To solve the problems of under-estimation of sparsity at low Signal-to-Noise Ratio (SNR) and over-estimation of sparsity at high SNR, a wide-band spectrum sensing algorithm using sparsity estimation based on Gerschgorin theorem was proposed. Firstly, Gerschgorin theorem was used to separate the signal disk and noise disk in order to estimate the sparsity. Then, the spectrum support set was obtained by using Orthogonal Matching Pursuit (OMP) algorithm. Finally, the wide-band spectrum sensing was accomplished. The simulation results show that, the SNR of the proposed algorithm, AIC-OMP (Akaike Information Criterion-Orthogonal Matching Pursuit) algorithm and MDL-OMP (Minimum Description Length-Orthogonal Matching Pursuit) algorithm need 4.6 dB, 8.5 dB and 9.7 dB respectively while their detection probability reaching to 95%; the false alarm probability of the proposed algorithm tends to 0 when the SNR is higher than 13 dB, which is far lower than that of BPD-OMP (Bayesian Predictive Density-Orthogonal Matching Pursuit) algorithm and GDRI-OMP (Gerschgorin Disk Radii Iteration-Orthogonal Matching Pursuit) algorithm. Therefore, the proposed algorithm takes account of sparsity estimation performances under both low SNR and high SNR, and the spectrum sensing performance of the proposed algorithm is better than that of AIC-OMP algorithm, MDL-OMP algorithm, BPD-OMP algorithm and GDRI-OMP algorithm.

In allusion to the problem that the computational complexity of Volterra for nonlinear adaptive filtering algorithm increases in power series, a second-order Volterra adaptive filter algorithm based on Set-Membership-Filtering (SMF) under the α-stable distributions noise was proposed. As the object function of SMF involved all signal pairs of input and output, through the threshold judgment of the p square of output errors amplitude the weight vectors of Volterra filter were updated, not only reducing the complexity of filtering algorithm, but also improving the robustness of the adaptive algorithm for input signal correlation. And the update formula of the weight vectors was derived. The simulation results show that the proposed algorithm has lower computational complexity, faster convergence rate, and better robustness against the noise and the input signal correlation.