Coded Collaborative Spectrum Sensing With Joint ... - IEEE Xplore

IEEE TRANSACTIONS ON WIRELESS COMMUNICATIONS, VOL. 14, NO. 4, APRIL 2015

2017

Coded Collaborative Spectrum Sensing With Joint Channel Decoding and Decision Fusion Marwan Hadri Azmi, Member, IEEE, and Harry Leib, Senior Member, IEEE

Abstract—This paper considers the integration of channel decoding with fusion based decision, for coded collaborative spectrum sensing (CSS) employing local Neyman-Pearson (NP) testing at each sensor. We derive a belief-propagation (BP) algorithm for joint channel decoding and decision fusion (JCDDF), based on a factor graph model for coded CSS schemes. Using the Lloyd-Max method, we also propose a new methodology for the local sensor to quantize its observation. The design of the quantizer embeds the binary NP test outcome in the quantization bits. Using the JCDDF algorithm, we show that coded CSS paired even with a short (8,4) extended Hamming code outperforms not only uncoded CSS, but also schemes where channel decoding and decision fusion are executed separately. Then, we consider the design of good channel codes for such CSS schemes. We demonstrate that the JCDDF algorithm employing unequal error protection (UEP) coding improves performance and outperforms equal error protection coding. Furthermore, we present a simple code search algorithm for identifying short UEP codes. Using such UEP codes, we finally show that a performance improvement over uncoded CSS can be attained also without bandwidth expansion using higher order modulations. Index Terms—Spectrum sensing, cognitive radio, belief propagation, unequal error protection (UEP), Neyman-Pearson test, Lloyd-Max quantization.

I. I NTRODUCTION

S

PECTRUM sensing is a key component in cognitive radio (CR) systems. Cooperative, or collaborative, spectrum sensing (CSS) addresses the hidden terminal problem [1] in CR systems, and hence improves the reliability of detecting a primary user (PU) signal. A CSS scheme can be considered as a distributed detection wireless sensor network, where each sensor node (SN) makes a local decision that is reported to a fusion center (FC) for final decision making called decision fusion [2]. The design of optimal and suboptimal local decision and fusion rules has been well investigated in the wireless sensor networks literature. Most of the earlier studies consider error free reporting SN-FC channels, e.g. see [3]–[5] for more extensive references. Distributed detection with imperfect

Manuscript received March 31, 2014; revised August 14, 2014; accepted November 17, 2014. Date of publication December 8, 2014; date of current version April 7, 2015. The associate editor coordinating the review of this paper and approving it for publication was W. Choi. M. H. Azmi was with the Department of Electrical and Computer Engineering, McGill University, Montreal, QC H3A 0E9, Canada. He is now with the Wireless Communication Centre, Universiti Teknologi Malaysia, Johor Bahru 81310, Malaysia (e-mail: [email protected]). H. Leib is with the Department of Electrical and Computer Engineering, McGill University, Montreal, QC H3A 0E9, Canada (e-mail: harry.leib@ mcgill.ca). Digital Object Identifier 10.1109/TWC.2014.2378789

reporting channels brings new challenges in optimizing the local decision and fusion rules. In a parallel fusion problem with noisy reporting channels, the optimality of the likelihood ratio test (LRT) is investigated in [6]. The fusion problem with fading and noisy reporting channels is studied with channel state information (CSI) in [7] and without CSI in [8]. Multiple access SN-FC channels are considered in [9], and virtual multiple-input multiple-output SN-FC channels where the FC is equipped with multiple antennas are considered in [10]–[12]. Initial studies of CSS schemes assume error free SN-FC reporting channels. The schemes in such early works can be divided into two classes: hard decision combining schemes employing fusion methods such as logical AND, OR and Mout-of-K rules [13], [14], and schemes employing soft decision combining techniques such as those based on LRT approaches [14], [15] and summation of SNs received signal energies [16]. Noisy SN-FC channels in CSS schemes are considered in [17]–[19]. Among these works, [19] provides an insight into statistical collaborative sensing using a new probabilistic inference approach. The concept behind this approach is to probabilistically model a CSS scheme by a factor graph (FG), and consider decision fusion as a probabilistic inference problem that can be tackled using belief propagation (BP) algorithms. The results in [19] demonstrate that probabilistic inference outperforms conventional approaches such as AND, OR, M-outof-K, maximal ratio combining and selection combining. The BP algorithms have been used for spectrum sensing in a variety of related problems, such as heterogeneous detection [20]–[22]. The concept of integrating channel decoding and fusion has been proposed initially for sensor networks using lowdensity generator matrix (LDGM) codes [23]. This idea has been extended using a scalable joint decoding and data fusion algorithm for star-type networks based on low-complexity concatenated Zigzag codes [24], where Zigzag-based data fusion not only has a lower encoding and decoding computational complexity, but also outperforms LDGM-based data fusion [23]. Further performance improvement, especially by lowering the error floor [23], [24], can be obtained using concatenated BCH-LDGM codes [25]. Here, LDGM codes can efficiently exploit the intrinsic spatial correlation between the information gathered by the sensors, whereas BCH codes can lower the error floor. In [26], the problem of joint decoding and data fusion has been studied in data gathering sensor networks, modeled as the Chief Executive Officer problem, using turbo codes. In this study, at the FC two vertical soft-in soft-out decoders and two horizontal decoders, associated with each SN, iteratively exchange and update extrinsic information applying the knowledge of correlation among sensors’ data. Finally, [27] studies

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Fig. 1. Block diagram of a collaborative spectrum sensing scheme.

simple distributed channel coding schemes for sensor networks, focussing on possible strategies to combine the decoding and fusion operations at FC. While previous works [19]–[22] applied the BP algorithm to CSS, none has considered the integration of decision fusion with channel decoding. In other words, all decisions made at the local SN are forwarded to FC through noisy SN-FC channels without forward error correction (FEC) coding. In CSS, decoding of a channel code and final decision making based on fusing local decisions from SNs can be viewed as instances of inference done separately. The objective of channel decoding is to infer the transmitted data from collaborating SNs, while the objective of the final decision, based on fused local decisions, is to infer about the state of the PU frequency band that is being sensed. The outcome of the first inference process, i.e. channel decoding, is only an intermediate result since we are really interested in the outcome of the second inference process. Another approach is to view channel decoding and final decision making as one inference process, resulting in joint channel decoding and decision fusion (JCDDF). Conceptually, there is a similarity between the JCDDF framework for CSS and distributed joint source-channel coding (DJSCC) for relay systems [28]. Aimed at minimizing the endto-end distortion in relay systems, a DJSCC algorithm recovers the source output by solving the allocation problem of bits used to describe the original source, and coding bits combating channel errors. In CSS, the original source is the availability of the PU signal modeled as a binary random variable (RV). This binary source is observed by the SNs using a decision statistic RV that is quantized and protected by channel coding bits for transmission to the FC. The JCDDF framework aims at solving the detection problem of the PU being active or not, by allocating efficiently the quantization bits and the channel coding bits at the SNs. The JCDDF framework setting is slightly different than DJSCC in the sense that the original binary source is observed through a channel before encoding. A related approach is studied in the context of distributed energy generation (DEG) in microgrid, where a channel code is used to protect the quantized observation of the system state information (SSI), i.e. the original source [29]. However, while the observation at the SN in CSS can be viewed as a noisy RV that requires a LRT for detecting the original binary source, the observation in DEG naturally forms a convolutional code due to the linear dynamics of the system state. Hence in DEG, further protecting the quantized observation with another channel code forms a

concatenated structure, where the SSI is decoded iteratively using the BP algorithm. In this work, we study the advantages of combining channel decoding and fusion based decision into one algorithm for CSS with local binary Neyman-Pearson (NP) testing at each SN. Similarly to [30]–[32], we assume time synchronized operation, with nodes transmitting over orthogonal channels, avoiding inter-node interference. Synchronization could be achieved, for example, by the use of a Global Positioning System (GPS) receiver, a technology that at present is implemented in many commercial user terminals. However, there are also synchronization techniques, not requiring each node to have a GPS receiver [33]. Specifically, this paper addresses two fundamental questions concerning JCDDF for CSS schemes: (1) Does this joint algorithm outperforms separate channel decoding and decision fusion (SCDDF)? (2) What are good channel codes for such a joint algorithm? The contributions of this paper are threefold. The first is a new quantization method for the SN, where the local NP test decision is embedded as the most significant bit (MSB). The second contribution is the derivation of the BP algorithm for JCDDF with application to CSS. The third contribution is the design of good short codes for JCDDF when used in CSS based on unequal error protection (UEP). Furthermore, we also present a simple search algorithm for finding good short UEP codes. The continuation of this paper is organized as follows. Section II presents the system model and basic definitions. In Section III, we propose a methodology for each SN to quantize its local observation based on the Lloyd-Max technique. Next, we develop the JCDDF procedure by deriving the FG and BP algorithm in Section IV. Section V addresses the complexity of the JCDDF procedure. In Section VI, we derive an upper bound to the performance of CSS with energy detection. A linear UEP code is discussed and a simple code search algorithm is presented in Section VII. Section VIII presents Monte-Carlo simulation results concerning the performance of JCDDF for CSS. Conclusions and future directions are discussed in Section IX. II. S YSTEM M ODEL Consider a CSS scheme with one source (i.e. one PU), K > 1 local SNs, and a FC, as illustrated in Fig. 1. Let the sensors be indexed by 1, 2, . . . , K, and define the set K = {1, 2, . . . , K}. The CSS scheme solves a binary hypothesis testing problem between hypotheses H0 (PU not active) and H1 (PU active). To

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solve this binary hypothesis problem, the FC collects information from all K SNs. Let xk = [x1,k , x2,k , . . . , xN,k ], ∀ k ∈ K , be the complex baseband input signal vector to the measuring device at the k-th SN, resulting from the observation of the PU signal over N sampling intervals. The probability density function (PDF) of the local observation vector xk under hypothesis H j , for j = {0, 1}, is denoted by p(xk |H j ). We use p(·) and P(·) to denote the PDF and probability mass function (PMF), respectively. We also make no distinction in denoting a RV and its value for the sake of simplicity. Let ϑ(·) be the function used by the measuring device to map the observation vector onto an one dimensional test statistic. Then the output of the k-th measuring device can be written as yk = ϑ(xk ), ∀ k ∈ K . The role of the testing device is to utilize the test statistic provided by the measuring device to make a local decision about the state of the PU signal. This local binary hypothesis problem is solved under the NP framework that employs the LRT L1,0 (yk ) =

p(yk |H1 ) , p(yk |H0 )

(1)

where p(yk |H j ) is the PDF of yk under hypothesis H j , for j = {0, 1}. The k-th SN decides H1 if and only if L1,0 (yk ) ≥ λk , where the threshold λk can be found for a given local (k) probability of false alarm Pf l from (k) Pf l



= yk :L1,0 (yk )≥λk

p(yk |H0 ) dyk .

(2)

We model the test statistics yk under hypotheses H0 , H1 as Gaussian RVs. This model is widely used in spectrum sensing, especially when the measuring device is an energy detector [34]–[36]. According to the central limit theorem (CLT) [37], for a large number of sensing samples N the output of an energy detector is well approximated as Gaussian distributed [38]. Hence the PDF of yk under hypothesis H j is   (yk − µ j )2 1 exp − p(yk |H j ) =  for j = {0, 1}, (3) 2σ2j 2πσ2 j

where µ0 = Nσ2wk , σ20 = 2Nσ4wk , µ1 = N[P1 σ2gk + σ2wk ], and σ21 = 2N[P1 σ2gk + σ2wk ]2 [19]. Here, σ2gk corresponds to the channel gain between the PU and k-th SN, and P1 is the power of the PU baseband signal. Furthermore, the background noise at k-th SN is modeled as additive circularly symmetric complex Gaussian (CSCG) [39] with zero mean and variance σ2wk . Hence, the signal-to-noise ratio (SNR) for the PU to the k-th SN channel is defined as SNR1,k = P1 σ2gk /σ2wk . In this work, we consider a wireless communication link between the SN and FC, where the computed log-likelihood ratio (LLR) at the SN is quantized, and sent to FC. The FC then makes the final decision based on these quantized LLRs. Let d be the number of bits available for quantizing the LLR, and D = 2d be the number of quantization levels. Let lk and ¯lk denote the computed and quantized LLR, respectively. The quantized LLR ¯lk can assume the values ¯lt,k , where t ∈ {1, . . . , D}, and (t) (t) (t) uk = [ud,k , . . . , u1,k ] denotes the corresponding binary word (refer to Fig. 2).

Fig. 2. An example of 3 bits quantizer for generating uk from lk . The LloydMax technique is used in each region H0 ,H1 using two different conditional PDFs p0 (lk |lk < λ˘ k ) and p1 (lk |lk > λ˘ k ).

The binary vector uk = [ud,k , . . . , u1,k ], where ui,k = {0, 1}, of the k-th sensor is then encoded by a (nc , d) linear block code, where nc is the code length, d/nc is the code rate, and nc ≥ d. Let C ⊂ Bnc be the set of 2d distinct codewords that defines the code, where B = {0, 1}. The encoding of the vector uk onto a codeword ck = [c1,k , . . . , cnc ,k ] can be written as ck = uk · G, where G is the d × nc generator matrix. The codeword ck is then mapped to a vector of symbols from a two-dimensional signal constellation Ω of size M = |Ω|. The bits in ck are grouped into consecutive blocks of length m = log2 M, each mapped onto a constellation point mk ∈ Ω, resulting in a vector mk of ns = nc /m coded symbols. We assume that nc and M are selected such that ns is an integer. Denoting the mapping function as ψ(·), we can write mk = ψ(ck ), ∀ k ∈ K . The modulated signal vectors mk ∀ k ∈ K are sent over independent channels to the FC. The channel between the k-th SN and FC is characterized by the PDF p(rk |mk )∀ k ∈ K , where rk is the received signal at the FC from the k-th sensor. This yields K parallel received vectors {rk }Kk=1 at the FC, which can be used to decide on one of the hypotheses H j , j = {0, 1}. Assuming the SNs employ an orthogonal multiple access scheme, the received vector rk at the FC from the k-the SN can be modeled as rk = mk + nk ,

∀k ∈ K ,

(4)

where nk ∼ C N (0, σ2nk I) is a CSCG noise vector, I is an identity matrix, and each SN employs transmission power P2 . The SNR for the k-th SN to FC channel is defined as SNR2,k = P2 /σ2nk . III. Q UANTIZATION OF LLR AT THE S ENSOR N ODES Quantizer designs for SNs is a subject that has been addressed in the literature. The optimum 1-bit hard decision quantizer is equivalent to finding optimum decision thresholds under the Bayesian [6] and NP [40] criteria. Instead of making only a hard decision, the SN can quantize the decision statistic using

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multi-bit uniform [41] or Lloyd-Max [42] methods. While the Lloyd-Max method is applied in [42] under a Bayesian criterion, we propose a new multi-level quantizer adopting the Lloyd-Max method under a NP criterion, which is more compatible for spectrum sensing since the priors P(H j ) in the CR system are normally unknown. To design an optimum quantizer for each SN, we require the PDF of the LLR. Using (1) and (3), the LLR can be expressed as       p(yk |H1 ) σ0 (yk −µ0 )2 (yk − µ1 )2 lk = ln − = ln + , (5) σ1 p(yk |H0 ) 2σ20 2σ21 where ln(·) denotes the natural logarithm. After some algebra, the LLR in (5) can be written as lk = s(yk ) = A · y2k + B · yk +C, where A =

SNR1,k (SNR1,k +2) , 4Nσ4w (SNR1,k +1)2 k

B = − 2σ2

SNR1,k

wk (SNR1,k +1)

(6) and C =

− ln(SNR1,k + 1). By applying the RV transformation theorem [43], the PDF of the LLR can be derived from (3) and (6) as p(yk |H j ) for j = 0, 1, (7) p(lk |H j ) = ∑  r |s (yk )| y =y(r) k

k

where s (yk ) is the first derivative of s(yk ) from (6), and yk is B2 , the r-th solution of (6) for the corresponding lk . For lk ≥ C − 4A √ 2 −B± B −4A(C−l ) (r) k , and the quadratic (6) has two solutions yk = 2A hence the PDF of the LLR in (7) has two terms in the sum. Now, we propose a method for quantizing lk such that the MSB of the quantization vector uk is always the local decision of the NP test, i.e. ud,k = 1 and ud,k = 0 if the SN decides H1 and H0 , respectively. The two associated decision regions are: the region where lk < λ˘ k denoting the decision region of H0 , and lk ≥ λ˘ k denoting the decision region of H1 . Here λ˘ k = ln(λk ) is the local NP threshold at k-th SN. Once the MSB bit is determined, the remaining d − 1 quantization bits are used to indicate the distance between lk to the local threshold λ˘ k . We call these d − 1 quantization bits as the reliability information. To determine the optimum sets of quantization levels ¯lk and associated thresholds bk in each decision region, we employ the Lloyd-Max technique. The pair of quantization levels ¯lk = {¯l0,k , . . . , ¯lD/2−1,k } and thresholds bk = {b0,k , . . . , bD/2,k } for the decision region of H0 can be found by designing a d − 1 bits Lloyd-Max quantizer using the conditional PDF

p(lk |H0 ) for lk < λ˘ k p0 (lk |lk < λ˘ k ) = Pr[lk λFC |H1 ) =



λFC P1 σ2g +σ2w

(33)

where η is the threshold determined by a given probability of false alarm Pf at the FC. Since we assume that yk ’s are independent, using (31) and (32), the LR in (33) can be expressed as

∑ σ2w (SNR1,k + 1) yk ≷ α,



(35)

H0

where α = ln(η) + N ∑Kk=1 ln(1 + SNR1,k ). In general, the local SNs are to work under different per(k) formance requirements (local probabilities of false alarm Pf l

VII. U NEQUAL E RROR P ROTECTION C ODES Since the MSB bit contains the NP test output, it is desirable to provide more error protection for this bit than to reliability information. We consider unequal error protection (UEP) codes that achieve this task and can be used with the JCDDF algorithm. Consider first the notion of protection level. The i-th digit of a UEP code has protection level fi if it can be decoded correctly even though the entire codeword may be decoded incorrectly when no more than fi errors occur. Based on Lemma 5 in [53], the highest possible protection level fi for any i-th information bit of a linear (nc , d) code can be determined from the number of parity checks, i.e. fi ≤ (nc − d)/2 . Then Lemma 1 in [53] concludes that the weight of an arbitrary codeword with nonzero i-th information bit must be at least 2 fi + 1 for the i-th information bit of a (nc , d) linear code to have a protection level fi . For our code searching procedure, Lemma 5 in [53] serves as the design criterion, while Lemma 1 in [53] is used to determine the protection level f1 of the MSB bit by checking the weight of 2d−1 codewords associated with a nonzero MSB information bit of a particular UEP code from the search space. We add additional constraints when searching for UEP codes. The first constraint is to limit the search to only systematic codes with generator matrices of the form

(k)

and detection Pdl ) optimized based on the PU-SN channels’ SNR1,k . However, in practice, SNR1,k can be assumed to change in a bounded range. Hence, assuming an optimal setup where local SNs experience the highest similar SNR1,k in the possible range, guarantees an upper bound to the sensing performance. Thus, assuming that all K PU-SN channels experience equal SNR1,k = SNR1 and also σ2wk = σ2w , the test becomes K

YFC =

α · σ2w (SNR1 + 1) = λFC . SNR1 H0 H1

∑ yk ≷

k=1

(36)

The test of (36) consists of comparing the summation of all measured energies yk from local SNs to a threshold λFC determined by the Pf . Using (30), this summation can be further expressed as ⎧ σ2w ⎨ K K N k · χ1 under H0 2 YFC = ∑ yk = ∑ ∑ |xi,k | = P σ2 +σ22 (37) 1 gk ⎩ wk k=1 k=1 i=1 · χ under H , 1 1 2 where the RV χ1 follows a central chi-square distribution with 2NK degrees of freedom. Hence, the probabilities of false alarm Pf and detection Pd at the FC can be computed using [52]   Γ KN, λσFC 2 wk (38) Pf = P(YFC > λFC |H0 ) = Γ(KN)

G = [Id P],

(40)

where Id represents a d × d identity matrix and P corresponds to the d × (nc − d) parity matrix. Using (40), the problem of finding UEP codes with f1 protection level for the MSB bit is equivalent to designing a proper P matrix. We adopt a brute-force method for testing all possible matrices P to find the required UEP codes. There are a total of 2d×(nc −d) matrices over {0,1} of size d × (nc − d) [54]. Let pi denote the i-th column of P for i = 1, 2, . . . , nc − d. A vector pi of length d over {0,1} can assume 2d − 1 forms excluding the all zero vector. Allowing an all zero column in our search algorithm would reduce the length of the UEP code. Let Z be the set of all 2d − 1 valid vectors for pi . Notice that some of the matrices P may be equivalent. For example a matrix P generated by permuting or re-ordering the columns of another matrix P results in equivalent G = [Id P] and G = [Id P ] matrices representing similar codes with different order of parity bits in codewords. The number of distinct P matrices is determined by computing the number of unordered selections with unlimited repetitions of nc − d objects from a set Z of 2d − 1 objects [55], also known as the (nc − d)-selection of Z, and is given by [54]  d  (2d + nc − d − 2)! 2 + nc − d − 2 . (41) nP = = d nc − d (2 − 2)!(nc − d)!

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It turns out that the search space is manageable for designing short block length UEP code, e.g. there are only nP = 38760 possible P matrices for searching the (10,4) UEP codes. The second constraint further reduces the search space by excluding any nP unordered P matrices containing at least one row of all zeros. Let us illustrate the reason behind this exclusion with an example. For nc = 6 and d = 4, the generator matrix G1 of a systematic code with a matrix P having all zeros in its last row is ⎤ ⎡ 1 1 1 0 0 0 1 0⎥ ⎢0 1 0 0 (42) ⎦. ⎣ 0 0 1 0 1 1 0 0 0 1 0 0 As a result of having this condition, the last information digit in vector uk is not included in the parity checks. Hence among the nP unordered P matrices, we only consider matrices without all zeroes rows in our search space. The search algorithm for (nc , d) UEP codes with protection level f1 for the MSB bit can be summarized as follows: 1) Set the protection level of the MSB bit to f1 ≤ (nc − d)/2 . 2) Generate all possible Pi matrices, i = 1, . . . ., nP . Let κ be the set of all generated Pi matrices. 3) Remove from set κ any Pi matrix containing an all zeros row. 4) For each remaining Pi in set κ, generate codewords ck = uk · Gi where Gi = [Id Pi ], for all 2d−1 information bit vectors uk with MSB bit equal to 1. 5) Keep Gi as one of the UEP codes with protection level f1 for the MSB bit if the weight of all 2d−1 codewords ck from step 4 is greater than or equal to 2 f1 + 1. The final outcome of our code search algorithm is a set of UEP codes with f1 protection level for the MSB bit. As we are applying a brute-force method of testing all possible P matrices, the search space of the proposed algorithm increases with the code length. For longer UEP codes, we begin by designing short UEP codes using our algorithm, and then the code extension method of [56] is used to further increase the protection level for the MSB bit. VIII. S IMULATION R ESULTS This section presents Monte-Carlo simulation results demonstrating the performance of the JCDDF technique for spectrum sensing. In these simulations, we set P1 = 1, σ2gk = 1, N = 500, and hence, SNR1,k = 1/σ2wk . Initially we assume all PU-SN (dB) channels have equal SNR, weak PU signals all with SNR1,k = −10 dB, and K = 5 collaborating sensors. The SN power is set to P2 = 1 resulting in SNR2,k = 1/σ2nk . Fig. 5 illustrates the PDF of the LLR under hypotheses H1 and H0 for this case. The PDFs of the LLR in Fig. 5 are generated from (3) and (7). We see that the PDFs of the LLR under hypotheses H1 and H0 are not Gaussian. Monte-Carlo simulations are performed using Matlab to obtain pairs of probabilities of false alarm Pf and detection Pd at FC by setting several thresholds λFC in (28), such that a

(dB)

Fig. 5. The distribution of LLR under H0 and H1 for SNR1,k = −10 dB of PU-SN channel, P1 = 1, σ2hk = 1 and N = 500.

Fig. 6. The ROC curves comparing the uncoded case with different number (dB) (k) of quantization bits for SNR1,k = −10 dB, N = 500, Pf l = 0.1 and Eb/No = 13 dB.

Receiver Operating Characteristic (ROC) curve can be plotted. The Pf and Pd are computed by generating Gaussian RVs yk for each SN from p(yk |H0 ) and p(yk |H1 ), respectively. Using the generated yk , each k-th SN performs a local NP test, produces the quantized bits uk , and forms the codewords ck . Then ck from all K SNs are transmitted through noisy SNFC channels and the LRT in (27) is computed. Each (Pf , Pd ) point in the ROC curve is estimated from at least 2000 error events at the FC, defined as deciding H1 when the PU is not active for Pf , or deciding H0 when the PU is active for probability of miss detection Pm = 1 − Pd . The JCDDF is performed with 5 local channel decoding iterations. We found that using more than 5 local iterations does not provide any further improvement. We first consider the effects of quantizing the test statistics at each SN using our proposed quantizer for uncoded CSS with

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Fig. 7. The ROC curves comparing the uncoded case with different number (dB) (k) of quantization bits for SNR1,k = −10 dB, N = 500, Pf l = 0.3 and Eb/No = 13 dB.

Binary Phase Shift Keying (BPSK) modulation. Figs. 6 and 7 depict the ROC curves when the local probabilities of false (k) (k) alarm at k-th SN are Pf l = 0.1 and Pf l = 0.3, respectively, for SN-FC channels of Eb/No = 13 dB. We see that quantization with d = 4 is sufficient to operate very close to the (k) upper bound of Section VI for both Pf l . We also see that the ROC curves for d = 1 have less points with long interpolation line. The SN-FC channels with high Eb/No = 13 dB produce an effect equivalent to an error-free channel where the local decision at each SN can be recovered perfectly at the FC. Fig. 8 shows that indeed the ROC curve for SN-FC channel of Eb/No = 13 dB is approaching the upper bound assuming (k) error-free SN-FC channels for Pf l = 0.1 and d = 4. For d = 1 and K = 5, there are only 6 values for the likelihood ratios (LRs) of (27) corresponding to the combinations of 5 perfectly recovered bits of local decisions u5 = {u1,1 , u1,2 , u1,3 , u1,4 , u1,5 } from all SNs, where ui,k = {0, 1}. These 6 LRs correspond to the situations when 0, 1, 2, 3, 4 or all 5 SNs decide H1 . Here, the ordering on which SNs decide H1 does not matter because all SNs experience similar SNR1,k , e.g. similar LR is obtained for u5 = {0, 0, 1, 0, 1} or u5 = {1, 0, 0, 1, 0}. Since there are only 6 LRs, there can only be 7 points on the ROC curve, each point corresponds to the different threshold λFC defining the decision region. In Figs. 6 and 7, not all 7 points are included due to the scaling of the plot. The two obvious points that are not in the figures are (Pf , Pd ) = (0, 1) and (Pf , Pd ) = (1, 0). Notice that points on the interpolation lines of the ROC curve can be achieved by a two way randomized LRT. Fig. 8 illustrates the effect of SN-FC channel quality on the sensing performance of uncoded CSS. We observe that the ROC curves at the FC improve when the quality of SN-FC channel increases. The upper bound in Fig. 8 is derived in Section VI assuming that each SN transmits its observation through a noise free channel to the FC. We hope to reduce the effects of noise on the SN-FC channels and approach such performance with channel coding.

Fig. 8. The ROC curves comparing the uncoded collaborative spectrum sens(dB) ing schemes with different SN-FC channel qualities for SNR1,k = −10 dB, (k)

N = 500, Pf l = 0.1 and d = 4.

Fig. 9. The ROC curves comparing the uncoded CSS, the SCDDF, and (dB) (k) JCDDF algorithms for SNR1,k = −10 dB, N = 500, Pf l = 0.1 and Eb/No = 3 dB. Both SCDDF and JCDDF algorithms are executed using (8,4) extended Hamming code.

Next, Fig. 9 presents simulation results for the JCDDF and SCDDF algorithms with d = 4 and SN-FC channels of Eb/No = 3 dB using the standard form of an (8,4) extended Hamming code. We see that the SCDDF algorithm is inferior not only to the JCDDF algorithm but also to uncoded CSS. This shows that the coding gain of the (8,4) extended Hamming code is very small at SN-FC channels of Eb/No = 3 dB. However, the JCDDF algorithm using a similar code, and under similar SN-FC channel achieves better sensing performance than the uncoded CSS. Hence we see the advantages of joint channel decoding and fusion as performed by the JCDDF algorithm. Now, we investigate the use of UEP coding for local decision and reliability information transmission using different protection levels. We first consider coding scheme of two different

AZMI AND LEIB: CODED COLLABORATIVE SPECTRUM SENSING WITH JCDDF

Fig. 10. The ROC curves comparing the sensing performance using the (dB) (k) 2-codes UEP schemes for SNR1,k = −10 dB, N = 500, Pf l = 0.1 and Eb/ No = 3 dB. The MSB bit is protected using repetition codes while the remaining d − 1 reliability information are protected by binary linear block codes.

channel codes to protect two classes of information, refer to as the 2-codes UEP. Using such an approach, local decisions are protected by a repetition code, and reliability information by a linear binary block code. For a fair comparison with the (8, 4) Hamming code, we use the same number of information bits d = 4 and parity bits mc = 4. Then, we allocate mc,1 parity bits to the repetition code of length 1 + mc,1 and mc,2 parity bits to the block code of length 3 + mc,2 , where mc,1 + mc,2 = 4. Fig. 10 illustrates the ROC curves for possible combinations of the 2-codes UEP. We see that the worst performance for 2-codes UEP occurs when all 4 parity bits are used to protect only the reliability information and the local decision is transmitted without any protection. Note that not only this 2-codes UEP has the worst performance among all other 2-codes UEP schemes, but it is also worse than the uncoded CSS. Next, we consider the other extreme, where all 4 parity bits are used to protect only the NP decision. We see that the ROC curve of this 2-codes UEP scheme improves significantly and outperforms uncoded CSS. The best 2-codes UEP scheme is achieved when 2 parity bits are used to protect the local decision and the other 2 to protect the reliability information (3 repetition/2 parities scheme). This demonstrates a need for balancing error protection between these two classes of information even though protecting the local decision seems more critical. We can see that the sensing performance of the 2-codes UEP starts to deteriorate when more parity bits are used to protect the local decision. This is because over protecting the local decision results in the reliability information to be less protected and hence is degrading sensing performance. The 2-codes UEP approach can be implemented naturally using a time-sharing protocol [57], where first and second time slots are used to transmit the two codes separately. These two time slots with codes of different protecting levels can be seen as two channels with two rates. In context of

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Fig. 11. The ROC curves comparing the sensing performance of the JCDDF (dB) algorithm with UEP coding and (8,4) Extended Hamming codes for SNR1,k = (k)

−10 dB, N = 500, Pf l = 0.1 and Eb/No = 3 dB.

broadcast channels, [58] shows that the achievable rate of timesharing protocols can actually be exceeded by using a single properly designed code. This broadcasting argument intuitively shows that better UEP can be obtained by using one code rather than two codes, which motivated the study of UEP based on a single code in [57]. Hence, also in our work, we proceed with single code UEP schemes. Using the search method of Section VII, we found the following UEP channel code named UEP8-3, defined by the following parity check matrix ⎤ ⎡ 1 0 1 1 1 0 0 0 ⎢1 1 0 0 0 1 0 0⎥ ⎥ ⎢ HUEP8−3 = ⎢ ⎥. ⎣1 0 0 0 0 0 1 0⎦ 1 0 0 0 0 0 0 1 The UEP8-3 code has a MSB protection level of 2. Fig. 11 illustrates the sensing performance of the UEP8-3 code, showing that it outperforms the (8,4) extended Hamming code and also the best 2-codes UEP scheme of Fig. 10 slightly. Simulation results over weaker SN-FC channels of Eb/No = −1.5 dB are presented in Fig. 12. We see that over a weak SN-FC channel, the JCDDF algorithm paired with an (8,4) extended Hamming code provides a lower performance when compared to uncoded CSS. However, the JCDDF algorithm performance improves when UEP8-3 code is used. For example, when Pf = 0.05 at the FC, the uncoded CSS only achieves Pd = 0.77, while the JCDDF with UEP-3 code achieves Pd = 0.86. Next, we consider longer and stronger UEP codes at lower rate by applying techniques from [56]. We also consider increasing bandwidth efficiency without degrading the performance by using Quadrature Phase Shift Keying (QPSK) with Gray mapping, which is equivalent to two orthogonal BPSK signals [59]. As a result, when retaining the same Eb/No as BPSK, the symbol energy of QPSK is doubled [60]. The first

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Fig. 12. The ROC curves comparing the sensing performance of the JCDDF algorithm using the UEP8-3, UEP12-3 and UEP16-3 codes with QPSK/BPSK (dB) (k) modulations for SNR1,k = −10 dB, N = 500, Pf l = 0.1 and Eb/No = −1.5 dB.

Fig. 13. The ROC curves comparing the sensing performance of the JCDDF algorithm using the UEP8-3, UEP12-3 and UEP16-3 codes with higher order (dB) (k) modulations for SNR1,k = −10 dB, N = 500, Pf l = 0.1 and Eb/No = −1.5 dB.

longer UEP code named UEP12-3 with nc = 12 and rate of 4/12 is defined by its parity-check matrix   HUEP8−3 [0] HUEP12−3 = H1 ⎡ ⎤ 1 0 1 1 1 0 0 0 0 0 0 0 ⎢ 1 1 0 0 0 1 0 0 0 0 0 0⎥ ⎢ ⎥ ⎢ 1 0 0 0 0 0 1 0 0 0 0 0⎥ ⎢ ⎥ ⎢ 1 0 0 0 0 0 0 1 0 0 0 0⎥ ⎢ ⎥. =⎢ ⎥ ⎢ 1 0 0 0 0 0 0 0 1 0 0 0⎥ ⎢ 1 0 0 0 0 0 0 0 0 1 0 0⎥ ⎢ ⎥ ⎣ 1 0 0 0 0 0 0 0 0 0 1 0⎦ 1 0 0 0 0 0 0 0 0 0 0 1

see that even in this case coded CSS with the proposed JCDDF algorithm still outperforms uncoded CSS. We also observe that coded CSS with lower bandwidth efficiency achieves better performance, e.g. using similar UEP16-3 code and Gray mapping with QPSK from Fig. 12 provides higher sensing performance than with 256-QAM from Fig. 13. Later, we found that applying our proposed techniques using higher-order modulations with different mapping schemes can further improve performance. We observe in Fig. 13 that by adopting natural binary ordering mapping [60] with 256-QAM, the performance of coded CSS using the UEP16-3 code improves, and it is now comparable with coded CSS using similar UEP16-3 code but with QPSK of Fig. 12. This illustrates that coded CSS with higher bandwidth efficiency can perform as good as the coded CSS with lower bandwidth efficiency if proper higher order modulations and mappings are used. It is also worth to mention that, at the same Eb/No, the coded CSS scheme adopting higher-order modulation increases the total energy consumption in the CR network. While we assume no energy constraint at the SN to investigate the JCDDF algorithm potential, this fact becomes important when considering battery operated SN. Taking into account also this constraint amounts to a spectrum and energy efficient design [61], [62], and is beyond the scope of this paper. Next, we relate the performance gain shown by the JCDDF algorithm to cognitive wireless communications. In such a context, higher Pd translates to better protection for PU, while lower Pf translates to better opportunity for the CR to use free channels. For example at Pd = 0.9, as set by the requirement of the IEEE 802.22 standard [63], under similar bandwidth efficiency in Fig. 13 the JCDDF algorithm using the UEP163 code with 256-QAM and natural binary ordering mapping requires Pf = 0.07, while uncoded CSS requires Pf = 0.14. This shows that the JCDDF algorithm provides an increase of 50% in opportunity availability compared to uncoded CSS. Furthermore, we also see that the JCDDF algorithm with such a code satisfies the specification of the IEEE 802.22 standard

The UEP12-3 code construction begins with the UEP8-3 code. Four extra parity bits are added on top of the UEP8-3 code, where the four additional parity check constraints of H1 only involve the first column of the UEP8-3 code’s parity check matrix, i.e. the MSB bit. This provides extra protection to the MSB bit. Same techniques are used to obtain even longer UEP16-3 code with nc = 16 and rate 4/16. The performance of these longer codes is presented in Fig. 12. We see that these UEP codes provide a further small improvement when compared to the shorter UEP8-3 code. All reported results so far are attained with BPSK or QPSK modulations, where the performance improvements of coded CSS with the JCDDF algorithm come at the expense of increasing bandwidth compared to uncoded CSS. Next, we consider the JCDDF algorithm paired with UEP codes using higherorder modulations such that the coded CSS has the same bandwidth efficiency as the uncoded CSS using QPSK. Each SN in the uncoded case uses 2 QPSK symbols to forward d = 4 bits uk . Therefore, to operate under similar bandwidth efficiency when employing the UEP12-3 code for example, we need to use 64-Quadrature Amplitude Modulation (QAM). Simulation results for such systems are presented in Fig. 13. We

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Eb/No(2) = [1.3079, 1.0079, 0.7079, 0.4079, 0.1079], where SNs with strong sensing channels are experiencing strong reporting channels, to see if performance can further improve. We found that case 4 improves slightly the performance over case 3. We then study the other extreme case 5 with sensing channels of SNR(1) = [0.2, 0.15, 0.1, 0.04, 0.01] and reporting channels of Eb/No(2) = [0.1079, 0.4079, 0.7079, 1.0079, 1.3079], where the SN with the strongest sensing channel experiences the weakest reporting channel. We observed a significant degradation in the ROC curve of case 5 when compared to case 3. This shows that, SNs with stronger sensing channels while dominating the overall performance, they are more sensitive to the reporting channel quality. IX. C ONCLUSION

Fig. 14. The ROC curves comparing the sensing performance of the JCDDF algorithm using the UEP16-3 codes with 256-QAM and binary mapping for coded CSS with unequal sensing PU-SN and unequal reporting SN-FC channels.

by achieving Pd = 0.9 with Pf ≤ 0.1 [63], while uncoded CSS does not. Finally, Fig. 14 presents the ROC curves of the JCDDF algorithm using the UEP16-3 code with 256-QAM and binary mapping for K = 5. In this figure we consider unequal sensing PU-SN channels with SNR(1) = [SNR1,1 , . . . , SNR1,5 ] as well as unequal reporting SN-FC channels with Eb/No(2) = [Eb/No1 , . . . , Eb/No5 ]. For all studied cases, we kept the arithmetic mean of the sensing channels’ quality to 0.1 (i.e., −10 dB) and the reporting channels’ quality to 0.7079 (i.e., −1.5 dB), for benchmark comparison with case 1. The ROC curve of case 1 represents equal PU-SN channels of SNR1,k = 0.1, and equal SN-FC channels of Eb/Nok = 0.7079 reproduced from Fig. 13. In case 2, where the PU-SN channels remain equal at SNR1,k = 0.1, while the SN-FC channels experience Eb/No(2) = [0.1079, 0.4079, 0.7079, 1.0079, 1.3079], there are two reporting channels of higher and two of lower qualities than the average of 0.7079, and one reporting channel of Eb/No equal to 0.7079. We see that the weak reporting channels dominate the performance, hence producing a lower ROC curve for case 2 than case 1. Next, we study the opposite channel setting in case 3, where the PU-SN channels experience SNR(1) = [0.2, 0.15, 0.1, 0.04, 0.01], and all SN-FC channels have equal Eb/Nok = 0.7079. In this case there are two sensing channels that are above and two below the average of 0.1, while one sensing channel has SNR equal 0.1. An opposite effect is observed for case 3, where its performance improves over case 1. This shows that, in the case of unequal sensing channels, the strong ones dominate the performance. Next, we consider cases where the sensing channels as well as the reporting channels have different link qualities. Here the ordering of the sensing and reporting channels does matter, and hence due to space limitation we present results only for the two extreme cases. Since strong sensing channels are shown to dominate the overall performance, we consider case 4 with SNR(1) = [0.2, 0.15, 0.1, 0.04, 0.01] and

In this work, we derived a BP algorithm for JCDDF in coded collaborative spectrum sensing systems with local binary NP testing. Based on the Lloyd-Max method, we also proposed a new methodology for the collaborating SNs to quantize local decision variables. The design of our quantizer ensures that local decisions are embedded as MSB of the quantization bits. We demonstrated that coded CSS employing the JCDDF algorithm with the (8,4) extended Hamming code outperforms uncoded CSS as well as coded CSS employing the SCDDF algorithm. Hence integrating channel decoding with decision fusion provides performance gains. We analyzed the computational complexity of JCDDF, SCDDF and uncoded CSS. When paired with an (8,4) extended Hamming code the JCDDF algorithm requires only a complexity increase by a factor 6 and 1.2 over uncoded CSS and SCDDF, respectively. We then considered the design of channel codes for CSS systems, and showed that the JCDDF algorithm, when used with UEP coding, outperforms equal error protection. We also showed that coded CSS employing the JCDDF algorithm not only outperforms uncoded CSS but also can provide this advantage without bandwidth expansion using higher order modulation. We then showed that proper bits to symbols mappings in coded CSS employing the JCDDF algorithm with higher order modulations can further improve performance. Finding more powerful codes and mappings for such schemes constitutes a subject for further work. Finally, we simulated the JCDDF algorithm for coded CSS with unequal sensing and reporting channels’ qualities. We found that the SNs with stronger sensing channels dominate the overall performance; however they are more sensitive to the reporting channel errors. R EFERENCES [1] D. Cabric, S. M. Mishra, and R. W. Brodersen, “Implementation issues in spectrum sensing for cognitive radios,” in Proc. 38th Asilomar Conf. Signals, Syst. Comput., Pacific Grove, CA, USA, Nov. 2004, pp. 772–776. [2] K. B. Letaief and W. Zhang, “Cooperative communications for cognitive radio networks,” Proc. IEEE, vol. 97, no. 5, pp. 878–893, May 2009. [3] P. K. Varshney, Distributed Detection and Data Fusion. New York, NY, USA: Springer-Verlag, 1996. [4] R. Viswanathan and P. Varshney, “Distributed detection with multiple sensors: Part I—Fundamentals,” Proc. IEEE, vol. 85, no. 1, pp. 54–63, Jan. 1997. [5] R. Blum, S. Kassam, and H. Poor, “Distributed detection with multiple sensors: Part II—Advanced topics,” Proc. IEEE, vol. 85, no. 1, pp. 64–79, Jan. 1997.

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Marwan Hadri Azmi received the B.Eng. degree in electrical and telecommunications from the Universiti Teknologi Malaysia in 2003, the M.Sc. degree in communications and signal processing from the Imperial College of Science, Technology and Medicine, University of London in 2005, and the Ph.D. degree from the University of New South Wales, Australia, in 2012. He is currently a Senior Lecturer at Wireless Communication Centre, Universiti Teknologi Malaysia. From 2012 to 2014, he spent his Sabbatical leave of absence at the Department of Electrical and Computer Engineering, McGill University. His research interests include communication, information and coding theory focusing on cooperative communications, spectrum sensing for cognitive radio and LDPC coding.

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Harry Leib (S’83–M’87–SM’95) received the B.Sc. (cum laude) and M.Sc. degrees from the TechnionIsrael Institute of Technology, Haifa, Israel, in 1977 and 1984, respectively, and the Ph.D. degree from the University of Toronto, Canada, in 1987, all in electrical engineering. During 1977–1984, he was with the Israel Ministry of Defense, working in the Communication Systems area. After completing his Ph.D. studies, he was with the University of Toronto as a Post-doctoral Research Associate and as an Assistant Professor. Since September 1989, he has been with the Department of Electrical and Computer Engineering, McGill University, Montreal, where he is now a Full Professor. He spent part of his Sabbatical leave at Bell Northern Research, Ottawa, Canada (1995–1996). During the other part of his Sabbatical leave (1996) he was a Visiting Professor in the Communications Lab, Helsinki University of Technology, Finland. At McGill, he teaches undergraduate and graduate courses in communications, and directs the research of graduate students. His current research activities are in the areas of digital communications, wireless communication systems, detection, estimation, and information theory. Dr. Leib was an Editor for the IEEE T RANSACTIONS ON C OMMUNICA TIONS (2000–2013), and an Associate Editor for the IEEE T RANSACTIONS ON V EHICULAR T ECHNOLOGY (2001–2007). He has been a guest co-editor for special issues of the IEEE J OURNAL ON S ELECTED A REAS IN C OM MUNICATION on “Differential and Noncoherent Wireless Communication” (2003–2005), and on “Spectrum and Energy Efficient Design of Wireless Communication Networks” (2012–2013).