Autonomous Compressive Sensing Augmented Spectrum Sensing

Transcription

1 Autonomous Comressive Sensing Augmented Sectrum Sensing Zhang, X; Ma, Y; Gao, Y; Zhang, W 218 IEEE. Personal use of this material is ermitted. Permission from IEEE must be obtained for all other uses, in any current or future media, including rerinting/reublishing this material for advertising or romotional uroses, creating new collective works, for resale or redistribution to servers or lists, or reuse of any coyrighted comonent of this work in other works. For additional information about this ublication click this link. htt://qmro.qmul.ac.uk/xmlui/handle/ /36767 Information about this research object was correct at the time of download; we occasionally make corrections to records, lease therefore check the ublished record when citing. For more information contact scholarlycommunications@qmul.ac.uk

2 1 Autonomous Comressive Sensing Augmented Sectrum Sensing Xingjian Zhang, Student Member, IEEE, Yuan Ma, Member, IEEE, Yue Gao, Senior Member, IEEE, and Wei Zhang, Fellow, IEEE Abstract This aer rooses a new sectrum sensing technique, referred to as autonomous comressive sensing (CS) augmented sectrum sensing, which can be develoed to rovide more efficient sectrum oortunities identification than geolocation database methods. Firstly, we roose an autonomous CS-based sensing algorithm that enables the local secondary users (SUs) to automatically choose the minimum sensing time without knowledge of sectral sarsity or channel characteristics. The comressive samles are collected block-by-block in time while the sectral is gradually reconstructed until the roosed stoing criterion is reached. Moreover, a CS-based blind cooerating user selection algorithm is roosed to select the cooerating SUs via indirectly measuring the degeneration of signal-to-noise ratio (SNR) exerienced by different SUs. Numerical and real-world test results demonstrate that the roosed algorithms achieve high detection erformance with reduced sensing time and number of cooerating SUs in comarison with the conventional comressive sectrum sensing algorithms. Index Terms Comressive sensing, cognitive radio, wideband sectrum sensing, sectrum access framework. I. INTRODUCTION Regulatory bodies worldwide are facing that the raid growth of wireless communication industry is overwhelming current static sectrum suly, and thus encourages an urgent need for imroved sectrum assignment strategy to mitigate the ga between the available sectrum and the demand [1], [2]. A key finding of the U.S. 212 President s Council of Advisers on Science and Technology (PCAST) reort [3] is that advanced sectrum sharing technologies have the otential to transform sectrum scarcity into abundance based on the following two factors: first, it is well recognised that many licensed frequency bands are under-utilized in ractice either over time or geograhy locations [4]; second, there have been some raid advances towards the develoment of dynamic sectrum access such as cognitive radio technology [5] [7]. To that end, the academia, industry, and regulatory bodies are closely collaborating to ursue olicy and technology Coyright (c) 215 IEEE. Personal use of this material is ermitted. However, ermission to use this material for any other uroses must be obtained from the IEEE by sending a request to ubs-ermissions@ieee.org. This work was suorted by the Engineering and Physical Sciences Research Council (EPSRC) in the U.K. with grant EP/R711X/1, and by the Australian Research Councils Projects funding scheme under Projects DP and LP Xingjian Zhang, Yuan Ma and Yue Gao are with the School of Electronic Engineering and Comuter Science, Queen Mary University of London, London E1 4NS, U.K. ( s:{xingjian.zhang, y.ma, yue.gao}@qmul.ac.uk). Wei Zhang is with the School of Electrical Engineering and Telecommunications, University of New South Wales, Sydney, NSW 252, Australia ( wzhang@ee.unsw.edu.au). innovations based on the aradigm of the shared sectrum. Recently, the MHz (referred to as 3.5 GHz band) Citizens Broadband Radio Service (CBRS), is considered for the sectrum sharing by Federal Communications Commission (FCC) in the US. Meanwhile, UK Office of Communications (Ofcom) has ublished the call for inut [8] which considers the 3.8 GHz to 4.2 GHz as the first band where they aly the sectrum sharing framework. In order to share the sectrum efficiently and limit the interference among users, three-tiered sectrum access framework was introduced in the abovementioned shared sectrums [9], [1], where the incumbent users as the rimary users (PUs) oerate at the to tier, while the CBRS users as the secondary users (SUs) oerate at the second or third tiers holding riority access license (PAL) or generalized authorized access (GAA), resectively. Each tier accets interference from tiers above and is rotected from tiers below. One of the vital imortant arts of the three-tiered sectrum access framework is how to identify available sectrum bands while rotecting the oeration of existing users. The current shared sectrum access systems either utilize geolocation database to determine which ortion of the sectrum is unoccuied or make use of environmental sensing caability (ESC) system to sense the resence of the incumbent users [4]. Based on the exerience of the TV white sace (TVWS) database oeration [11], the existing geo-location database technology is caable of facilitating the three-tiered access to the shared sectrum [12]. However, some of the PUs sectrum usage information rovided by database might be missed or out of date. Besides, the database only rotects the communication of the PUs. Therefore, both of the PUs and the SUs may suffer from severe interference and some sectrum oortunities are not efficiently utilized [13]. ESC is a grou of RF sensors and a decision system deloyed in the coastal areas, which is designed to detect the resence of the shiborne incumbent users [14]. However, ESC sensors are normally deloyed close to the ocean, which may be far from many metroolitan areas. Moreover, ESC sensors should be deloyed with a desired level of redundancy to maintain fault tolerance to sensor outage. In contrast, the sufficient amount of the CBRS access oints as the SUs are widely deloyed to rovide secondary sectrum access in both urban and rural areas, which could be the nearest infrastructures to most user devices. Therefore, the Citizens Broadband Service Device (CBSD) sensing network, which consists of CBRS access oints and CBRS users with sensing caability, is an ideal solution for identifying the

3 2 sectrum oortunities [4]. Remarkably, there are two key challenges to realize the CBSD sensing network in three-tiered sectrum sharing framework. Firstly, to make the best of the shared sectrum, a wide ortion of the sectrum must be sensed (u to 4MHz in UK sectrum sharing framework [1]). Since the samling rate of A/D converters in the SUs should be higher than twice of sectrum bandwidth due to the Nyquist-Shannon s samling theorem, the A/D converters with very high samling rate must be emloyed and large amounts of sectrum data have to be rocessed afterwards, which is unrealistic to be installed in the commercial SUs with restricted energy resources, e.g., mobile sensors and IoT devices. To alleviate the bottleneck of high rate A/D converters and the massive data rocessing burden after samling, comressive sensing (CS) [15], [16] was alied to acquire wideband signals using the lower samling rates than Nyquist rates by exloiting the sarse nature of the wideband sectrum as shown in Fig. 1. Due to the shorter roagation distance as the result of higher central frequencies (3.5GHz or above) used in three-tiered sectrum access framework, most sectrum occuancy status varies with users accessing or releasing the sectrum randomly. Therefore, the sarsity of the wideband signals is also varying and unknown [17]. Conventional CS theory requires rior knowledge of signal sarsity to calculate the sufficient number of comressive samles for signal reconstruction. Since the sarsity level is often unknown in ractice, most of CS aroaches assume a large sarsity level and choose the excess number of comressive samles to guarantee the quality of reconstruction. It turns out that these aroaches require more sensing time or higher samling rates to collect comressive samles, which causes larger sensing latency and therefore loses the advantage of using CS technologies. Secondly, to overcome the signal-to-noise ratio (SNR) degeneration caused by multi-ath fading, shadowing, and random noise over wireless channels, cooerative sectrum sensing (CSS) has been shown to increase the reliability of sensing by exloiting the satial diversity across the multile SUs [18], [19]. However, a large number of the SUs articiating in CSS network leads to extensive energy consumtion and transmission overhead due to sensing reorting and sensing decision at the fusion center. Therefore, only the SUs with high detection caabilities should be selected. It is shown in [2] that the best detection erformance is usually achieved by cooerating only with the SUs that have the highest SNR values. In general, the SNRs exerienced by the different SUs are unknown in advance, so that it is hard to identify SUs which have the best detection caability. Motivated by the above challenges, the contribution of this aer is two-fold. 1) Firstly, in order to reduce both the sensing time and data rocessing burden, and rovide the exact signal reconstruction without any extra channel assumtion including rior knowledge of sarsity, we roose an autonomous CS-based sensing algorithm that enables the local SUs to choose the number of comressive samles automatically. More secifically, instead of assuming the uer limit of sarsity level, which would not take Power (dbm) Frequency (MHz) Fig. 1. The real-time sectrum occuancy recorded at QMUL ( N W). The figure shows that the sectrum is sarsely occuied on F = [, 6] MHz. the full advantage of CS due to redundant samles collection, the roosed algorithm can autonomously terminate the samles acquisition when the roosed Euclidean distance D is smaller than a given threshold. The roosed algorithm could therefore achieve the minimum sensing time under the given samling rate. 2) Secondly, we roose a CS-based blind cooerating user selection algorithm over wide sectrum without any rior knowledge of the rimary signals, sensor locations. More secifically, by observing the reconstruction error of CS is degraded with the SNR exerienced by SUs, i.e., lower SNR leading to larger reconstruction error under given samling rate and sensing time, the roosed algorithm emloy the same mechanism as the roosed autonomous CS-based sensing algorithm to indirectly comare the degenerating of SNRs according to the aroximated reconstruction errors. Additionally, erformance analysis of the roosed autonomous CS augmented sectrum sharing scheme is resented to show its efficiency on dynamic sectrum sharing. Furthermore, the roosed algorithms are tested by the simulated signals as well as the real-world signals. The rest of this aer is organized as follows: Section II discusses the related work on sectrum sensing. In Section III, the reliminary system and signal model is described. Section IV introduces the roosed autonomous CS-based sensing algorithm. Section V develos the roosed blind cooerating user selection algorithm for selecting SUs with high SNR. Section VI analyzes and validates the roosed algorithms over simulated and real-world TVWS signals. Conclusions are drawn in Section VII. II. RELATED WORK Recently, there are some works emloying CS into sectrum sensing. In [21] and [22], novel frequency-domain cyclic refix (CP) autocorrelation based comressive sectrum sensing algorithms were roosed to detect PUs in the resence of noise uncertainty and frequency selectivity. By making use of sarsity in the sectral domain, CS was utilized to construct the autocorrelation of the received signal from its subband samle sequences. In [12] and [23], hybrid frameworks are

4 3 roosed to incororate the advantages of both geolocation database and CS-based sectrum sensing. However, the aforementioned works require the rior knowledge such as instant sarsity level of the wideband sectrum for signal reconstruction. Therefore, to eliminate the rior knowledge of instant sectral sarsity level in CS-based sectrum sensing. Authors in [24] roosed a sarsity order estimation method to obtain the minimum samling rate. To further imrove the sarsity order estimation erformance, a dynamic sarsity uer bound adjustment scheme was roosed in [25] for obtaining a roer sarsity uer bound. Comared with these algorithm, the roosed autonomous CS-based sensing algorithm can automatically choose the number of comressive samles without any sarsity estimation efforts. To solving the cooerating SUs selection roblem in sectrum sharing framework, with the knowledge of the SUs locations, the authors in [26] addressed the user selection roblem by selecting a set of SUs which exerience uncorrelated shadow fading. The knowledge of the distance between SUs and base station is required by those algorithms which also need the central coordination, i.e., the sensing results should be sent to the fusion center for selection. In [27], without the rior knowledge of the SUs locations, three methods for selecting the SUs based on hard local decisions were roosed, which outerform the urely random selection method of SUs. Moreover, a correlation-aware user selection scheme was roosed in [28], which was develoed by adatively selecting the SUs based on the evaluation of the correlation exerienced by the SUs. However, the aforementioned algorithms are under the circumstance of narrowband sensing rather than wideband one and therefore are not suitable for wideband CSS. In [29], a hybrid double threshold based CSS scheme was roosed, which could imrove the detection erformance at SUs by exloiting both local decisions and global decisions feedback from the fusion center. Based on order statistic information of the reorting links between SUs and fusion center, a multiselective sensing scheme was roosed in [18]. The links with high SNRs are selected and the number of selected links is decided centrally. Although the two schemes could be alied in wideband CSS, the selection rocess would be inefficient since the schemes introduce large latency due to the sequential manner of sensing. Our roosed blind user selection algorithm in this aer could cature the whole wide sectrum at the same time based on CS but utilizes a few comressive samles to select the SUs with high detection caabilities. III. SYSTEM AND SIGNAL MODELS In this section, the reliminary system and signal models of the roosed autonomous CS augmented sectrum sharing scheme are resented. A. System Model In the conventional three-tiered sectrum access framework, the resonsibility of the sectrum access system (SAS) is to manage all the incumbent and secondary oerations based on the information obtained from the incumbent database and PUs Incumbent Database Incumbent Detection (ESC) Sectrum Aceess System Cooerative Sectrum Sensing CBSDs CBSD Sensing Network Fig. 2. The roosed sensing-augmented sectrum sharing architecture the incumbent detection, i.e., ESC. The incumbent database rovides all the necessary sectrum usage and oerational information of the incumbent users. ESC detects the resence of shiborne incumbent users with a grou of RF sensors and the interference from the unregistered users. As shown in Fig. 2, the roosed scheme adot the CBSD sensing network that consists of the CBRS access oints and the CBRS users with sensing caability to identify sectrum oortunities and the unregistered users oerating on the target sectrum. Moreover, due to the centralized nature of SAS and the availability of the multile SUs, the roosed scheme can utilize the CSS scheme over the SUs within the same secondary access network to deal with the issues such as multi-ath and shadowing, which also can increase the satial diversity and reduce the robability of dee fading across all the SUs. B. Signal Model Sensing in the three-tiered sectrum access framework aims to find the sectrum holes which could be used for secondary access and identify the unwanted interference event over the whole shared sectrum. Let x(t) be a real-valued continuoustime signal received at the RF front end of the local SU, such that N sig x(t) = s i (t) + n(t), (1) i=1 where N sig is the number of ongoing transmission signals which san over the total band of W Hz, s i (t) is the i- th signal and n(t) refers to additive white Gaussian noise with zero mean and variance σn. 2 In the conventional Nyquist samling system, we could obtain a discrete time sequence x[k] = x( k f N ), k =, 1,..., N 1 by using the Nyquist samling rate f N over the total sensing time T N. N is the number of Nyquist samles as N = f N T, N Z. Based on the Nyquist samling theory, the samling rate f N is required to be higher than 2W samles er second and therefore a lot of samles would be generated to rocess, which slow down the rocessing seed and cause large ower consumtion. Therefore, such Nyquist samling rate schemes over wideband sectrum are likely unrealistic to be imlemented in the commercial SUs. This redicament urges us to aly CS technologies to reduce the number of samles while remaining the total bandwidth W unchanged. In a CS-based sectrum sensing aroach, the main task is to reconstruct x[k] or its discrete Fourier transform (DFT)

5 4 x = {(x 1, x 2,..., x N ) T ) x R N } from comressive samles. Secifically, since the wideband sectrum is ractically under-utilized, x(t) tyically bears a sarse roerty in the frequency domain such that its DFT x R N is a k-sarse vector, i.e., {x i : x i } s. Therefore, the wideband sectrum signal acquisition could be accomlished with a sub- Nyquist samling rate f s < 2W, resulting in fewer samles, and x[k] or x could be reconstructed from the comressive samles [3], which is exressed by the following analytical model: y = Φx + ξ subject to x s, (2) where Φ R M N is the measurement matrix to collect the comressive samles y R M from the original signal x, which could be imlemented using sub-nyquist samlers, e.g., random demodulator [31] and modulated wideband converter [32], in which controllable measurement matrices have been roosed to realize CS. M Z (with s < M < N) refers to the dimension of y, and reresents the number of nonzero elements in the vector, which is also treated as the measure of sarsity. The comressive ratio in this comressive signal acquisition is given by ρ = M/N < 1 and total sensing time T s = M/f s. ξ R M is the noise erturbation, whose magnitude is constrained by an uer bound δ, i.e., ξ 2 < δ. IV. THE PROPOSED AUTONOMOUS CS-BASED SENSING ALGORITHM In this section, we resent an autonomous CS-based sensing algorithm alied in local SUs of the CBSD sensing network. A. Algorithm descrition In CS theory, the number of comressive samles M is chosen regarding the sarsity level s of the signal in order to guarantee the quality of reconstruction, e.g., M Cs log(n/s) for a Gaussian measurement matrix, where C denotes a constant [15]. The sarsity level s of the sectrum is assumed to be known in most of the CS-based sectrum sensing aroach. These aroaches intend to assume a maximum sarsity level s max to ensure a high successful recovery rate since the sarsity level is often unknown and fluctuates in ractice. Therefore, the required number of comressive samles is larger than the necessary amount, which causes unnecessary sensing latency or higher samling rate for collecting extra samles. In contrast, our autonomous CS-based sensing algorithm is adative to actual sarsity level, where the sensing time T s is divided into several time intervals and the wideband signal is acquired block-by-block in time until the stoing criterion regarding reconstruction accuracy is reached. Therefore, the waste of samles can be averted and the sensing latency or samling rate could be further reduced. Additionally, the remaining sensing time can be utilized for data transmission. Secifically, the roosed algorithm divides the total sensing time T s into P time intervals where ( [1, P ]) refers to the index of each time intervals. Let y reresents a vector contains all the samles which are collected until the end of the -th time interval, and M denotes the number of elements in vector y, where < M 1 < < M. y and M reresent a vector contain the samles collected during the - th time interval and the number of samles collected in each time interval, resectively, i.e., M = M M 1. The collected samles vector y could be utilized for signal reconstruction by solving the l 1 -norm minimization roblem: arg min x 1 subject to Φ x y 2 2 δ, x R N where Φ denotes a M N matrix and x is the reconstructed signal from y. The original wideband sectrum signals tend to be comressible rather than sarse in the realworld environment, which can be well aroximated by sarse signals, but the reconstruction errors can only be diminished but not vanished [33]. Therefore, we utilize a roer constant arameter λ R + to balance the objective of minimizing the reconstruction error and the solution sarsity according to the Lagrange multilier theorem, such that the roblem (3) could be equivalently solved by the following unconstrained otimization roblem: arg min x R N Φ x y λ x 1. In addition, the choice of λ deends on the noise level of the original signal, e.g., the value of λ should be increased when the noise floor is higher [34]. As the fewer measurements are usually required for the l ν -norm minimization aroach comared with the l 1 -norm minimization aroach [35], we consider the aroximation of the l -norm by the l ν -norm instead of the l 1 -norm in (4): arg min x R N Φ x y λ x ν ν. In contrast to the l 1 -norm, the l ν -norm with < ν < 1 is nonconvex. As convex otimization techniques are no longer alicable, the global minimizer is not guaranteed and general NP-hard due to the nonconvexity of the l ν -norm minimization. To that end, iterative reweighted least square (IRLS) algorithm was roosed to solve this roblem by solving a sequence of the aroximation subroblems [36]. The solution sequence generated by the IRLS algorithm converges to the local minimum as the sarsest solution which is also the actual global l ν -norm minimizer under certain assumtions such as the null sace roerty (NSP) on Φ [35]. However, the comutational burden of l ν -norm minimization is higher than that of l 1 - norm minimization. To reduce the iterations and seed u the convergence of reconstruction, we adot the adatively regularized iterative reweighted least square (AR-IRLS) reconstruction algorithm [37] which moves the estimated solutions along an exonential-linear ath by regularizing the weights in each iteration with a series of non-increasing enalty terms. Secifically, the iterative estimates {x (l) } l=1 of x is given by x (l) w (l) Φ x y λ x 2(w (l) ) x R N := arg min 2, (3) (4) (5) (6) := (w(l) (1),..., w(l) (N) ), where x 2(w) 2 denotes N i=1 w ix 2 i ) ) ν 2 + ɛ ( ( w (l) (j) = x (l 1) (j) and w(l) (j) is defined as 2 1 < ν < 1. (7)

6 5 Algorithm 1 Autonomous CS-based sensing algorithm Require: Equally divide the total sectrum sensing time T s into P time intervals and set the start time interval index = 1. Samling rate f s, number of samles M collected in each time interval and the reconstruction error threshold κ. Ensure: The reconstructed signal x 1: for = 1,..., P do 2: Samling the wideband signal using f s till the time interval + 1 so as to obtain the comressive samles vector y and the samles y +1 collected in time interval : Reconstruct the sectral from y by utilizing AR-IRLS algorithm to solve the l ν -norm minimization roblem arg min x R N Φ x y λ x ν ν, which leads to a sectral reconstruction x. 4: Calculate the roosed Euclidean distance D = Φ M x y : if D smaller than threshold κ is true 6: Terminate the signal acquisition rocess. 7: else 8: = + 1 9: end if 1: end for After convergence, x (l 1) will be sufficiently close to x (l 1), so that x 2(w(l) ) 2 = N j=1 w(l) (j) x2 (j) = N j=1 ((x(l 1) (j) )2 + ɛ) ν 2 1 x 2 (j) would be close to x v v. In order to rovide stability and ensure that a zero-valued comonent in x (l) does not strictly rohibit a nonzero estimate at the next iteration, ɛ > [38] is adoted to regularize the otimization roblem in (7). To simlify the illustration of the roosed algorithm, we define a function F ν as [ ] 1 N F ν (x, Φ, w) := 2 Φx y λ w (i) x 2 (i), (8) i=1 Therefore, the estimate in each iteration is equal to x (l) := arg min F ν(x, Φ, w (l) ), (9) which requires solving a least squares roblem that can be exressed in this matrix form: ( ) 1 = W (l) Φ t Φ W (l) Φ t + λi y, (1) x (l) where W (l) is the N N diagonal matrix with 1/w (l) (i) as the i-th diagonal element and Φ t refers to the transose of the sensing matrix Φ. Once x (l) is obtained, we then udate the weights accordingly. Reeating the whole rocedure of signal acquisition and reconstruction, a sequence of sectrum reconstruction by increasing the number of time intervals, i.e., x 1, x 2,..., x, would be obtained. We now analyze the stoing criterion of signal acquisition. After each signal reconstruction rocess, the roosed algorithm decides whether the reconstruction of the original signal is accurate enough or not. If the reconstructed signal does not satisfy certain accuracy requirement of sectral detection, the algorithm should require more time intervals until the accuracy requirement is met. However, since the original signal x is unknown before the reconstruction in real-world, the exact reconstruction error e = x x 2 2, could not be obtained to determine how accuracy the reconstructed signal is. Therefore, we measure the reconstruction error e indirectly and set stoing criterion in such a ractical way. As the comressive samles vector y could be treated as the linear rojection of the original signal x during the samling rocess in (2), the Euclidean distance D between the samling result obtained by alying the same linear function, i.e., sensing matrix, to the reconstructed signal, and the actual comressive samles should not be too far, otherwise we shall tell the reconstructed signal x is quite different from the original signal x with high robability. Secifically, the roosed Euclidean distance D is defined as and y +1 is obtained by D = Φ M x y , (11) y +1 = Φ M x + ξ, (12) where Φ M denotes a M N matrix. The Johnson- Lindenstrauss Lemma resented in [39] asserts that a highdimensional sace can be rojected into a low-dimensional signal, where the dimension is equal or larger than O(ζ 2 logn) so that all distances are reserved u to a multilicative factor between 1 ζ and 1 + ζ with < ζ 1/2. Therefore, we demonstrate the rigorous relationshi between the roosed Euclidean distance D and the actual reconstruction error e by roving the oint that e = x x 2 2 calculated in high-dimensional, i.e., dimension of x, could be rojected into D calculated in low-dimensional, i.e., dimension of y +1, within the boundary factor of 1 ± ζ in Theorem 1. If the roosed Euclidean distance D is larger than the given threshold, the algorithm would continue the signal acquisition, otherwise the acquisition is terminated. For a given threshold κ which is redefined according to the reconstruction accuracy requirement, the minimum sensing time of the wideband signals would adat to the actual sarsity levels of the sectrum. The outline of the roosed algorithm is summarized in Algorithm 1. B. Theoretical guarantee In theorem 1, we rove that the actual reconstruction error e could be estimated by the roosed Euclidean distance D within the boundary factor of 1 ± ζ. Theorem 1. Given multilicative factor ζ (, 1/2], γ (, 1) and M Cζ 2 log(1/2γ), we have [ D Prob (1 + ζ) e D ] 1 γ, (13) (1 ζ) where the arameter C deends on the concentration roerty of random variables in measurement matrix Φ M [39]. D and e are defined as before.

7 6 Proof. With the aid of Johnson-Lindenstrauss Lemma, if the number of row r in Φ M is equal or larger than Cζ 2 log(1/2γ), we have (1 ζ) X 2 2 Φ M X 2 2 (1 + ζ) X 2 2, (14) where ζ (, 1/2] and γ (, 1). Then we relace X in (14) by x x and obtain Actual Reconstruction Error The Proosed Euclidean Distance (1 ζ) x x 2 2 Φ M (x x ) 2 2 (1 + ζ) x x 2 2. (15) Since measurement matrix Φ M could be seen as a linear rojection from R N to R M, we can transform (15) into (1 ζ) x x 2 2 Φ M x y (1 + ζ) x x 2 2. (16) Finally, to obtain the observation that e = x x 2 2 could be bounded and estimated by D = Φ M x y , we change the (16) to another form (17) and simlify it to (18): 1 (1 + ζ) Φ M x y x x (1 ζ) Φ M x y , (17) D (1 + ζ) e D (1 ζ). (18) Therefore, when the row number M in Φ M is equal or larger than Cζ 2 log(1/2γ), the distance between D and e could be bounded u to a multilicative factor between 1 ζ and 1 + ζ. Hence, we could state that the actual reconstruction error e could be estimated by the roosed Euclidean distance D when M is larger than a lower bound and D could be utilized as the stoing criterion of the algorithm. See Aendix for The roof of that (17) is satisfied with robability larger than 1 γ. V. CS-BASED THE PROPOSED BLIND COOPERATING USER SELECTION ALGORITHM In this section, we resent a CS-based blind cooerating user selection algorithm alied in the CBSD sensing network for selecting the SUs with high SNR in the roosed scheme without the degradation of the detection erformance by utilizing fewer SUs. A. Algorithm descrition In a CBRS sensing network, not every SU could roduce informative sectrum sensing results due to the different deloyment scenarios of the SUs. Moreover, as the number of cooerating SUs grows, the energy efficiency of the network decreases [4] and the sensing erformance of the network only marginally increases once the number of cooerating SUs is sufficiently large [41]. Therefore, it is not an otimal choice to cooerate all SUs no matter whether they have high detection caability or not. The otimal erformance could be achieved by selectively cooerating among SUs with high sensing erformance of the transmission signals [42] where the sensing erformances of SUs are fundamentally limited SNR (db) Fig. 3. r-mse vs. average SNR between the actual reconstruction error and the estimated reconstruction error. by the signal transmission channels since the reconstruction accuracy would be effected by the SNR of received signals. As shown in Fig. 3, if the samling rate is fixed and sufficient for signal reconstruction, reconstruction erformance would be affected by the SNR of the transmission signal, which is likely caused by the channel fading, i.e., shadowing and multi-ath. Therefore, CS could be utilized for cooerating user selection and the roosed autonomous CS-based sectrum sensing scheme could erform user selection without extra SNR estimation algorithms. The SUs with high SNR, could be selected by utilizing the roosed D to aroximate the unknown reconstruction error. Secifically, the comressed samles vector y is divided into two vectors y r (y r R r 1 ) and y v (y v R v 1 ) for estimating the reconstruction error. According to the acquisition model in (2), these two vectors can be exressed as y r = Φ r x + ξ and y v = Φ v x + ξ, resectively, where x R N 1, Φ r R r N and Φ v R v N. Parameter r as the number of comressed measurements in y r, is determined to ensure the successful reconstruction, and v is set to guarantee the sufficient accuracy of reconstruction error estimation as illustrated in Theorem 1. To select the suitable cooerating SUs, one can comare the estimated reconstruction error e with a redefined threshold which could be determined according to the detection caability requirement of SUs. Moreover, without the effort of signal reconstruction, only the locally collected samles should be sent to the fusion center for SUs selection under the centralized manner or be assed to other SUs under the distributed manner of the distributed CSS network. VI. EXPERIMENTAL RESULTS As a roof of concet for the roosed scheme, we verify the effectiveness of the roosed algorithms using both simulated signals and real-world signals in this section. A. Exeriment Setus and Performance Measures Consider the simulated wideband signal x(t) F = [, 5] MHz, whose DFT is denoted as x sim which contains u to k active channels: x(t) = k Ei B i sinc(b i (t t i ))e j2πfit + n(t), (19) i=1

8 7 (a) Fig. 4. (a) The outdoor antenna. (b) The RFeye node. (c) The catured ower sectrum density at Queen Mary University of London [43]. where sinc(x) = sin(πx)/(πx), E i, t i and f i reresent the energy, the time offset, and the central frequency of the i- th sub-band and n(t) denotes the noise. The i-th sub-band covers the frequency range [f i Bi 2, f i + Bi 2 ]. Tyically, the critical influences of a signal transmission channel consist of ath loss, small-scale fading, e.g., multi-ath, and large-scale fading, e.g., shadowing [26]. In each CBSD sensing network, the ath loss could be aroximately the same for all SUs since the maximum distance among SUs are assumed to be much smaller than the distance between the PUs and the SUs. For the fading effects, the multi-ath effect exhibits a Rayleigh distribution, which could cause random variations in the SNR at the SUs, while the shadowing effect could be viewed as extra losses via a series of obstacles which is notoriously hard to model accurately and its statistics can vary widely with the deloyment environments [41]. Therefore, we assume the SNR is varying in some channels for the different SUs in order to model both the large-scale and the small-scale fading effects. To demonstrate the effectiveness of the roosed scheme over the wideband sectrum with the varying bandwidths and ower levels of rimary signals, the bandwidths B i of i-th rimary signal is varying from 5 to 2 MHz and the corresonding central frequency f i is randomly located in [ Bi 2, W Bi 2 ]. The total sensing time is assumed as T = 1µs, and thus the number of samles collected by the Nyquist samling rate could be calculated as N = T f NY Q. Rather than using the Nyquist samling rate f NY Q 2W = 1 MHz, we adot the sub-nyquist samling rate f s < 2W which is deended on the maximum sarsity level s max that can be estimated by long-term sectral observations. In the conventional CS aroaches, the number of comressive samles M = T f s = K s max log(n/s max ) [15] should be determined by the worst case of sarsity level s max to guarantee a very high accetable reconstruction frequencies over the total sensing time T since the actual sarsity level is unknown in the realworld. In the roosed scheme, the total sensing time T is divided into P = T f s / M time intervals, where P Z +. The signal acquisition rocess would be terminated once the stoing criterion is reached. Therefore, the actual sensing (b) (c) time of the roosed scheme is equal or lower than T. The rest of sensing time could be utilized for data transmission besides, the shorter sensing time would revent the further interference to the PUs. The real-world signals x real are received by an RFeye node, which is an intelligent sectrum monitoring system that can rovide real-time 24/7 monitoring of the radio sectrum [44]. As shown in Fig. 4, the RFeye node is located at Queen Mary University of London ( N W), and the antenna height is about 15 meters above ground. To measure the reconstruction accuracy, we resent the reconstruction error x x 2 2 by the conventional average relative mean square error (r-mse): r-mse = x x 2 2 x 2, (2) 2 where x denotes the reconstructed signal, x = x sim in the simulation mode and x = x real in the real-time mode. To quantify the detection erformance we comute the detection robability, i.e., the fraction of occuied channels correctly being reorted as occuied. The estimated active channel set is comared against the original signal suort to comute the detection robability under 2 trials. B. Results over Simulated Signals To rove the effectiveness of the roosed scheme and verify the theoretical results in Theorem 1, we comare the actual reconstruction error and the roosed Euclidean distance D which is referred as stoing criterion with the different number of time intervals in Fig. 5. It shows that the original signal is successfully reconstructed and the signal acquisition could be terminated at the time interval = 1, rather than = 5 (total sensing time) by the conventional CS-based algorithms. Since the roosed Euclidean distance D become very close to the actual reconstruction error when the actual reconstruction error becomes sufficiently small, D could be utilized as the stoing criterion to terminate the signal acquisition rocess as resented in Theorem 1. Moreover, Fig. 5 shows that the reconstruction accuracy could not be significantly imroved by collecting additional samles. Therefore, the roosed scheme utilizes less sensing time than that of conventional CS aroaches with the same sub-nyquist samling rate. The remaining sensing time can be utilized for future data transmission, besides, the shorter sensing time would revent the further interference to the PUs. Since the PUs and the SUs could randomly enter or leave the shared sectrum, the sarsity levels of the received wideband signals in ractice are unknown and fluctuant. A ractical CSbased sensing algorithm should be robust against different signal sarsity levels. Therefore, in Fig. 6, we demonstrate the erformance of the roosed scheme under the different sarsity levels with a fix samling rate f s =.5f NY Q. From Fig. 6, it can be observe that the roosed scheme could successfully reconstruct the signals and terminate the sensing rocess at the time interval = 8, 15, 2 under the sarsity levels s =.5N,.1N,.15N, where the higher sarsity levels of the signals would lead to the more time

9 8.15 Actual reconstruction error Stoing criterion E S r -M Number of Time Intervals Fig. 5. r-mse vs. number of time intervals between the actual reconstruction error and the stoing criterion D when sarsity level is fixed as s =.1N for the roosed scheme Proosed scheme with user selection (2MHz) Proosed scheme without user selection (2MHz) Proosed scheme with user selection (4MHz) Proosed scheme without user selection (4MHz) Sarsity Level Fig. 8. Detection robability vs. the sarsity level (N) between the roosed algorithm with and without cooerating user selection under different samling rates = 2MHz and 4MHz Number of Time Intervals Sarsity level =.5N Sarsity level =.1N Sarsity level =.15N Fig. 6. r-mse vs. number of time intervals under different sarsity levels s =.5N,.1N,.15N for the roosed scheme Sarsity Level Traditional CS-based sensing scheme Proosed scheme with large ste length Proosed scheme with small ste length Two ste CS-based scheme Fig. 7. Average sensing time (µs) vs. the sarsity level (N) between the roosed scheme and other CS-based sectrum sensing algorithms. intervals needed for guaranteeing the reconstruction accuracy. Therefore, without the rior knowledge of the actual sectral sarsity, the roosed scheme can autonomously adot a roer number of time intervals for signal reconstruction. In Fig. 7, we resent the comarison among the two-ste CS-based sectrum sensing scheme [24] (termed two-ste CS-based scheme), the conventional comressive sectrum sensing scheme [45] (termed traditional CS-based scheme) and the roosed scheme. We use the average sensing time in µs instead of the number of time intervals to measure the reduction of the sensing cost, since only the roosed scheme needs to divide the total sensing time into multile small time intervals. Without loss of generality, we test different schemes with a fixed samling rate f s =.5f NY Q. To illustrate the imact of adoting different ste lengths M, the roosed scheme is tested with both the large ste length and with the small ste length, which adots M = 5 and M = 5, resectively. It is shown in Fig. 7 that the erformance of the roosed scheme is influenced by the ste length M. If the M is too large, the roosed scheme will lose its advantage and be worse than the two-ste CS-based scheme. To understand this, we consider an extreme setting: the total number of time intervals is set to 1 and thus the ste length become M = M = T f s, where the roosed scheme is degraded to the conventional comressive sectrum sensing scheme which could not work with unknown sarsity levels efficiently. Therefore, M should not be too large in order to kee the effectiveness of the roosed scheme. However, if M is too small, it will require many stes, e.g., maximum 25 time intervals are required if M = 2 in this simulation, although it is more likely to reach the minimum sensing time. Therefore, there is a trade-off need to be balanced between comutational comlexity and the effectiveness of the roosed scheme. To illustrate the functionality of the roosed CS-based blind cooerating user selection algorithm, we show the detection robability against the sarsity level between the roosed scheme with and without cooerating user selection under different samling rates (2 MHz and 4MHz) in Fig. 8. In the roosed scheme, we select half of the SUs to erform CSS for demonstration urose. The maximum number of the cooerating SUs could be set according to the caacity in the ractical network environment. It is shown that the detection robability of the roosed scheme with user selection is always higher than or equal to that of the roosed scheme without user selection. Therefore, there is no degeneration of the detection robability when cooerating with fewer SUs. Moreover, the detection robability is imroved when sarsity level of the wideband sectrum is high, i.e., higher occuancy ratio, under different samling rates. That is because the roosed cooerating user selection scheme could take out the SUs with bad detection results, e.g., malicious users, which could affect the overall detection erformance. C. Analysis on Real-world Signals To analyze the erformance of the roosed scheme with real-world signals over the different sectrums, e.g., TVWS sectrum and 3.5GHz sectrum in the UK, we comare the r-mse of the roosed scheme against the two-ste CS-based sectrum sensing scheme with the same samling rate in Fig. 9. It is shown that the roosed scheme not only can work roerly in the 3.5GHz shared sectrum, but also can

10 9 deal with the TVWS sectrum. Particularly, as the real-world 3.5GHz sectrum is much sarser than the TVWS sectrum in the UK, the required sensing time of the 3.5GHz sectrum is less than that of the TVWS sectrum. The roosed method outerforms the two-ste CS in terms of sensing time under give samling rate since the adoted AR-IRLS reconstruction algorithm requires fewer comressive samles to achieve the same reconstruction accuracy comared with the basis ursuit denoising (BPDN) reconstruction algorithm adoted in twoste CS [37]. The roosed scheme is suitable for the ractical measurements and can be extended to other shared sectrums like TVWS and the bands with the higher central frequencies. VII. CONCLUSION In this aer, we have roosed an autonomous CS augmented sectrum sharing scheme to rovide more efficient sectrum oortunities identification within the CBSD sensing network. In order to tackle the challenges of realizing the CBSD sensing network, firstly we roosed an autonomous CS-based sensing algorithm which enables the local SUs to automatically choose the minimum sensing time while guaranteeing the exact wideband signal reconstruction. To enhance the detection erformance and use fewer SUs in each CBSD sensing network, a CS-based blind cooerating user selection algorithm is roosed to select the SUs which could roduce informative sectrum sensing results according to the detection SNR of the transmission signals. The robust erformance of the roosed CS-based autonomous sensing scheme has also been validated over both simulated signals and real-world signals recorded by the RFeye node at QMUL. Numerical analysis and exerimental results have shown that the roosed scheme could not only adatively select an aroriate number of time intervals without the estimation of sarsity level but also offer exact signal reconstruction for varying bandwidth of channels and ower levels under different unknown sarsity levels. In comarison with conventional comressive sectrum sensing schemes and two-ste CS-based sectrum sensing schemes, it is shown that the roosed scheme can achieve the better detection erformance as well as the shorter sensing time and fewer number of cooerating SUs. Additionally, the remaining sensing time can be utilized for data transmission and avoiding the further interference to the ongoing rimary transmissions. These benefits enable the roosed scheme to be imlementable for sectrum sharing, esecially over the 3.5GHz sectrum and the higher frequencies. Moreover, we shall extend the roosed scheme with advanced detector such as frequency domain autocorrelation [22] and maximum - minimum energy detection sensing algorithm [46] to further enhance the ability against the noise uncertainty and frequency selective channel in future work. APPENDIX PROOF OF THE THEOREM 1 Let X R n be an arbitrary fixed unit vector, i.e., X 2 2 = 1 for simlicity, and the linear rojection X Y is defined by n Y (i) = A (ij) X (j), i = 1, 2,..., r, (21) j= Proosed scheme over 3.5GHz sectrum Two-ste CS-based scheme over 3.5GHz sectrum Proosed scheme over TVWS sectrum Two-ste CS-based scheme over TVWS sectrum Sensing Time Fig. 9. r-mse vs. the sensing time (µs) over different real-world sectrum signals. where A (ij) are indeendent random variables with E[A (ij) ] = and Var[A (ij) ] = 1, which has an uniform sub-gaussian tail. Since Y could be seen as a linear combination of the A (i) which is the i-th row of A, Y (i) has an uniform sub-gaussian tail as well. Therefore, according to the Proosition 3.2 in [39], we could define a random variable as Z = 1 (Y 2 r (1) + + Y (r) 2 r), (22) where Z has a sub-gaussian tail u to r. Therefore, Y is distributed as Z/ r and we can get Prob[ Y ζ] = Prob[ Y ζ 2 + 2ζ] Prob[ Y ζ] = Prob[Z 2ζ r]. (23) As ζ (, 1/2], by utilizing the Chernoff-tye inequality, we have Prob[Z 2ζ r] ex a(2ζ r) 2 = ex 4aζ2 Cζ 2 log(2/γ) γ 2 (24) for C 1/2a. Alying the same rincile and the similar calculation as above, Prob[ Y 2 1 ζ] γ/2 could be demonstrated as well. Therefore, we can get the conclusion that Prob [ (1 ζ) X 2 2 AX 2 2 (1 + ζ) X 2 2] 1 γ. (25) Then we relace X in (25) by x x to obtain (26). As A refer to the linear rojection X Y, we could get (27) and its another form (28), shown below: Prob [ (1 ζ) x x 2 2 Φ M (x x ) 2 2 (1 + ζ) x x 2 2] 1 γ, (26) Prob [ (1 ζ) x x 2 2 Φ M x y [ Prob (1 + ζ) x x 2 2] 1 γ, (27) 1 (1 + ζ) Φ M x y x x 2 2 ] 1 (1 ζ) Φ M x y γ. (28) Finally, we shall simlify (28) to the result [ D Prob (1 + ζ) e D ] 1 γ. (29) (1 ζ)

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12 11 [46] S. Dikmese, P. C. Sofotasios, M. Renfors, and M. Valkama, Maximumminimum energy based sectrum sensing under frequency selectivity for cognitive radios, in Cognitive Radio Oriented Wireless Networks and Communications (CROWNCOM), 214 9th International Conference on, Oulu, Finland, Jun. 214, Xingjian Zhang (S 16) received the B.Sc. degree (First Class Hons.) in telecommunications engineering from Beijing University of Posts and Telecommunications, Beijing, China. He is currently working towards his Ph.D. degree in the School of Electronic Engineering and Comuter Science, Queen Mary University of London since 214. His current research interests include cooerative wireless sensor networks, comressive sensing, real-time sectrum monitoring and analysis, and Internet of things (IoT) alications. Yuan Ma (S 15-M 17) received the B.Sc. degree (First Class Hons.) in telecommunications engineering from Beijing University of Posts and Telecommunications, Beijing, China, and the Ph.D. degree in electronic engineering from Queen Mary University of London, London, U.K., in 213 and 217, resectively. She is currently an Assistant Professor with the College of Information Engineering, Shenzhen University, Shenzhen, China. Her research interests include cognitive and cooerative wireless networking, sub-nyquist signal rocessing, and sectrum analysis, detection, and sharing over TV white sace. Wei Zhang (S 1-M 6-SM 11-F 15) received the Ph.D. degree in electronic engineering from the Chinese University of Hong Kong, Hong Kong, in 25. He was a Research Fellow with the Hong Kong University of Science and Technology, Clear Water Bay, Hong Kong, from 26 to 27. He is currently a Professor with the University of New South Wales, Sydney, NSW, Australia. His research interests include cognitive radio, 5G, heterogeneous networks, and massive multile inut and multile outut. He is the Editor-in-Chief of the IEEE WIRE- LESS COMMUNICATIONS LETTERS. He is also an Editor for the IEEE TRANSACTIONS ON COMMUNICATIONS. He served as an Editor for the IEEE TRANSACTIONS ON WIRELESS COMMUNICATIONS from 21 to 215 and the IEEE JOURNAL ON SELECTED AREAS IN COMMUNI- CATIONS (Cognitive Radio Series) from 212 to 214. He articiates actively in committees and conference organization for the IEEE Communications Society. He is Vice Chair for the IEEE Wireless Communications Technical Committee. He is an elected member of the SPCOM Technical Committee of the IEEE Signal Processing Society. He also served in the organizing committee of the 216 IEEE International Conference on Acoustics, Seech and Signal Processing, Shanghai, China, and the IEEE GLOBECOM 217, Singaore. He is TPC co-chair of the 217 Asia-Pacific Conference on Communications and the 219 International Conference on Communications in China. He is a member of the Board of Governors of the IEEE Communications Society. He was a reciient of the IEEE Communications Society Asia-Pacific Outstanding Young Researcher Award 29 and the IEEE ComSoc TCCN Publication Award 217 as well as four best aer awards in international Conferences. Yue Gao (S 3-M 7-SM 13) is a Reader in Antennas and Signal Processing, and Director of Whitesace Machine Communication Lab in the School of Electronic Engineering and Comuter Science at Queen Mary University of London (QMUL) in the UK. He worked as Research Assistant, Lecturer and Senior Lecturer at QMUL after having received his PhD degree from QMUL in 27. He is currently leading a team develoing theoretical research into ractice in the interdiscilinary area among smart antennas, signal rocessing, sectrum sharing and internet of things (IoT) alications. He has ublished over 14 eer-reviewed journal and conference aers, 2 atents, and 2 book chaters. He is a coreciient of the EU Horizon Prize Award on Collaborative Sectrum Sharing in 216, and Research Performance Award from Faulty of Science and Engineering at QMUL in 217. He is an Engineering and Physical Sciences Research Council (EPSRC) Fellow from He is an Editor for the IEEE Transactions on Vehicular Technology, IEEE Wireless Communication Letter and China Communications. He is serving as Cognitive Radio Symosium Co-Chair of the IEEE GLOBECOM 217. He served as the Signal Processing for Communications Symosium Co- Chair for IEEE ICCC 216, Publicity Co-Chair for IEEE GLOBECOM 216, and General Chair of the IEEE WoWMoM and iwem 217. He is a Senior Member of IEEE, a Secretary of the IEEE Technical Committee on Cognitive Networks, and an IEEE Distinguished Lecturer of Vehicular Technology Society.