Research On Compressive Sensing Recovery Algorithm Based On Bayesian Theory

With the increasing demand for mobile communication, it is more difficult toachieve the allocation of spectrum resource. Thus, this problem can be solved bycognitive radio technology. Spectrum sensing is regarded as the key of cognitiveradio and its purpose is to detect the hole of spectrum. Since traditional spectrumsensing could only sense a single part of spectrum, people propose the widebandspectrum sensing technology to improve the detective precision. During the processof wideband signal sensing, the extremely high sample rate is the limitation of thistechnology. Therefore, people start to use compressive sensing method to solve thisproblem. Bayesian Compressive Sensing is a new method, which is proposed inrecent years to construct the sparse signal model by different prior probability. Thismethod can also provide the error range of restored signal with excellentperformance. Thus, the focus of this paper is on the Bayesian compressive sensingrecovery algorithm of wideband spectrum sensing.In this paper, we first introduce the process of Bayesian modeling. Then,modify the compressive radio algorithm with Laplace prior method and propose afast algorithm-L-BSC algorithm. At the same time, this paper combine the methodof adaptive measurement matrix under Bayesian framework with the proposed fastalgorithm to obtain an adaptive fast algorithm. The simulation result shows that thiskind of adaptive fast Bayesian algorithm could perform well not only under thecondition of restoring ordinary signal, but also can be reconstructed with highaccuracy in wideband spectrum sensing scenario. It can also provide outstandingspectrum detect ability. Therefore, this algorithm is thought to be well performedand applied in wideband compressive spectrum sensing.Considering the sparse block structure in frequency domain resulted from theprocess of spectrum allocation in wideband spectrum sensing, this paper adoptedthe framework of BSBL (Block Sparse Bayesian Learning). Besides, another twoalgorithms based on this framework are also introduced. Under the former theory,this paper studied the algorithm with the combination of BSBL and group lasso,which is named as BSBL-Group Lasso algorithm. This method can greatly decreasethe iteration times and increase the effectiveness with the insurance of performance.In order to solve the problem that some block partition of signals could not beobtained, this method is modified to achieve the BSBL-EEM and BSBL-EBOalgorithms. Simulation results show that this method can get high restorationaccuracy with better detective ability in wideband compressive spectrum sensing.The BSBL-EEM and BSBL-EBO algorithms could apply widely with better restoration accuracy even when the block situation of users' definition is differentfrom the actual signal with the unknown of block partition of signals.