Research On Deterministic Measurement Matrix And Sparse Recovery Algorithm With Applications To WCSS

Cognitive radio(CR) implements spectrum sensing to detect spectrum holes for dynamic spectrum access, improving the spectrum utilization. Recently, due to the more flexible spectrum access opportunity, wideband spectrum sensing has played an important role in CR. The existing techniques are based on the classical Nyquist sampling theorem, which requests the sampling rate of wideband signal larger than two times of highest frequency or width, resulting in high price of hardware implementation in sampling front-end. However, primary user(PU) only uses few spectrum, which contributes to the sparsity of wideband signal in frequency domain, and its frequency representation demonstrates the spectrum utilization well. Compressive sensing(CS), as a novel signal sampling and coding technology, is based on the sparse representation of the original signal in a certain domain, and achieves the Sub-Nyquist sampling by simultaneously sampling and compressing the original signal as well as the latter exact recovery.With the aid of sparsity of wideband signal in frequency domain, wideband compressive spectrum sensing(WCSS) directly acquires fewer incoherent measurements with Sub-Nyquist sampling rate, i.e., compressive measurement, and recovers the sparse wideband spectrum, achieving the reduction of sampling burden as well as fast and reliable sensing at the same time. Although some developments have been made in the application research on WCSS, measurement matrix for effective compressive measurement and robust recovery algorithm are still open questions. This thesis focuses on the deterministic measurement matrix and recovery algorithm in CS with their applications in WCSS.The main contributions and results of this thesis can be summarized as follows:We propose the Matrix Construction based on shrinkage and gradient descent(MCSGD) algorithm to construct a deterministic measurement matrix of low coherence. The MCSGD algorithm optimizes measurement matrix by using shrinkage and gradient descend methods in each iteration, and its convergence is guaranteed. The deterministic measurement matrix by MCSGD algorithm has small coherence coefficient, cumulative coherence coefficient and average coherence coefficient. Simulations of recovering sparse signal are utilized to prove the recovery performance improvement of the orthogonal matching pursuit(OMP) algorithm when incorporated with the constructed deterministic measurement matrix.Based on SVD and gradient descend, we proposed the matrices construction algorithm(MCA) to simultaneously construct a pair of deterministic measurement matrix and sensing dictionary that have low coherence and cross-coherence, with which the measurement matrix and recovery algorithm are collaboratively constructed. Based on the idea of interactive minimization, MCA optimizes measurement matrix and sensing dictionary by using SVD and gradient descend methods in each iteration. The constructed deterministic measurement matrix and sensing dictionary are with small(cross-) coherence coefficient and small cumulative(cross-) coherence coefficient. Simulations of recovering sparse signal are utilized to prove the recovery performance improvement of the collaboratively designed recovery algorithm when incorporated with the constructed deterministic measurement matrix and sensing dictionary.Sufficient conditions are given for OMP algorithm to guarantee an exact estimation of the original support from noisy single measurement vector(SMV) measurement signal. Compared with the existing sufficient conditions, the proposed ones are more relaxed.Moreover, we analyse the influence of fusing multi-candidate estimators upon recovery error. Afterwards, we introduce a more robust sensing dictionary-based diversified OMP(SDDOMP) algorithm according to the random forest idea, and a fusion rule based on the minimum mean-squared-error(MMSE) estimator, which respectively forms and fuses multi-candidate estimators. Simulations of recovering sparse signal are utilized to prove the validity of the proposed sufficient conditions, and the robustness of the proposed SDDOMP algorithm and fusion rule in low SNR scenarios.The sensing dictionary-based orthogonal matrix matching pursuit(SDOMMP) algorithm is proposed to solve the multiple measurement vector(MMV) joint sparse recovery problem. It exploits the low cross-coherence between sensing dictionary and measurement matrix to exactly select a measurement atom with a high probability in each iteration. With the aid of coherence coefficient and cross-coherence coefficient, we derive the sufficient conditions, under which the proposed SDOMMP algorithm can exactly estimate the original support. Simulation of recovering joint sparse data with know sparsity are utilized to prove the effectiveness of the proposed SDOMMP algorithm in joint sparse recovery.The proposed deterministic measurement matrix and(joint) sparse recovery algorithm are applied into WCSS. For single-user local WCSS, we construct deterministic measurement matrix and design robust recovery algorithm in case of know sparse representation matrix. For multiple-user collaborative WCSS, we propose fusion center(FC)to efficiently estimate the sparsity in parallel during the receiving frame, achieving the reductions of false alarm and the joint sparse recovery waste. Simulations and experiments validate that, in low SNR and serious transmission failure scenarios, our proposals can robustly sense the wideband spectrum and effectively detect the channels respectively.