Joint Wideband Spectrum Sensing in Frequency Overlapping Cognitive Radio Networks Using Distributed Compressive Sensing

Transcription

1 The 2 Military Communications Conerence - Track 2 - Network Protocols and Perormance Wideband Spectrum Sensing in Frequency Overlapping Cognitive Radio Networks Using Distributed Compressive Sensing Ukash Nakarmi and Nazanin Rahnavard School o Electrical and Computer Engineering Oklahoma State University Stillwater, OK s: {ukash.nakarmi, nazanin.rahnavard}@okstate.edu Abstract The emerging paradigm o open spectrum market calls or quick, eicient and dynamic approach or spectrum sensing. Conventional spectrum sensing methods or cognitive radios are capitalized over the narrow band sensing without addressing the wideband spectrum sensing. In wideband networks, one by one scanning o spectrum is unattractive because o its complexity, agility constraints, and data acquisition cost. Existing wideband spectrum sensing schemes do not exploit the gain o joint sparsity in the requency overlapping networks. In this paper, wideband spectrum sensing or requency overlapping cognitive radio networks using the emerging compressive sensing paradigm and joint reconstruction is proposed. Simulation results veriy the eectiveness o proposed joint spectrum sensing approach in jointly sparse requency overlapping cognitive radio networks. I. INTRODUCTION The increasing demand or wireless resources and spectrum have created spectrum scarcity. However, spectrum utilization studies show that these scarce wireless spectrum has been distributed and used ineiciently [], [2]. This bottleneck in spectrum scarcity and ineicient usage is addressed by the dynamic spectrum access policy. Cognitive radio (CR) with ability to sense unused spectrum and opportunistically transmit over spectrum holes is proposed in [3], [4]. The undamental challenge in the cognitive radio implementation is detection o the vacant spectrum (holes) [5]. The current trends in spectrum sensing and cognitive radios are well explained in many survey reports [6], [7]. Many o the spectrum sensing algorithms deal with the narrow band sensing which are tailored energy detector and power spectral density o the narrow band signal. Wideband spectrum sensing requires ast and dynamic spectrum analysis over larger spectrum band. Recent paradigm in sparse sampling, compressive sensing (CS) [8], [9] provides solution to sparse signal reconstruction as an optimization problem. In [], [] CS sampling, orward dierentiation and singular value decomposition methods are used or wideband spectrum sensing purpose. These approaches provide wideband spectrum sensing in a simple individual network. To eliminate the need o high speed analog to digital converters and digital signal processors in wideband sensing, techniques such as random demodulators, parallel signal processing are proposed in [2], [3]. The NTIA s requency allocation chart [4] shows many networks overlap in the requency zone because o spectrum scarcity. The spectrum overlapping or jointly sparse requency overlapping network in cognitive radio network comes into picture because o spatial diversity o primary and secondary transmission power [5]. In this paper, we propose joint reconstruction or wideband spectrum sensing in requency overlapping networks using distributed compressive sensing. The rest o the paper is structured as ollows. Section II provides mathematical ormulation o the general spectrum sensing problem in a single network. In Section III, we introduce the requency overlapping network and ormulate the spectrum sensing problem or it. reconstruction scheme and joint reconstruction or the compressed measurement are presented and compared. Section IV provides simulation results or the proposed joint wideband spectrum sensing in requency overlapping networks and inally, Section V concludes the paper. II. PROBLEM STATEMENT Let us consider a wideband communication model with primary and secondary (cognitive radios) users coexistence as shown in the Fig.. The total communication bandwidth o the system is divided into N subbands each centered at requency n,wheren =, 2, 3,...,N.VeryewotheN subbands are occupied by the primary users at a given geographical and temporal region. Let us suppose, out o N subbands, S<<Nare occupied by primary users during sensing time. The unoccupied channels by primary users over given spatiatemporal region called, spectrum holes, are opportunistically accessed by the cognitive users keeping the rights o the primary sae. The cognitive radios in the system need to detect these spectrum holes or secondary communication. At time t, the received signal at m th cognitive user can be expressed as: y m (t) = N x n (t) g nm (t)+w m (t), () n= //$26. 2 IEEE 35

2 Network Bandwidth Primary users All other decvices are secondary users(sensing device) Fig.. Occupied Channels Vacant Channels Primary and secondary users coexistence where, represents the convolution, x n (t) is the signal o n th primary user, g nm (t) denotes the channel gain response, and w m (t) is additive white gaussian noise with zero mean and variance o σw 2. In requency domain, () can be represented as: y (m) = N n= D (nm) g x (n) + w m, (2) where D (nm) g is a diagonal N N channel gain matrix between n th primary and m th CR. x and w represent corresponding requency response o x(t) and w(t), respectively and elements g (nm) o D (nm) g are given by: g (i,j) =; i j; and i, j {, 2,...N}, (3) and, g (i,j) = g (i,j) ; i = j; and i, j {, 2,...N}. (4) However, we know that at any time t, only ew o the N channels are occupied. Let Ŝ be the set o occupied channels such that Ŝ ˆN. ˆN is the set o bands under consideration. Thus or all n : n/ Ŝ x n (t) =. (5) From (5), ˆN is sparse. Accordingly, () and (2) reduce to, and, y m (t) = s Ŝ x s (t) g sm (t)+w m (t), (6) y (m) = s Ŝ D (sm) g x (s) + w m. (7) This sparseness o signal in the requency domain makes CS possible or the spectrum sensing purposes in cognitive radio network. The requency response o the channels occupied by the primary users are non-zero values, whereas, those o vacant channels are zero. Hence, the total requency response o the signal under consideration is a sparse signal. In CS, instead o taking point by point samples as in conventional sampling, each sample taken is linear unctional o the sparse signal. Consider the problem o reconstructing N length, S sparse signal X. Let us consider an M N dimension, where M < N, sensing matrix Φ. We can obtain M compressed measurements, Y, using, Y = ΦX. Since, M < N, the recovery o X rom compressed measurements Y is ill-posed in general. Interestingly, provided X is sparse in some domain and the measurement matrix Φ satisies the restricted isometry property (RIP) [8], the signal X can be recovered rom the measurement vector Y. The recovery o S non-zero elements o signal X is actually the solution o the l norm minimization problem. Unortunately, solving l is prohibitively computationally complex. However, the approximate solution o X can be obtained using l minimization as: ˆX = arg min X l, s.t. Y =ΦX, (8) For secondary communication in the cognitive radio network, inding the set Ŝ is the most important and irst requirement. The complexity o spectrum sensing depends upon the requirements o an application. In cognitive radio spectrum sensing, our primary concern is inding which o the S bands among N are occupied rather than the exact signal strength o the the occupied channels. In cognitive radio network, the problem o spectrum sensing using energy detector, at each m th CR boils down to distinguishing between binomial hypotheses. The signal energy o each o the subband is compared with the threshold λ e which is the unction o noise and channel characteristics. I the received signal is greater than λ e the channel is said to be occupied else it is taken as vacant. Finding an optimal λ e is an agenda in the communication channel modeling research [6]. In conventional spectrum sensing, each secondary user senses and detects each o the band individually. This requires large number o measurements in the system and increases data acquisition cost [7], []. Besides, each sensing device/cognitive radio needs to have sensing bandwidth entirely over the communication band making the sensing process more prone to noise. Moreover, all the CRs have to be silent and synchronized during the sensing period. In large overlapping networks, or in spatially distant CRs, synchronization cannot be guaranteed due to spatial diversity o primary transmission power. This creates jointly sparse requency overlapping networks over large spatial domain [5]. III. PROPOSED WIDEBAND COMPRESSIVE SPECTRUM SENSING IN FREQUENCY OVERLAPPING NETWORKS In this paper, we present a novel, joint wideband spectrum sensing scheme or requency overlapping cognitive radio network, based upon the new sparse signal acquisition scheme called compressed sensing or which signal reconstruction is an optimization problem. We extend our work in wideband compressive sensing or cognitive radios [7] into a requency overlapping network and present joint reconstruction scheme or spectrum sensing in requency overlapping networks. A. Distributed Wideband Spectrum Sensing in Frequency Overlapping Network The NTIA s requency allocation chart clearly shows the requency overlapping over dierent system protocols to meet The terms sensing device and cognitive radio have been used interchangeably in this paper 36

3 the band scarcity issue. Let us consider two network systems S and S 2 with some overlapping operating bands as shown in Fig. 2. We call the networks S and S 2 as the requency overlapping networks and denote it with network H N.The theoretical backgrounds on joint sparse signal can be ound in literatures [8], [9]. Let B s and B s2 represent the spectrum band o S and S 2 respectively, where B s = N and B s2 = N 2. B sc denotes the requency overlapping between S and S 2 and B sc = N c. The total number o bands (channels) under consideration is : N T = N + N 2 N c. In jointly sparse requency overlapping networks, or each o the network, (7), takes the orm o: y (m) i = D (sm) gi (x (s) i + x(s) c )+wm, (9) s Ŝi where, i =, 2 reers to corresponding network, x (s) i and x(s) c, denote the spectral innovation o i th network and joint sparse portion, respectively, as illustrated in the Fig. 2, and all other notations have same meaning as in (7). We consider, each o the network consists o M s sensing devices and each sensing device takes m s compressed measurements. So total number o measurements taken in each network = M s m s = M. S S2 (ly Sparse) Overlapping Bands Innovation Sparse Innovation Occupied Channels Vacant Channels the physical realization o sampling matrix Φ is an important issue. The sensing matrix Φ M N in our model is the elementwise combination o the two matrices: random requency selective matrix F M N and channel response matrix H M N. i.e Φ=F (. )H, () where, (. ) represent element wise product. We consider each o the M s sensing device/cr consists o m s ilter banks, where M s m s = M. Each ilter bank is collection o random bandpass ilter tapped at L random bands. For simplicity, we assume the ilters are ideal ilters with unity gain and zero phase. Hence, F is a binary matrix with constant row weight L. Also, i L m denotes the the set o band index o the ilters in the m th requency selective ilter bank, then: F m,n = ;i, n L m, () else, F m,n =. (2) Similarly, the channel response matrix is deined by: H = h m,n, m =, 2,...M and n=, 2,...N, (3) where, h m,n is the channel response between m th sensing device and the n th primary signal, and is unction o the channel modeling. From () and (), we can have : Sparse Innovation Band Primary users Bs All other decvices are secondary users(sensing device) Bsc Sparse Innovation Bs2 Band 2 Φ m,n = F m,n H m,n ; if m,n =, (4) else, Φ m,n =. (5) Hence, the sensing matrix Φ is a constant row weight matrix. 2) Compressed Measurement Y : Let the sensing matrix Φ Fig. 2. Schematic o overlapping networks and overlapping spectrum bands Let X = [x () i ] N and X (2) = [x (2) i ] N2 represent the test statistic or the spectrum sensing in two networks S and S 2 respectively and X (c) =[x (c) i ] Nc represents that o overlapping portion. A vector V o length N is said to be K sparse i V contains only K non-zero elements, i.e. V l = K, where,l denotes norm zero. Also, the support o a vector, V =[v i ] N is deined as : supp(v )={i,v i,i =, 2,...N}. Let, supp(x ) = K and supp(x 2 ) = K 2. K and K 2 denote number o occupied channels in network and 2, respectively. It should be noted that in spectrum sensing or cognitive radios, our objective is to ind the supp(x ) and supp(x 2 ) and hence detect primary users and ind the spectrum holes. In compressive sensing, it is the method o data acquisition which makes it distinct rom conventional sampling approaches. In the ollowing subsections, we describe the sampling approach, the structure o sparse sampling matrix Φ, data acquisition techniques and decoding approaches. ) Sensing Matrix Φ: In previous works [2], [8] the mathematical models o compressive sensing have been explained thoroughly. From the implementation point o view or network systems S and S 2 be represented by [Φ ] M N and [Φ 2 ] M2 N 2 respectively, with the characteristics as explained in Section III-A. For ease in calculation, we assume M = M = M 2 and N = N 2 = N. Each sensing device samples the spectrum bands in the corresponding network system in S and S 2. Each sensing device gives m s compressed measurements and each network consists o M s sensing devices. For each system, the total number o compressed measurements sent to the individual controller unit is then M = M s m s.thei th compressive measurement at m th sensing device is given by: y (i) m =Φ (m,:) X, (6) i =, 2...m s,m =:number o sensing devices (M s ) Hence, Y and Y 2, denoting the compressed measurement at network system and 2 respectively, can be written as: Y i =Φ i X i ; i =, 2. (7) Similarly, in case o the noisy measurements, it is aected with additive white gaussian noise o zero mean and variance σ 2, W (,σ 2 ). Y i =Φ i X i + W i ; i =, 2. (8) 37

4 3) Compressive Sensing Decoding: The solution to the compressive sensing decoding is an optimization problem. CS decoding algorithm based upon the norm optimization like Basis pursuit (l ) minimization is discussed in [9], [8], [2]. In the ollowings, we irst provide a quick reerence to individual compressive spectrum sensing and individual reconstruction, then we illustrate the joint reconstruction scheme or the requency overlapping networks. 3.a. Reconstruction In individual reconstruction scheme, each network reconstructs its compressively sensed test statistics individually without cooperating with other networks and the decision about the spectrum occupancy is made accordingly using thresholding [6]. The reconstructed test vectors in individual reconstruction is give by: ˆX i = arg min X i l s.t. Y i =Φ i X i ; i =, 2, (9) where as in case o the noisy measurements the optimization constraint is minimized as: Y i Φ i X i 2 σ 2, (2) 3.b. Reconstruction The number o required measurements or CS reconstruction is a unction o the sparsity o the signal. It has been shown that the number o samples required or the CS reconstruction is in the order o CKlog ( ) N K [8], [9]. In overlapping networks, the individual reconstruction requires redundant numbers o samples or reconstruction. In individual reconstruction, the number o measurements required depends on (K + K 2 ).In [5], the LASSO algorithm with iterative user consensus is used to detect the overlapped bands. However, the advantage o common sparse elements in joint reconstruction is not exploited, and individual reconstruction is required in each network. In joint reconstruction, the number o measurements required or reconstruction depends on (K +K 2 K c = K T ). It has been shown that the the number o required measurements or CS reconstruction depends upon the sparsity, hence the joint reconstruction will have the measurement gain. Moreover, only one joint optimization is perormed or the reconstruction o the both networks. We implement joint reconstruction scheme or spectrum sensing in requency overlapping networks and compare it with the conventional individual reconstruction scheme and the iterative LASSO consensus algorithm [5]. In joint reconstruction scheme, cognitive users in each network take the compressed measurements o spectrum in their network. The CS measurements are sent to a common controller unit. Let the measurements or the joint reconstruction be denoted by Y as, Y = [ Y Y 2 ], (2) where, Y and Y 2 are compressed measurements o networks S and S 2, respectively. reconstruction matrix Φ joint or reconstruction o the spectrum test statistics, X := X i X c, X i2 be represented as: [ ] ΦA Φ Φ joint = C Φ null. (22) Φ null Φ C2 Φ B I I c denotes the set o the overlapping bands o two networks, ˆX i and ˆX i2 denote innovation bands o network and 2 respectively, and (φ) j denotes the j th column o the Φ, then: Φ A =(Φ ) j j ˆX i, Φ B =(Φ 2 ) j j ˆX i2, Φ C =(Φ ) j j I c, Φ C2 =(Φ 2 ) j j I c, (23) and Φ null are null matrices. Then the joint reconstruction optimization or X is perormed as: ˆX = arg min X l s.t. Y =Φ joint X. (24) In case o noisy measurements the constraint o optimization is modiied accordingly as in (2). IV. SIMULATION AND RESULTS For evaluating our perormance we deine ollowing perormance measurement parameters. (S.R = 2M N T ): Sampling rate is deined as the ratio o the number o compressed measurements to the total number o channels. Probability O Detection (POD): It is the ratio o total number o hits to the sums o total hits and miss. Hit is an event when we decide the presence or absence o primary user correctly, whereas, any other wrong decision is termed as miss event. Error o Reconstruction (EOR): EOR is the ratio o energy dierence between reconstructed and original signal to the energy o the original signal. Sparse Overlapping Factor (SOF = Kc K T ): SOF is the ratio o number o occupied channels in the overlapping bands to the total number o occupied channels in the network. Measurement Gain (MG): For the given probability o detection, measurement gain is deined as: MG = # o measurements required in joint reconstruction # o measurements required in individual reconstruction For simulation purpose we take total number o channels, N T =, out o which, N c = 3% are overlapping, the sparsity, ( KT N T = %), and SOF =.5 unless stated otherwise. Compressed measurements at dierent sampling rate are obtained and reconstructed. The results provided are 38

5 the average o simulations. Both noisy and noiseless measurement schemes are simulated. From Figs. 3 and 4, it is clearly observed that or the same number o compressed measurements, the joint reconstruction algorithm has better perormance than the individual reconstruction. We see that the POD approaches or joint reconstruction at sampling rate o 3% whereas it is at 44% or the individual reconstruction. This gain in measurements is the consequence o sparse overlapping elements and joint reconstruction. The EOR or joint reconstruction approaches to zero or the sampling rate o as low as 28% where as or that o individual reconstruction it occurs at 4%. We see that or same perormance the joint reconstruction requires less number o samples. This reduces the data acquisition cost and the redundancies. Probability o Detection Probability o Detection Fig. 5. Error o Reconstruction Fig POD using individual and joint reconstruction in noisy measurements EOR using individual and joint reconstruction in noisy measurements Error o Reconstruction Fig. 3. POD using individual and joint reconstruction Measurement Gain Sparse Overlapping Factor Fig. 7. Measurement gain or varying SOF when POD= Fig. 4. EOR using individual and joint reconstruction Figs. 5 and 6 are the perormance measurement under noisy measurements.the perormance under noisy measurements degrades both in terms o probability o detection and reconstruction error, however the joint reconstruction scheme still perorms better than the individual reconstruction. Fig. 7 shows the eect o the varying SOF on the measurement gain between the individual reconstruction and the joint reconstruction. It shows the measurement gain or POD =.99. We can clearly see that the measurement gain increases as the SOF increases. This implies that the number o measurements required in joint reconstruction or same perormance decreases comparatively to individual reconstruction when there are more occupied channels in the overlapping region. We also compare our perormance with the iterative LASSO consensus scheme in [5]. In [5], the requency overlapping scheme is illustrated using multihop cognitive network with some common bands and innovation bands between multiple hops in a network. Fig. 8 is the Receiver operating characteristics (ROC) comparison and Fig. 9 shows the comparison o reconstruction error. We clearly observe that the joint reconstruction scheme has better receiver operating characteristics where as the error o reconstruction is comparable to that o in iterative LASSO consensus. Probability o Primary Dectection reconstruction LASSO consensus Probabilty o Flase Alarm Fig. 8. ROC perormance comparison, For SNR=-5dB, S.R=.6 and Sparsity=4% 39

6 Error o Reconstruction Fig. 9. LASSO consensus reconstruction Number o Iterations EOR comparison, For SNR=-5dB, S.R=.6 and Sparsity=4% We also reconstruct the original time domain signal using individual and joint reconstruction methods in Figs. and, respectively, at sampling rate o 32%. Comparing these igures, we observe that the signal reconstructed using the joint reconstruction matches more closely to the original signal. X(t) Original Reconstructed Time(t) Fig.. Original time domain signal and reconstructed signal using individual reconstruction method X(t) Original ly Reconstructed Time(t) Fig.. Original time domain signal and reconstructed signal using joint reconstruction method V. CONCLUSION In this paper, we proposed a novel wide band spectrum sensing or cognitive radios in the requency overlapping networks using distributed compressive sensing and joint reconstruction. The concept have been demonstrated through the theoretical explanation and have been validated using the simulation results. A distributed compressive sensing or cognitive radio network in the requency overlapping system has been explored. Proposed joint reconstruction scheme or spectrum sensing exploits the joint sparsity in requency overlapping networks and eiciently reduces the number o samples required. It is shown that the proposed scheme outperorms the individual reconstruction scheme and has better receiver operating characteristics compared to LASSO consensus algorithm. This is because the overlapping channels can be exploited to enhance the compressive decoding using joint reconstruction scheme. VI. ACKNOWLEDGEMENT This material is based upon work supported by the National Science Foundation under Grant No. CCF REFERENCES [] FCC, Spectrum policy task orce report, In Procc. o the Federal communications comissions (FCC 2), Washigton, DC, USA, Nov 22. [2] M.Islam,C.Koh,S.Oh,X.Qing,Y.Lai,C.Wang,Y.-C.Liang,B.Toh, F. Chin, G. Tan, and W. Toh, Spectrum survey in singapore: occupancy measurements and analysis, Proc. o 3rd International Conerence on Cognitive Radio Oriented Wireless Network and Communications (CROWNCOM 8), singapore, May 28. [3] J. Mitola, Cognitive radio: An Integrated Agent Architecture or Sotware Deined Radio. Doctor o technology, Royal Inst. Technology. (KTH), Stockholm, Sweden, 2. [4] S. Haykin, Cognitive radio: Brain empowered wiless communications, IEEE Journal on selected areas in communications, vol. 23, February 25. [5] D. Cabric, S. Mishra, and R. W. Brodersen, Implementation issues in spectrum sensing, Asilomar Conerence on Signal, Systems and Computers, November 24. [6] I. F. Akyildiz, W.-Y. Lee, M. C. Vuran, and S. Mohanty, Next generation/dynamic spectrum access/cognitive radio wireless networks: Asurvey, Computer Networks, vol. 5, no. 3, pp , 26. [7] T. Yucek and H. Arslan, A survey in spectrum sensing algorithms or cognitive radio applications, IEEE communications surveys and tutorials, vol., no., pp. 6 3, 29. [8] D. Donoho, Compressed sensing, IEEE transaction on inormation theory, vol. 52, pp , April 26. [9] E. Candes, J. Romberg, and T. Tao, Robust uncertainty principles: exact signal reconstruction rom highly incomplete requency inormation, Inormation Theory, IEEE Transactions on, vol. 52, no. 2, pp , 26. [] Z.Tian and G. Giannaskis, Compressed sensing or wideband cognitive radios, Proc. o International Conerence on Acoustic Speech and Signal Processing, pp. IV/357 IV/36, April 27. [] J.Meng, W.Yin, H.Li, and Z.Han, Collaborative spectrum sensing or sparse observation using matrix completion or or cognitive radio network, The 35th International conerence on acoustic, speech, and signal processing, (ICASSP), 2. [2] Z. Yu, X. Chen, S. Hoyos, B. M. Sadler, J. Gong, and C. Qian, Mixedsignal parallel compressive spectrum sensing or cognitive radios, International Journal o Digital Multimedia Broadcasting, 2. [3] S. Kirolos, J. Laska, M. Wakin, M. Duarte, D. Baron, T. Ragheb, Y. Massoud, and R. Baraniuk, Analog-to-inormation conversion via random demodulation, 26. [4] [5] F. Zeng, C. Li, and Z. Tian, Distributed compressive spectrum sensing in cooperative multihop cognitive networks, IEEE Journal o Selected Topics in Signal Processing, vol. 5, pp , Feb 2. [6] F. Digham, M. Alouni, and M. Simon, On the energy detection o unknown signal over ading channels, IEEE conerence on communication, vol. 5, pp , May 23. [7] U.Nakarmi and N. Rahnavard, A new approach to spectrum management in cognitive radio networks, In proc. o International conerence on smart technologies or materials, communications, controls, computing and Energy, (ICST), pp. 3 7, Jan 2. [8] M. F. Duarte, S. Sarvotham, M. B. Wakin, D. Baron, and R. G. Baraniuk, sparsity models or distributed compressed sensing, Online Proceedings o the Workshop on Signal Processing with Adaptative Sparse Structured Representations (SPARS), 25. [9] M. F. Duarte, S. Sarvotham, D. Baron, M. B. Wakin, and R. G. Baraniuk, Distributed compressed sensing o jointly sparse signals, in Proceedings o the 39th Asilomar Conerence on Signals, Systems and Computation, (Paciic Grove, CA), pp , Nov. 25. [2] P. Huber, Projection pursuit, The annals o statistics, vol. 3, pp , 985. [2] C. Dossal, M.-L. Chabanol, G. Peyré, and J. Fadili, Sharp support recovery rom noisy random measurements by l minimization, CoRR, vol. abs/.577, 2. 4