Wideband compressed sensing for cognitive radios using optimum detector with no reconstruction

Cognitive radios need devices capable of sensing a large range of frequencies in order to detect the presence of primary networks and reuse their bands when they are not occupied. Due to the large spectrum to be sensed and the high power signal dynamics, low-cost implementation of the analog front-ends leads to imperfections. In this paper, we solve this problem with compressed sensing. The introduced maximum likelihood method is computationally simple since it does not require any signal reconstruction, unlike most methods in the current literature. Moreover, the metric is optimum, works for any modulation scheme and is independent of the emitted signal knowledge. The results are supported with Matlab simulations, a statistical study is performed and the probability of error is plotted for different cases, proving the efficiency of the estimator in a range of plausible SNRs and subsampling factors.