Compressed Sensing Algorithm And Its Application In Spectrum Sensing

Compressed Sensing (CS) is a new method in signal processing where one seeks to samplesparse signals under far below the Nyquist sampling rate. The ideas break through Nyquistbandwidth restriction on the sampling rate and give a big contribution to the development of themethod of signal sampling. Since the spectrum of cognitive radio is sparse, it uses CS algorithm inthe wideband spectrum sensing in order to improve the spectrum utilization rate.The cumulative coherence can judge whether the OMP algorithm can correctly reconstructsignal, so it gives the method to estimate the probability of correctly reconstructing signals with thecumulative coherence.It takes the research of the measurement matrix and sparsity estimation in thefields of wideband spectrum sensing algorithm based on compressed sensing. The main work of thisthesis is as follows:1.It gives a probability estimation method based on the truncated estimation. Thereconstruction ability of the OMP algorithm principle depends on the cumulative coherence level ofmeasurement matrix. It gives the probability estimation of cumulative coherence constraint boundby using random variable truncated estimation, so as to judge whether the OMP algorithm cancorrectly reconstruct signal.2.It proposes a spectrum estimation method based on random matrices broadband. In order tomeet the requirement of full rank,it uses the sparse rule to make the measurement matrix.Since itcan’t know all the sparse rules, it proposes wideband spectral reconstruction method based onrandom matrices which are easy to constructe.With this method, it solves the problems of unknownsome sparse rules.3.It proposes a edge spectrum sensing method based the sparse estimation.The sparsity isunable to ascertain in advance,it proposes a sparse estimation method to estimate the actualsparsity.With the estimated sparsity, it gives a new broadband CS algorithm. This algorithm caneffectively improve the spectrum utilization rate, and reduce the unnecessary sampling overhead.