Compressed Receiver for Multipath DSSS Signals

A compressed sensing (CS) assisted receiver for direct sequence spread spectrum (DSSS) signals transmitted over multipath frequency-selective channels is studied in this paper. We present a bit-error-rate analysis for the CS-domain maximum ratio combining receiver with perfect channel state information (CSI), and hence, the CS-induced signal-to-noise ratio (SNR) penalty is quantized. Moreover, to alleviate such penalty, we build a deterministic low pass sinusoid (LPS) matrix, which proves more suitable for the pulse-shaped DSSS signals than the commonly-used random sensing matrices. Furthermore, a joint channel estimation and symbol detection (JCESD) scheme based on structured least-squares search (SLSS) is proposed, whose performance is very close to the analytical lower bound and is far better than that of the orthogonal matching pursuit (OMP) based approach. Our numerical results show that, in contrast to a conventional receiver sampling at a Nyquist rate and relying on perfect CSI, the proposed CS-assisted SLSS-JCESD receiver may reduce the sampling rate requirement by 50% at SNR loss of about 1.2 dB.