Wideband Spectrum Sensing for Cognitive Radios

Transcription

1 Wideband Spectrum Sensing for Cognitive Radios Zhi (Gerry) Tian ECE Department Michigan Tech University February 18, 2011

2 Spectrum Scarcity Problem Scarcity vs. Underutilization Dilemma US FCC fixed spectrum access policies have useful radio spectrum pre-assigned inefficient utilization PSD at any time and location, most spectrum is unused GHz Source: Spectrum Sharing Inc. 1

3 Spectrum Sharing under User Hierarchy CRs opportunistically use the spectrum Secondary User (SU) legacy users cognitive radio Primary User (PU) legacy users power frequency cognitive radios Cognitive radio network problems Finding holes in the spectrum: wideband spectrum sensing Allocating the open spectrum: dynamic resource allocation Adjusting the transmit waveforms: waveform adaptation 2

4 Challenge 1: Wideband Signal Acquisition Choices for RF Circuits: multiple NB or single WB? multiple narrowband (NB) circuits Freq. Band 1 LNA Band 2 LNA Band N LNA LO 1 LO 2 LO N wideband (WB) circuit LNA Fixed LO AGC AGC AGC AGC NB filter A/D WB filter multiple RF chains, BPFs number of bands fixed LO filter range is preset simple (energy/feature) detection within each BPF single RF chain flexible to dynamic PSD burden on A/D: f s ~ GHz complex wideband sensing Effective SNR (SNR eff ) for DSP determined by front-end circuits A/D A/D A/D SNR eff Wideband Sensing SNR eff A. Q: Sahai How and can D. we Cabric, alleviate IEEE DySpan DSP burden 2005 on wideband circuit design? 3

5 Challenge 2: User Hierarchy IEEE requires CRs to sense PU signals as low as -114dBm Operating Conditions Protection of primary systems Random sources of interference and noise Technical Challenges Sensing at low SNR Modulation classification Short sensing time Robustness to noise uncertainty Interference identification Q: How can we alleviate noise uncertainty effects at low SNR? 4

6 Challenge 3: Wireless Fading If no energy detected on a band, can CR assume PU is absent? Detection performance limited by received signal strength Wireless: deep fading, shadowing, local interference missed detection, hidden terminal problem Spatial diversity against fading PUs f CR 1 f CR 2 f multiple (random) paths unlikely to fade simultaneously f Q: How can we collect cooperation gain at affordable overhead? 5

7 Road Map for Wideband Sensing Local Compression + Network Cooperation Compressed Sensing with sub-nyquist-rate sampling Exploiting the Sparsity in the received signal (in freq. domain) Making use of Compressive Sampling to reduce sampling rates Compressed Cyclic Feature based Sensing Exploiting the Sparsity in both freq. & cyclic-freq. domains Making use of Cyclic Statistics for robustness to noise uncertainty and low SNR conditions Multiple-CR Cooperative Sensing 6

8 Limits on Sampling Rates CR j 1 n N f Spectrum occupancy ratio r nz = N nz /N 1 Wide band of interest: BW = B Lower bounds on sampling rates f s What is the lowest f s for reconstruction without aliasing? Nyquist rate = 2B What is the lowest f s for reconstruction of CR signals? Motivating factor for CR is low spectrum utilization Landau rate = 2B eff = 2 r nz B < Nyquist rate Challenge: locations of occupied bands are unknown Compressed Sensing (CS) 7

9 Basics of Compressed Sensing (a1) s is sparse (nonzero entries unknown) (a2) H can be fat (K N); satisfies restricted isometry property (RIP) Compressive sampling [Chen-Donoho-Saunders 98], [Candès et al 04-06] Given y and H, unknown s can be found with high probability Sparse regression [Tibshirani 96], [Tipping 01] Least-absolute shrinkage selection operator (Lasso) Ex. (scalar case) closed-form solution variable selection + estimation 8

10 f Sub-Nyquist-rate Sampling F -1 analog input r(t) CS-ADC S c r f r t x t digital samples CS recovery r f r f : N 1 discrete representation Received signal r(t) :t [0,NT s ] Fine-resolution (Nyquist-rate) representation: Sparsity in frequency: N nz = r f 0 N Linear sampling Compression in time (M/N): S c : K N N nz K N Various designs of random samplers [Kirolos etal 06, Hoyos etal 08] 9

11 Spectrum Hole/Edge Detection Spectrum reconstruction Spectrum hole detection (edge detection on wavelet basis) 100% 90% 75% 50% 33% 20% [Tian-Giannakis 07] 10

12 Road Map for Wideband Sensing Local Compression + Network Cooperation Compressed Sensing with sub-nyquist-rate sampling Exploiting the Sparsity in the received signal (in freq. domain) Making use of Compressive Sampling to reduce sampling rates Compressed Cyclic Feature based Sensing Exploiting the Sparsity in both freq. & cyclic-freq. domains Making use of Cyclic Statistics for robustness to noise uncertainty and low SNR conditions Multiple-CR Cooperative Sensing 11

13 Cyclostationarity in Modulated Signals Modulated signals are cyclostationary processes Cyclic features reveal critical signal parameters: - carrier frequency - symbol rate - modulation type - timing, phase etc. Non-cyclic signals (e.g. noise) do not possess cycle frequencies x(t) +T 0 t t+ t+t 0 t+t 0 + t 1 t 1 + T 0 t 12

14 Why Cyclic Statistics (1) Energy detection vs. feature detection [Sahai-Cabric 05] spectrum density ( = 0) spectral correlation density (SCD) High SNR Multi-harmonics peaks at f Low SNR f f f no noise components when 0 13

15 Why Cyclic Statistics (1) Spectral Correlation Density (SCD) [Gardner 88] (a) (b) (c) Magnitudes of estimated SCD a) a BPSK signal corrupted by white noise and five AM interferences b) the BPSK signal alone c) the white noise and five AM interferences overlapping in PSD, separable in SCD 14

16 Cyclic Feature Detection Cyclostationarity-based approach for detection insensitive to unknown signal parameters cyclic statistics robust to multipath resilient against Gaussian noise can differentiate modulation types and separate interferences Issues with cyclic feature detection Cyclostationarity is induced by OVER-sampling excessive sampling-rate requirements Cyclic statistics converge slowly with finite samples long sensing time Cyclic Feature Detection and Classification using Compressive Sampling 15

17 Wideband Cyclic Feature Detection Cyclic feature detection over a wide band Goal is to perform simultaneous detection of multiple sources Need to alleviate the sampling rates and sensing time Exploiting signal sparsity in two dimensions Sparsity in frequency domain low spectrum utilization Sparsity in cyclic-freq. domain modulation-dependent cycles 16

18 Wide band of interest: Multiple PU signals: Received signal: Cyclic spectrum (SCD): S(α, f) nonzero for Folded SCD of sampled signal: Signal Model [ f max,f max ] x i (t), i =1,...,I x(t) = I i=1 x i(t)+w(t) cyclic-freq freq Aliasing-free condition: f s =1/T s 2f max Cyclic spectrum of digital samples. The central diamond region is the non-zero support [Gardner 91] 17

19 x(t) x t S x (,f) sparse Problem Setup Cyclostationarity in communication signals time-varying (TV) covariance is period in time Sparse signal recovery z t : {z[n]} CS-ADC (sub-nyquist) compressive samples z t = Ax t Sparse Signal Recovery to reconstruct S x (,f) from samples z[n] at sub-nyquist rate S x (, f) recovered SCD r x (n, ν) =E{x(nT s )x(nt s + νt s )} =E{x t (n)x t (n + ν)} r x (n, ν) =r x (n + kp, ν), n, k, ν M N f s 2D cyclic spectrum is NOT LINEAR in the time-domain samples CS framework not immediately applicable 18

20 Defining Cyclic Spectrum 2 nd -order Statistics: covariance and spectra FT in n (shifted) Cyclic Covariance r x (c) (a, ν) FT in v Cyclic-frequency: Frequency: Time-varying Covariance r x (n, ν) Cyclic Spectrum SCD s (c) x (a, b) Time-varying Spectrum s x (n, b) a [0,N 1] α = 1 a NT s b [0,N 1] f = 1 (b N 1 NT s 2 z t = Ax t E{x t (n)x t (n + ν)} ) ( f s 2, f s 2 ) Q: How can we relate sub-nyquist data and sparse SCD linearly? 19

21 Vector-form Relationship (1) Linking time-varying covariance matrix with cyclic spectrum TV covariance matrix: R x = E{x t x T t } r x (0, 0) r x (0, 1) r x (0, 2) r x (0,N 1) r x (0, 1) r x (1, 0) r x (1, 1) r x (1,N 2) R x = r x (0, 2) r x (1, 1) r x (2, 0) r x (2,N 3) r x (0,N 1) r x (N 1, 0) Degree of freedom: N(N + 1)/2 r x =[r x (0, 0),r x (1, 0),,r x (N 1, 0),r x (0, 1),r x (1, 1),,r x (N 2, 1),,r x (0,N 1)] T R N(N+1) 2. Vectorized cyclic spectrum s (c) x =vec{s (c) x } =(I F) N 1 ν=0 (DT ν G ν )B T r x }{{} :=T 20

22 Vector-form Relationship (2) Linking time-varying covariance matrices TV covariance of compressed data R z =E{z t z T t } R M M Finite-sample estimate: ˆR z = 1 L l z t,lz T t,l Degree of freedom: M(M + 1)/2 r z =[r z (0, 0),r z (1, 0),,r z (M 1, 0),r x (0, 1),r z (1, 1), Relationship:,r z (M 2, 1),,r z (0,M 1)] T. z t = Ar t R z = AR x A T Linear representation for compressed covariance r z = Q M vec{ar x A T } = Q M (A A)vec{R x } = Φr x M(M +1) 2 1 N(N +1)

23 Sparse Cyclic Spectrum Recovery Reformulated linear relationship r z = Φr x Φ : M(M+1) under-determined Prior Information s (c) x 2 N(N+1) 2 is highly sparse is positive semi-definite (psd) R x L 1 -norm regularized LS (LR-LS) s (c) x = Tr x min r x Tr x 1 + λ r z Φr x 2 2 s.t. R x is psd, with vec{r x } = P N r x. Convex! 22

24 Summary of Reconstruction Steps {z t,l } l TV Covariance Estimation ˆR z = 1 L l z t,lz T t,l ˆr z Sparse Signal Recovery LR-LS ˆr x Cyclic SCD estimation = Tˆr x ŝ (c) x ŝ (c) x 23

25 Spectrum Occupancy Estimation Band-by-band estimation Region of relevance (α, f) : (a i,b i ): Is f (n) occupied or not? f + α 2 = f (n) f + α 2 f max b i + a i 2 = n bi N a i 2 f maxn f s N 2 f (n) = n N 1 2 N f s 2 α f s f s [ f s 2, f ] s 2 f (n) f s 2 f Relevant SCD vector for band n { } ĉ (n) : ŝ (c) x (a i,b i ) i f s 24

26 Multi-Cycle GLRT Binary hypothesis test on band n { H1 : ĉ (n) = c (n) + ɛ { } H 0 : ĉ (n) = ɛ c (n) : s x (c) (a i,b i ) : unknown true SCD; multiple cyclic freq. ɛ : N (0, Σ ɛ ): noise statistics determined by finite-sample effects, not ambient noise GLRT formulation Test statistics: T (n) =(ĉ (n) ) H Σ ɛ 1ĉ (n) Binary decisions by thresholding Fast algorithms possible based on modulation type, say, for BPSK i 25

27 Simulation: Robustness to Rate Reduction Probability of Detection vs. Compression Ratio (CFAR P FA = 0.1) Prob of Detection (P f = 0.1) Probability of detection % compression 50% compression Compression Ratio M/N Monitored band f max < 300 MHz 2 sources: PU 1 - BPSK at 100MHz; PU 2 - QPSK at 200MHz; Ts=0.04μs Cisco DSSS Spread spectrum 26

28 Simulation: Robustness to Noise Uncertainty Receiver Operating Characteristic (ROC): P D vs P FA (SNR=5dB, 66% compression) cyclic ED (noise uncertainty = 0, 1, 2dB) PD Cyclo, 0dB uncertainity Cyclo 1dB uncertainity Cyclo 2dB uncertainity ED 0dB uncertainity ED 1dB uncertainity ED 2dB uncertainity PFA outperforms energy detection (ED) insensitive to noise uncertainty 27

29 Simulation: Occupancy Estimation Techniques ROC (SNR = 5dB, 50% compression) 28

30 Classification using Cyclic Statistics 2D: Spectral Correlation Density (SCD) BPSK QPSK Spectral frequency f/f s Cycle frequency /F s Spectral frequency f/f s Cycle frequency /F s 1D: cyclic-frequency domain profile (CDP) Max. amplitude of Spectral Coherence I( ) BPSK Max. amplitude of Spectral Coherence I( ) QPSK Cycle frequency /F s [Kim etal. 2007] Cycle frequency /F s 29

31 Simulations: Classification Confusion Matrix (SVM Classifier) BPSK QPSK DS-BPSK DS-QPSK BPSK 95.45% 0% 4.55% 0% QPSK 0% 90.9% 9.09% 0% DS-BPSK 9.09% 0% 59.09% 31.82% DS-QPSK 4.5% 4.5% 36.46% 54.54% When compression ratio is adequate for detection, classification accuracy is comparable to non-compression Good separation of narrowband from spread spectrum Considerable confusion among spread spectrum signals 30

32 Summary and Future Work Exploitation of signal sparsity in 2D cyclic spectrum domain reformulated linear relationship between spectrum and covariance robustness to noise uncertainty capability in signal separation and classification Direct reconstruction of test statistics from compressive samples bypass the recovery of the entire cyclic spectrum reduce sensing time and responsiveness Sensing techniques for spread spectrum signals utilize fusion techniques to take advantage of all features in the wide spectrum of DSSS signals 31