basic cooperative energy detection under noise uncertainty. Section III briefly discusses the basics of Dempster-Shafer theory of evidence. Next, in section IV, we present in detail the proposed DST based CSS method. Section V presents the simulation results while Section VI concludes the paper /17/$ IEEE 360

3 017 9th International Conference on Communication Systems and Networks (COMSNETS) II. COOPERATIVE ENERGY DETECTION UNDER NOISE UNCERTAINTY In this section we discuss the traditional cooperative energy detection in a CR network, taking into account the well known CSS model. The initial subsections describe normal CSS without any noise uncertainty. Then noise power uncertainty in energy detection is discussed and how it effects the threshold criteria at the FC is explained. A. System Model Fig. 1 shows the considered CSS which consists of a primary user (PU), U number of SUs and a FC. The SUs evaluate energy based on their local observation, evaluate the corresponding decision statistic and send them to the FC via reporting channel. On receiving the data from all the local SUs the FC will employ fusion rule to combine all the data and based on the detection criterion arrive at global decision. In this paper it is assumed that the reporting channels are errorfree while the listening channels are additive white Gaussian noise (AWGN) channels. Figure 1. Cooperative Spectrum Sensing model In a distributed detection scheme the presence or absence of a primary user on locally observed signal samples can be formulated as a binary hypothesis testing problem. There are two hypothesis H 0 and H 1, where H 0 denotes the absence of PU signal and H 1 denotes the presence of PU signal. Considering the received signal model as: x[n] = { w[n], H 0 s[n]+w[n], H 1,n=1,..., N where x[n], w[n], and s[n] are the samples of received signal, AWGN and PU signal, respectively while N is the number of received samples. The noise samples w[n] are assumed to be zero mean with variance σ w. It is also a complex circular symmetric Gaussian random variable with a real and imaginary part w r [n] and w i [n] i.e. w[n] =w r [n]+jw i [n]. Therefore w(n) N c (0,σ w) w r (n),w i (n) N(0,σ w/) Several PU signals such as OFDM signals, are Gaussian signals []. Therefore the PU signal s[n] is also assumed as (1) complex circular symmetric Gaussian random variable with zero mean and variance σs. Consequently x[n] is also complex circular symmetric Gaussian random variable with zero mean and variance σx, i.e., x[n] N c (0,σx) and thus for different hypotheses we have ( ) H 0 : x[n] N c 0,σ ( w H 1 : x[n] N c 0,σ s + σw ) () B. Cooperative Energy Detection The signal energy can be evaluated from N received samples by N E i = x[n] (3) n=1 The distribution of received signal energy under hypothesis H 0 and H 1 is [11], [1] { N ( Nσ E i w, N(σw) ), : H 0 N ( Nσw(1 + snr), N(σw) (1 + snr) ) (4) : H 1 where snr is the normal signal to noise ratio at the individual CR node and can be expressed as snr = σs/σ w. In traditional sum fusion rule, each SU i sends the computed energy value E i to the FC, which are then added so that the final decision statistic at the FC is given by U T sum = E i (5) while the detection is made by comparing with a threshold so that H 1 T sum η (6) H 0 where η is the threshold of a Neyman Pearson detector with some false alarm constraint of P fa = β. This threshold η depends on the distribution of T sum and value of β. The distribution parameters μ sum0 (mean) and σsum 0 (variance) of T sum under H 0 are evaluated as: μ sum0 = UNσw and σsum 0 = UN(σw). Therefore the expression for threshold η is: η =Q 1 (β)σ sum0 + μ sum0 = (7) UN(σw)Q 1 (β)+unσw C. Noise power uncertainty AWGN is present in all types of receivers and transmitters. In case of spectrum sensing using energy detector the noise power plays a very crucial role. Drastic or unprecedented changes in noise level can severely degrade the detector performance [13]. The noise variance solely determines the distribution of white Gaussian noise. Generally we assume that the noise variance is known a priori, but determining the exact noise variance to infinite precision is not possible. In an energy detector the threshold under hypothesis H 0 is determined based on the noise variance. However the noise power may change or fluctuate in actual practical field thus 361

4 017 9th International Conference on Communication Systems and Networks (COMSNETS) leading to noise power uncertainty. So under such conditions the appropriate way to denote noise variance is by using a interval that signifies the lower and upper limits of noise variance i.e. σw [ ] σw L σw U. In our work we assume a nominal noise variance σw n, so the noise uncertainty interval can be also expressed as [ ] (1/ρ)σw n ρσ wn, where ρ>1 is a parameter that quantifies the size of uncertainty [3]. The upper and lower noise limits are based on how much deviation from nominal noise variance is present in noise power, which is measured in terms of db. Therefore if the deviation is ±ΔdB then the extreme bounds are given as σw L = σw n 10 ( Δ/10) (8) σw U = σ wn 10 (+Δ/10) In normal conditions the noise uncertainty is in the range of 1 db in the absence of interference [14]. However, in the presence of interference from other sources, the value can be significantly higher. In energy detection using Neyman Pearson criterion under noise uncertainty, the primary objective is to maximize the probability of detection P d, for a fixed P fa = β. This is achieved by selecting the upper noise limit σw U as the noise variance for estimating the threshold at fusion center. This helps in ensuring P fa β under any noise variance σw L σw σw U. Therefore modifying (7) the threshold for the test statistic T sum at the FC under noise uncertainty becomes, UN(σ w )Q 1 (P fa )+UNσ w η = max σw [σ w,σ L w U ] = UN(σw U )Q 1 (P fa )+UNσw u (9) III. DEMPSTER-SHAFER THEORY (DST) OF EVIDENCE Our proposed CSS scheme is based on DS theory of evidence. Since DST is not very well known in the field of communication, hence understanding the basic concepts of DST is important in order to correlate it to the standard CSS schemes. eeping this in mind, we have dedicated this section to DS theory which briefly discusses the basics of DST. The theory of belief or evidence theory was first proposed by Arthur P. Dempster in 1960s in the context of statistical inference. The theory was later developed by his student Glenn Shafer into a frame work for modeling epistemic uncertainty thus giving the name Dempster-Shafer theory [15]. In DST if we have a set of hypotheses Θ={θ 1,θ,θ 3 }, then a function m : Θ [0, 1] is called a basic probability assignment (BPA) whenever m(φ) =0 m(a) =1 (10) A Θ Here φ denotes the empty set. The quantity m(a) is called A s basic probability number, and it is the measure of the belief that is committed exactly to A and not to any subset of A. The value of m(a) always lies between 0 and 1. Here Θ is called the frame of discernment. Thus basic probabilities are assigned not to the elements of Θ, but to the power set of Θ which is (φ, θ 1,θ,θ 3, {θ 1,θ }, {θ 1,θ 3 }, {θ,θ 3 }, {θ 1,θ,θ 3 }). This is a key difference between Bayesian theory and DS theory. There are two more functions associated with m. They are belief or credibility function Bel and plausibility function Pl defined for all A Θ as Bel(A) = m(b) (11) B A Pl(A) = A B φ m(b) (1) The function Bel(A) signifes the minimum support (lower bound) of one s belief that hypothesis A is true, while Pl(A) denotes the maximum support (upper bound) or belief that A can be true if more evidence is available. Dempster rule of combination enables us to compute the orthogonal sum of several belief functions over the same frame of reference but based on distinct bodies of evidence. If there are two independent sources say 1 and, with basic probability assignment m 1 and m and focal elements (or hypotheses) A 1,A,...A k and B 1,B,...B l respectively, then the combined total support for an element A is given as: m 1 (A i )m (B j ) m 1 (A) =m 1 (A) m (A) = where = A i B j φ A i B j=a (13) m 1 (A i )m (B j ) (14) Here represents the basic mass associated with conflict between different sources and is introduced as a normalization factor and the symbol denotes orthogonal sum. If there are n number of such distinct independent sources then the Dempster combination rule is as follows: m(a) =m 1 m... m n (A) m 1 (A 1 )...m n (A n ) m(a) = where = A 1,A,...,A n Θ A 1 A... A n=a A 1,A,...,A n Θ A 1 A... A n φ, (15) m 1 (A 1 )...m n (A) (16) IV. PROPOSED DST BASED CSS Fig. shows the framework for the proposed DST based CSS. First step in this approach is estimating BPA for different hypotheses based on the energy of the received signal. Next, BPA values for each sensor or SU are discounted based on the noise uncertainty interval. In the final step, these discounted BPA values are used in the DST fusion rule at the FC. These steps are explained in detail in this section. Towards the end of this section, we also provide a proof for the optimality of the proposed DST based CSS for no noise-uncertainty case. 36

5 017 9th International Conference on Communication Systems and Networks (COMSNETS) Figure. Framework for proposed DST based CSS A. BPA calculation In DST based spectrum sensing for cognitive radio, assigning the basic probability to the different hypothesis is a crucial part as the end decision very much depends on the correctness of how the BPA are assigned. In DST, there is no fixed rule for assigning BPA to sets/facts or hypothesis belonging to any field/case or situation. As such, in some scenario they are assigned by experts in that particular field, or a person with great experience or may be formulated by using some equation. Here we propose a novel BPA calculation method which is based on energy of the received signal. Let us define a frame of reference for a SU performing local sensing as Θ={H 0,H 1 }, where H 0 denotes the hypothesis that the PU is absent and H 1 hypothesis denotes its presence. Then the power set of Θ is given as {φ, H 0,H 1, {H 0,H 1 }}. Here φ is a null set and m(φ) =0always which basically means that at least one of the hypothesis will be true. The set ω = {H 0,H 1 } represents the uncertainty/ignorance or the fact don t know. Now according to DST, if we have a statistical specification {q θ } θ Θ with an observation x, then x lends plausibility to a singleton {θ} Θ in strict proportion to the chance that q θ assigns x. Therefore the plausibility function can be given as: Pl x (θ) =cq θ (x) (17) for all θ Θ, where constant c does not depend on θ and Pl x : Θ [0, 1]. Then the support function/bpa for the set/hypothesis A is given as: m(a) =1 Pl x (Ā) (18) In this context the observation x is nothing but the energy of the received signal E i at the i th SU. We define the plausibility for hypothesis H 0 and H 1 as Pl Ei (H 0 ) = cp(e i H 0 ) (19) Pl Ei (H 1 ) = cp(e i H 1 ) (0) where ( ) 1 P (E i H 0 )= exp (E i μ 0i ) πσ0i σ0i (1) ( ) 1 P (E i H 1 )= exp (E i μ 1i ) πσ1i σ1i () c is a quantity that normalizes the plausibility values. Therefore we propose c to be taken as: 1 c = (3) P (E i H 0 )+P(E i H 1 ) Using equations (19),(0) and (3) the BPA for the hypothesis H 0 at the i th SU is obtained as: m i (H 0 )=1 Pl Ei (H 1 ) P (E i H 1 ) =1 P (E i H 0 )+P(E i H 1 ) m i (H 0 )= P (E i H 0 ) P (E i H 0 )+P (E i H 1 ) (4) Similarly BPA for hypothesis H 1 and ω at the i th SU can be obtained as m i (H 1 )= P (E i H 1 ) P (E i H 0 )+P (E i H 1 ) (5) m i (ω) =1 m i (H 0 ) m i (H 1 ) (6) B. BPA adjustment under noise uncertainty A SU in general, is ignorant of noise uncertainty or noise power fluctuation which prevails in all energy based CR nodes. So as long as we do not feed any uncertainty information into the system (detector/fusion center), the sum of m i (H 0 ) and m i (H 1 ) will always be one i.e. m i (H 0 )+m i (H 1 )=1and m i (ω) will always be equal to 0. Now the question is how to include this uncertainty data in the system or specifically how to determine the support value for m i (ω). DST describes a discounting rule, that states that if we have a degree of trust of 1 α in the evidence as a whole, where 0 α 1, then α is adopted as a discount rate and reduce the degree of support for each proper subset A of Θ from m(a) to (1 α)m(a). Bel α (A) =(1 α)bel(a) (7) for all proper A Θ. Then Bel α is a support function. So under noise uncertainty conditions the new BPAs for each SU will be, ˆm i (H 0 )=(1 α i )m i (H 0 ) (8) ˆm i (H 1 )=(1 α i )m i (H 1 ) (9) 363

6 017 9th International Conference on Communication Systems and Networks (COMSNETS) where α i denotes discount rate for i th SU. Here ˆm i (H 0 )+ ˆm i (H 1 ) < 1, therefore the support for m i (ω) is obtained as m ( ω) = 1 ˆm i (H 0 ) ˆm i (H 1 ) = 1 (1 α i )[m i (H 0 )+m i (H 1 )] = 1 (1 α i ) m i (ω) = α i (30) Thus we find that the support for uncertainty set m i (ω) is same as the discount rate α i. Now value of α i may be similar or dissimilar for different CR nodes depending on their noise variance interval. However, since 0 α i 1, wehaveto make sure that under any noise uncertainty interval and any arbitrary nominal noise variance, the α i value should always be confined between 0 and 1. C. Determining discount rate α In our work we propose a method for determining discount rate α under noise uncertainty conditions. The discount rates are measured individually for every SU thus each SU will have its own unique discount rate α i, depending on the noise uncertainty interval associated with it. Therefore the first piece of information required for calculating α i is the noise uncertainty interval. Now, as already discussed before, under noise power uncertainty, the objective in Neyman Pearson criterion based energy detection is to maximize P di (probability of detection at i th SU) for a given value of P fi (probability of false alarm at i ith SU)=β i. To obtain the threshold γ i for a single SU (U=1) under noise uncertainty we proceed as follows: ( ) P fi max σw [σ w,σ L w U ] Q γ i μ 0i σ 0i ( ) γi Nσw β i = Q U Nσ wu γ i = Nσ w U Q 1 (β i )+Nσ w U (31) Therefore the threshold at the i th SU, γ i, is a function of β i and upper noise variance σw U. Under this condition, the maximum probability of detection P di is achieved, when σw = σw U and minimum P di for σw = σw L. Now based on this threshold values, we obtain the best case (σw = σw U ) and worst case (σw = σw L ) ROC curves for one single user. Once this is estimated, we calculate α i as a difference between best case and worst case P di values. α i (β i )=P di (β i ) σ wu P di (β i ) σ wl (3) This technique helps us in ensuring 0 α i 1. In this context it is important to note that the β i value used for calculating α i at each individual SU is nothing but the Pfa value used at the FC. Therefore we can write β i = β. Note that with change in signal to noise ratio (SNR) at the CR node and N value (number of samples), the ROC curves with [ also change ] for the same noise power uncertainty interval σ wl,σwu. Therefore we can say that αi is a function of three parameters viz. β, SNR and N. However, considering N to be fixed for a CR node, α i becomes a function of β and SNR as long as the noise uncertainty interval remains constant. Thus (3) can be modified as: α i (β,snr) =P di (β,snr) σ wu P di (β,snr) σ wl (33) D. Data fusion at FC The discounting method described above is performed at the FC. The BPA m i (H 0 ) and m i (H 1 ) from each SU i is adjusted with the corresponding discount rate α i, where α i is chosen on the operating P fa = β of the fusion center. For identical CR nodes we can assume α 1 = α =... = α U = α. But if the noise uncertainty interval is different for each SU i the discount rates will also differ accordingly. The BPA adjustment is done according to the equations (8) and (9). The D-S combination rule is used to fuse the BPA from the U SUs which gives us the total support M(H 0 ) and M(H 1 ) for hypothesis H 0 and H 1 respectively. m i (A i ) A M(H 0 )= 1 A... A n=h 0 (34) and m i (A i ) A M(H 1 )= 1 A... A n=h 0 (35) Finally test statistic at the FC is taken as T ds = M(H H 1) 1 λ, (36) M(H 0 ) H 0 where λ is the threshold. In the proposed DST based CSS scheme the threshold λ is a function of the false alarm rate at the FC i.e. β and snr value at the individual CR node. For determining threshold λ, we take α i =0. This is because in order to find the threshold values for different false alarm rates, we choose σw = σw U and σw U exactly known to us. E. Optimality under no noise uncertainty In this subsection we show that under no noise-uncertainty condition Δ=0, the proposed DST based fusion rule boils down to the optimal fusion rule of likelihood ratio (LR). Note for Δ=0,wehaveσ wl = σ wu, which along with (33) mean that α i = m i (ω) =0. Therefore for this case, the test statistics T ds becomes T ds = M(H 1) M(H 0 ) = = = m i(h 1) m i(h 0) P (E i H 1) P (E i H 0)+P (E i H 1) P (E i H 0) P (E i H 0)+P (E i H 1) P (E i H 1 ) P (E i H 0 ) (37) 364

7 017 9th 9th International International Conference Conference on on Communication Communication Systems Systems and and Networks Networks (COMSNETS) (COMSNETS) 017 which is the optimal LR test statistic. Note that the sum fusion rule given by (5) is also an optimal fusion rule for binary hypothesis testing problem in () [II], [16]. Therefore the detection performance of tests with TSlI1Tl and T d. will have same performance in the absence of noise uncertainty (~ = 0) which will mean that 0: = 0, i.e., there is no discounting. V. SIMULATION RESULTS For our simulations, we assume that the PU signal is a complex and circular symmetric Gaussian signal. The number of samples used for evaluating received signal energy is N = 300. The nominal noise variance ()~, is taken as I. The nominal SNR is defined as SNR = ~.~ / (}~'" while SNR (in db) is defined as SNR (db) = 10 10glO(SNR). The number of SU for CSS is chosen as U = 5. The number of realizations to estimate probability of detection is 50,000. In order to evaluate the performance of the proposed scheme, two noise-uncertainty intervals ~ = ±0.5 and ~ = ±0.5 are considered for simulations. Figure 4. Plots of upper bound on the probability of detection (Pdi ((3,snr),, ), lower bound on the probability of detection (Prli((3,snr),, 11'L ll'u ), and their difference function (3 values for ~ = Q (the discounting factor) as a ±0.5 db and SNR = -10 db. 5 and 6 show the Pel vs SNR [db] plots for (3 = 0.1 and (3 = 0. for the sum and proposed DST fusion rules. First observation from these figures is that under no noiseuncertainty (~ = 0, i.e., 0: = 0), the performances of both fusion rules overlap. This is inline with our discussion that for 0: = 0, both the test statistics Tsum and Tels are equivalent to the optimal LR test statistic. Second observation is that even for low values of noise-uncertainty of ~ = ±0.5dB and ~ = ±0.5dB, significant performance degradation can be seen for these fusion rules. However, proposed DST based approach significantly outperforms the traditional sum fusion rule in the presence of noise uncertainty. Figure 3. Plots of upper bound on the probability of detection (Pdi (13, snr ),, ), lower bound on the probability of detection!i'l] (Pdi ((3, snr),, ). and their difference Q (the discounting factor) as a H'I" function (3 values for ~ = ±0.5 db and SNR = -10 db. In the first phase of simulation, we estimate the n values for a given false alarm and SNR. Fig. 3 shows the upper and lower bounds on the probability of detection Pel at the local detector given by P'ii((3, snr)ah'lt and Peli((3,' snr)a,respectively, for IJ'L ~ = ±0.5 and SNR = -10 db. The 0: is the difference between these two bounds given by (33) and is also shown in Fig. 3. Since we are considering identical SU, therefore the O:i value for all the CR nodes will be equal. Fig. 4 shows similar curves for for ~ = ±0.5 and SNR = -10 db. Figs. 3 and 4, it can be seen 0: takes higher values for higher values of ~, which indicates increase in the discounting rate with increase in amount of noise uncertainty. Once the alpha values are determined as a function of (3 and SNR, we proceed for Pel vs SNR simulations. Figs. Figure 5. Probability of detection (Pd ) vs SNR [db] curves for U = 5, ~ = ±0.5 db and (3 = 0.1. Here Q = 0 curves refer to the case of no noise uncertainty

8 017 9th 9th International International Conference Conference on on Communication Communication Systems Systems and and Networks Networks (COMSNETS) (COMSNETS) 017 Figure 6. Probability of detection (Pd ) vs SNR [dbj curves for U = 5, 6 = ±0.5 db and f3 = 0.. Here ex = 0 curves refer to the case of no noise uncertainty. ACNOWLEDGEMENT This work was supported by the Science and Engineering Research Board, Department of Science and Technology, India under grant no. ECRJ0 15/ VI. CONCLUSION In this paper we have proposed a novel scheme based on DST to deal with noise power uncertainty in energy-based cooperative spectrum sensing. A modified scheme is proposed for BPA estimation, which ensures that under no uncertainty condition (~ = 0), the DST based CSS fusion rule boils down to the optimal LR test. A new method is also proposed to determine the discount rate Ct, which effectively takes into the effect of uncertainty in the noise variance. Moreover we show that under the proposed BPA estimation scheme, the support for uncertaintylignorance set m.(w) is always equal to discount rate Ct. Simulation results demonstrate that the proposed scheme significantly outperforms the traditional sum fusion rule in the presence of noise-uncertainty while they have the same performace in the absence of any noise-uncertainty. [5] S. Chaudhari, J. Lunden, Y. oivunen, and H. Y. Poor, "Cooperative sensing with imperfect repolting channels: Hard decisions or soft decisions?" IEEE Transactions 0/1 Signal Processing, vol. 60, no. I, pp. 18-8, Jan 01. [6 J J. Zeng and X. Su, "On snr wall phenomenon under cooperative energy detection in spectrum sensing," in 10th Int. Conj: on Comm. and NeiH'. China: IEEE, 015, pp [7] P. Qihang, Z. un, W. Jun. and L. Shaoqian, "A distributed spectrum sensing scheme based on credibility and evidence theory in cognitive radio context," in 006 IEEE 17th Imernational Symposium on Personal, Indoor and Mobile Radio COlllmunications, Sept 006, pp [8] J. Li, J. Liu, and. Long, "Reliable cooperative spectrum sensing algorithm based on dempster-shafer theory," in Global Telecollllllunications Conference (GLOBECOM 010), 010 IEEE, Dec 010, pp [9] N. Nguyen-Thanh and I. oo, "An enhanced cooperative spectrum sensing scheme based on evidence theory and reliability source evaluation in cognitive radio context," IEEE Communications Letters, vol. 13, no. 7, pp , July 009. [10] N. N. Thanh and I. oo, "Evidence-theory-based cooperative spectrum sensing with efficient quantization method in cognitive radio." IEEE Transactions on Vehicular Technology, vol. 60, no. I, pp , Jan 011. [II] Z. Quan, S. Cui, and A. H. Sayed, "Optimal linear cooperation for spectrum sensing in cognitive radio networks," IEEE journal of selected topics in signal processing, vol., no. I, pp. 8-40, 008. [1] R. Umur, A. U. H. Sheikh, and M. Deriche, "Unveiling the hidden assumptions of energy detector based spectrum sensing for cognitive radios," IEEE Communications Surveys Tutorials, vol. 16, no., pp , Second 014. [13] Y. Zeng, Y.-c. Liang, A. T. Hoang, and E. C. Peh, "Reliability of spectrum sensing under noise and interference uncertainty," in 009 IEEE InfematiOlwl Conference 011 Communicatiolls Workshops. IEEE, 009, pp [14] S. Shellhammer and R. Tandra, "Performance of the power detector with noise uncertainty," IEEE Std /0134rO. [J 5] G. Shafer, A Mathematical Theor\' of Evidence. Princeton university press, [16J S. ay, Fundamental o{statistical Sigllal Processing: VillufIle 1I Detection Theon'. Prentice Hall, J 998. REFERENCES [I [1. F. Akyildiz, W-Y. Lee, M. C. Vuran, and S. Mohanty, "Next generation/dynamic spectrum access/cognitive radio wireless networks: A survey," Computer Nel\\'orks, vol. 50, no. 13, pp , 006. [OnlineJ. Available: I 009 [] S. Chaudhari, "Spectrum sensing for cognitive radios: Algorithms, performance, and limitations," Ph.D. dissertation, School of Electrical Engineering, Nov. 01. [3] R. Tandra and A. Sahai, "Snr walls for signal detection," IEEE journal of Selected Topics in Signal Processing, vol., no. I, pp. 4-17, Feb 008. [4] 1. F. Akyildiz, B. F. Lo, and R. Balakrishnan, "Cooperative spectrum sensing in cognitive radio networks: A survey," Physical Communication, vol. 4, no. I, pp. 40-6,011. [OnlineJ. Available: X