Sparse Optimization Algorithms In Cognitive Radio Networks

The fixed allocation of wireless spectrum resources results in low utilization rate and sparseness of some frequency bands. However, the resource sharing of spectrum from authorized users and cognitive users can improve the spectrum efficiency. The primary task of spectrum sharing is to detect the free spectrum rapidly and accurately. The speed of single-user spectrum sensing don't slow down regardless of the increasing number of cognitive users compared with collaborative spectrum sensing. This thesis will take a research on sparse optimization algorithms by means of single-user spectrum sensing.For the high complexity of wideband spectrum sensing based on cyclostationary feature detection in dual selective fading environment, this thesis proposed a kind of wideband spectrum sensing algorithm with fast and low-complexity. Based on the sparse convex optimization model of minimum 1l norm regularization, this algorithm aims at the flaw of redundant iterative computation in general linear bregman algorithm. It can accelerate the convergence speed by adding auxiliary variables to estimate iterations of residual staying almost constant in linear bregman algorithm and updating auxiliary variables to step out the process of redundant iteration. At the same time, it reduces the complexity of the algorithm. As a result, the effect of compressive sampling reconstruction, the detection probability and convergence speed of the modified algorithm are improved compared with unmodified algorithm in doubly selective fading environment.For poor performance of general stationary signals sensing in low SNR environment, this thesis proposed a kind of weighted linear bregman algorithm based on measurement matrix optimized. The observed matrix was optimized before a sparse optimization problem model is to be solved so that it can improve the effect of spectrum reconstruction in low SNR environment. At the same time, the sparse spectrum vector to be restored is superimposed on the weights in order to take advantage of the sparsity of the signal. So it makes the sparse solution in the next iteration sparser compared with the previous sparse solution.Thus the number of iterations reduces and the convergence rate of the algorithm is sped up. The results show that the anti-noise performance in low SNR and convergence speed etc. of the algorithm are improved by optimizing the observed matrix.