Spectrum Detection from Optimized Bayesian Compressed Sensing

In recent years, the Compressed Sensing (CS) theory remains in the spotlight in the signal processing field. Combining with the Compressed Sensing Theory, the spectrum detection technology could break through the limit of the Nyquist Sampling Theorem to slow down the sampling rate, and release the pressure for the hardware to deal with. So it is very useful for the spectrum sensing technology, especially for wideband spectrum sensing. This issue focuses on the Bayesian Compressed Sensing (BCS) algorithm, which given the prior of the original signal to purchase the maximum a posteriori estimation of the reconstructed signal. Then we improves it by reducing the relevance among the columns of the random Gaussian measurement matrix. After the optimization, we call the improved algorithm OBCS (Optimized-BCS) for short. The stimulations use Zero-Counting method for the judgment, and use BCS and OMP algorithm for comparisons. The results show that OBCS algorithm has the best performances in the targets of reconstruction error, detection probability and false-alarm probability.