Performance analysis of random demodulators with M-sequences and Kasami sequences

The theory of compressive sensing has recently been utilized to develop sub-Nyquist communication receivers that can reconstruct the input signal using sub-Nyquist sampling rates. Such samples are acquired randomly by projecting the input signal on random signals. Practically, these random signals can be generated by digital pseudo random signal generators, and the properties of these signals highly affect the reconstruction quality of the receiver. In this paper, we study the performance of the random demodulator, a compressive sampling based receiver, with two types of random sequences that are practical to implement: M-sequences generated by means of a linear feedback shift register, and Kasami sequences. We show that a random demodulator with a Kasami sequence generally outperforms that with an M-sequence in terms of minimum sampling rate and minimum sparsity levels for successful reconstruction.