Cyclostationarity-Based Spectrum Sensing for Wideband Cognitive Radio

Transcription

1 9 International Conerence on Communications and Mobile Computing Cyclostationarity-Based Spectrum Sensing or Wideband Cognitive Radio Qi Yuan, Peng Tao, Wang Wenbo, Qian Rongrong Wireless Signal Processing and Network Lab Key laboratory o Universal Wireless Communication Ministry o Education Beijing University o Posts and Telecommunications, Beijing, 876, China qiyuan@bupt.edu.cn Abstract This paper addresses the problem o cyclostationary detection when the signal spectrum is partly intercepted. The signal model or partial interception o spectrum is presented. Cyclostationary eature o signal is analyzed in this scenario and cyclic spectrum present region is also deined. An improved cyclic spectrum estimator as well as detection strategy or unknown eature location is proposed. Simulation results veriy that perormance o proposed algorithm can satisy the requirement o eature detection.. Introduction Spectrum sensing is one o the most critical components o cognitive radio (CR) technology. Reliable spectrum sensing unctionality needs to be equipped or CR users. Cyclostationary detector has been introduced or detecting weak signal in cognitive radio [6][5][9], since it has desirable perormance under low signal-to-noise ratio (SNR) and can be used or signal recognition and classiication. A CR system should provide invisible spectrum access over a wide requency range covering multiple communication standards thus wideband spectrum sensing as an important eature is required or CRs[7]. A tunable narrowband bandpass ilter(bpf) or a ilterbank composed o several narrowband ilters can be employed as radio rontend according to spectrum usage or wideband sensing[8]. Existing signal types and their requency locations are usually unknown to CR over a wide range o requency (above MHz), thereore signal spectrum may be intercepted partly by bandpass ilter. Current research o cyclostationary sensing are based on assumptions that signal spectrum is ully intercepted and center requency can be captured. However none o previous works concerns cyclostationary sensing when signal spectrum is partly intercepted. In this paper, we concern cyclostationary sensing when signal spectrum is partly intercepted. We introduce a signal model or partial interception o signal spectrum. With this model, we analyze eects o partial interception o signal spectrum on cyclostationary eature o signal and cyclic spectrum estimator. By applying weighting actor, we propose an improved cyclic spectrum estimator and a detection strategy when eature location is unknown. Simulation results demonstrated desirable perormance o the estimator and detection strategy are presented.. Signal Model or Partial Interception o spectrum Suppose that several spectrum bands whose requency boundaries locate at <... < N are to be detected or wideband CR. The n-th band is deined as B n : { B n, n < < n },n =,,...N. The bandwidth o narrowband BPF is assumed to be B w. When the tunable narrowband BPF is employed to search over wideband sequentially or the ilterbank ormed by multiple BPFs is applied to detect wide spectrum at a time[8], signal spectrum can be intercepted partly by BPF inevitably. The PSD structure o a wideband signal is illustrated in Fig., where the n-th band centered by c,n is intercepted partly by the BPF. The assumptions are adopted that the width o n-th band is B n = n n, with center requency at c,n =( n + n )/. Ater signal spectrum is intercepted partly by BPF, the width o n-th band remains in BPF is B p = H n, where ( L, H ) is passband o BPF. And only one signal band is captured by BPF but its location is unknown to CR. The bandpass representation o the signal can be deined as s(t) =Re[s l,n (t)e jπc,nt ] () where s l,n (t) is the lowpass representation o the signal. Ater signal spectrum is intercepted partly, the signal can /9 $5. 9 IEEE DOI.9/CMC

2 PSD B w n cn, n N Figure. The PSD structure o a wideband signal be described by N Freq. s p (t) =s(t) h BP (t) () where denotes convolution and h BP (t) the impulse response o BPF. For the simplicity o analysis, we may approximate requency response as H BP () =e jπm, L < < H (3) where M denotes the ilter order. When locates at other values, H BP () remains zero. Equivalent lowpass representation o signal whose spectrum is partly intercepted can be expressed as s lp (t) = [s(t) h BP (t) h + (t)]e jπcbp t = s + (t)e jπcbp t (4) where s + (t) denotes the analytical signal, h + (t) the impulse response o Hilbert transorm, and cbp the center requency o BPF, ( H L )/. 3. Cyclostationary Detection or partial interception o signal spectrum Cyclostationary eature can be described by cyclic spectrum which measures the density o spectral correlation, that is, the density o correlation between widely separated spectral components. When the spectrum is intercepted partly, cyclic spectrum will be deormed. 3.. Cyclostationary Feature or partial interception o signal spectrum Based on Linear Periodically Time-Variant transormation (LPTV) model [4], we can obtain cyclic spectrum o the equivalent baseband signal in equation (4): S α s lp () =S α s + ( + cbp ) (5) where α is cyclic requency o the signal. Since narrowband BPF and Hilbert transorm are time invariant, considering h(t) =h BP (t) h + (t) as impulse response unction o LPTV system, we can arrive at Ss α + () = H + ( + α/)ss α BP ()H+( α/) = H + ( + α/)h BP ( + α/)ss α () HBP( α/)h+( α/) (6) where H + () =u() is unit step unction and also the requency response o Hilbert transorm, complex conjugate. Besides, cyclic spectrum o baseband signal satisies its spectral support region []. Thus cyclic spectrum o equivalent baseband signal or partial spectrum interception is bandlimited to <B p α /, which is Ss α lp () = H BP ( + cbp + α/)ss α ( + cbp ) HBP( + cbp α/) (7) while Ss α lp () =or B p α /. We note that cyclic spectrum or partial spectrum interception depends on how much the signal spectrum is captured. When signal spectrum is ully covered, its whole cyclostationarity can be presented. However, as width o signal spectrum cut o by BPF increases, the present cyclic spectrum is deormed. In spectral support region, width o intercepted spectrum is B lp = H n = H c,n + B n / (8) while the cyclic requency which can be present satisies α < H c,n + B n / (9) That is, when width o captured signal spectrum equals to ( H c,n +B n /), cyclic spectrum locating at α > H c,n + B n / disappears. The present cyclic spectrum o partly intercepted signal spectrum is illustrated in Fig.. The diamond region with dashed line shows the spectral support region o signal moved to baseband rom center requency cbp while solid line denotes the spectral support region o equivalent baseband signal captured by BPF. When signal spectrum can be ully covered, the dashed diamond should be contained by the solid one. As captured signal spectrum reduces, the dashed diamond moved out o solid one along the axis. The intersection o dashed and solid diamond demonstrates present area o cyclic spectrum or partial spectrum interception and can be deined as cyclic spectrum present region. 3.. Cyclic Spectrum Estimator or Partial Interception o spectrum Considering received signal model, x(t) =s(t)+n(t), cyclic spectrum estimator [3] can be given by Ŝ α x () = MT (M )/ υ= (M )/ 8

3 B p α as Q = M L L p +. The smoothed spectral correlation o q-th group is B p B n B n cn, α = + B n cbp H c, n n Figure. The present cyclic spectrum o partly intercepted signal spectrum X T ( α/+υf s ) () where T denotes observation length, M spectral smoothing length, F s requency sample interval, X T () short-time Fourier transorm X T () = T t= x(t)e jπt. Suppose that when signal spectrum is intercepted partly, requency bins locating at ( α/ (M )F s /, α/ (M )F s /+ΔMF s ) are cut o and their valves are assumed to be estimation errors, X T () =ε. Then conventional estimator computes cyclic spectrum at certain (,α) as Ŝ α x () = cbp ΔM M MT [ υ= M ε α/+υf s + M υ=δm+ M X T ( α/+υf s )] = MT [ M υ=δm+ M XT ( α/+υf s )+ξ] () where ξ is accumulation o spectral correlation at requency bins cut o and M =(M )/. Note that spectral correlation exhibits at (M ΔM)F s requency bins. Conventional estimator averages over MF s requency bins with unknown locations o cut o ones, thus the estimated result is reduced. The reduction o the eature due to cut o requencies can be improved by weighted spectral correlation. Smoothing window is used or smoothed correlation with window length L. Two adjacent windows have P overlapped requency samples. The number o smoothing group is deined Ĩ q = T q +L υ=q X T ( α/+υf s ) () where q = (L P )q (M )/ is the start subscript o requency sample or each group. Then weight actors are applied or averaging over Q groups. Let w Re = [w Re,,..., w Re,q,...w Re,Q ] and w Im = [w Im,,..., w Im,q,...w Im,Q ] represent weight actors or real and imaginary parts o spectral correlation o Q groups respectively. Weight actors or real parts are provided by w Re,q = (Re{Ĩq}) Q q= (Re{Ĩq}) (3) For imaginary parts, weight actors can be obtained in a similar way. The improved cyclic spectrum estimator can be expressed as Ŝx α () =wĩt (4) where Ĩ = [ĨRe,jĨIm] = [Re{Ĩ},..., Re{ĨQ},jIm{Ĩ},..., jim{ĩq}] Note that weight actor or each group is set in proportion to its spectral correlation. Low correlation leads to high possibility o presence o requency bin cut o and relates to a low weight actor Cyclic Spectrum Detector or Partial Interception o spectrum When signal spectrum is intercepted partly, location o cyclic spectrum are unknown to CR. Thus to detect cyclostationary eature at speciic (,α) is not easible. We need to identiy location o cyclic spectrum. We search or maximum spectral correlation at certain cyclic requency over ( start, end ) with search interval Δ according to ˆk = arg max <k K [ Sα x ( k ) ] (5) where k denotes k-th requency bin. From equation (5), we can also obtain several locations with higher spectral correlation. Let a test vector or K requency bins at certain α is composed o ŝ α x =[Re{Ŝα x ( k, )},..., Re{Ŝα x ( k,k )}, Im{Ŝα x ( k, )},..., Im{Ŝα x ( k,k )}] (6) 9

4 Given that the hypothesis H represents the case where x(t) does not exhibit cyclostationarity with the cyclic requency α and H represents the case where x(t) does exhibit cyclostationarity, the ollowing binary hypothesis testing problem can be ormulated: H : {ˆk,n } K n= ŝ α x = Δ α x H :orsome{ˆk,n } K n= ŝ α x = s α x + Δ α x where Δ is the asymptotically normal distributed estimation error vector. The asymptotic complex normality o ŝ α x [] allows the ormulation o the ollowing generalized likelihood unction as the test statistic or the binary hypothesis test: T = ŝ α x ˆΣ x ŝα(t ) x (7) where ˆΣ x denotes estimated covariance matrix o ŝ α x []. Under null hypothesis, the distribution o the test statistic converges asymptotically to a central χ distribution with K degrees o reedom. Thereore, or a given alse alarm probability P, we can obtain threshold rom χ distribution table and decide presence o cyclostationarity. S s α ().. 5 α (Hz) (Hz).5 x 4 Figure 3. the cyclic spectrum present region when signal spectrum is ully captured 4. Simulation Results In the ollowing, the conidence o the proposed method has been investigated. OFDM signals are generated using quadrature phase shit keying (QPSK) modulated random data symbol. A 6-bin IFFT is used or the simplicity o analysis with subcarrier separation khz. Center requency o bandpass OFDM signal is 5kHz. Passband and bandwidth o BPF are ( L << H ) and B w =8kHz. The width o intercepted spectrum can be adjust by changing passband o BPF. Fig.3 and Fig.4 illustrate the cyclic spectrum present region when signal spectrum is ully captured and is partly intercepted respectively. For symmetry o cyclic spectrum, only α>are presented. We can observe that the cyclic spectrum present region is deormed or vanish moving along axis as signal spectrum is discarded. Fig.5 compares perormance o improved estimator with conventional one and relationship between detection probability and SNR is plotted. Speciic requency location =8kHz, α = F d =khz is chosen. L =5is selected or smoothing window with overlapped length P = L. Passband o BPF is set to be (khz, khz). The detection perormance improves by the proposed estimator as expected or partial spectrum interception. Fig.6 shows the detection reliability at dierent cyclic requencies, α = F d, F d. Two set o passbands (7kHz, 5kHz) and (khz, khz)are chosen or comparison. We can also note the perormance improvement by our proposed estimator. And eature at α =F d can be harder to detect than α = F d when signal spectrum is discarded too much. Thereore, we should choose smaller α to S s α ().. 5 α (Hz) (Hz).5 x 4 Figure 4. the cyclic spectrum present region when signal spectrum is partly intercepted detect or partial spectrum interception. Fig.7 indicates perormance o proposed detection method. start and end are set to be 4kHz and 8kHz. And Δ = 5Hz. Passband (khz, khz), (4kHz, khz), (7kHz, 5kHz) and (khz, 3kHz) are considered. Similar perormance can be observed when enough spectrum is intercepted. However perormance decreases as captured spectrum reduces. Moreover, compared to detection at certain location, perormance is more reliable considering multiple locations. 5. Conclusion In this paper, a signal model or partial spectrum interception is presented. The eects on cyclostationary eature are exploited and cyclic spectrum present region is deined.

5 Figure 5. P d vs SNR or comparing perormance o improved estimator with conventional one Figure 6. P d vs SNR or comparing perormance at dierent cyclic requencies An improved cyclic spectrum estimator based on weighting and its detection strategy or unknown eature location are proposed. Simulation results veriy that variation o cyclic spectrum coincides with our analysis. And improved detection perormance is demonstrated. Smaller cyclic requency exhibits more reliable perormance when spectrum partly intercepted. By searching eature over a requency range, detection perormance can be enhanced desirably. Figure 7. P d vs SNR or proposed detection method [] W. A. Gardner. Introduction to Random Processes with Applications to Signals and Systems. Macmillan Publishing Company, New York, 986. [3] W. A. Gardner. Measurement o spectral correlation. IEEE Transactions on Acoustics, Speech, and Signal Processing, ASSP-34(5): 3, October 986. [4] W. A. Gardner. Spectral correlation o modulated signals: Part i- analog modulation. IEEE Transactions on Communications, COM-35(6): , June 987. [5] J. Lunden, V. Koivunen, A. Huttunen, and H. V. Poor. Spectrum sensing in cognitive radios based on multiple cyclic requencies. nd International Conerence on Cognitive Radio Oriented Wireless Networks and Communications, pages 37 43, August 7. [6] M. Oner and F. Jondral. On the extraction o the channel allocation inormation in spectrum pooling systems. IEEE Journal on Selected Areas in Communications, 5(3): , April 7. [7] Z. Quan, S. Cui, A. H. Sayed, and H. V. Poor. Wideband spectrum sensing in cognitive radio networks. IEEE International Conerence on Communications, pages 9 96, May 8. [8] A. Sahai and D. Cabric. Cyclostationary eature detection. st IEEE International Symposium on New Frontiers in Dynamic Spectrum Access Networks, November 5. [9] A. Tkachenko, D. Cabric, and R. W. Brodersen. Cyclostationary eature detector experiments using reconigurable bee. nd IEEE International Symposium on New Frontiers in Dynamic Spectrum Access Networks, pages 6 9, April 7. Reerences [] A. V. Dandawate and G. B. Giannakis. Statistical tests or presence o cyclostationarity. IEEE Transactions on Signal Processing, 4(9): , September 994.