Sub-Nyquist Sampling of BPSK Signals via Feedback Structure

We consider the problem of sampling binary phase shift keying (BPSK) signals, which are widely used in communications and radar systems. Although sub-Nyquist sampling of such signals has been treated in various works, giant samples were needed. In this brief, a new sub-Nyquist sampling method based on a multichannel feedback structure is proposed for BPSK signals, which requires fewer samples. BPSK signals can be characterized by a finite number of parameters, namely, the carrier frequency, amplitude, locations of discontinuities, and phase of each symbol. Our feedback structure consists of a main channel and a feedback channel. The carrier frequency and amplitude can be estimated by the estimation of signal parameters by a rotational invariance technique algorithm in the main channel, while the phases and locations of discontinuities can be estimated by the annihilating filter in the feedback channel. The effectiveness of the proposed method is verified via simulations. In a noiseless situation, for a seven-segment BPSK signal lasting $1~{\mu } {s}$ with a 500-MHz carrier frequency, the equivalent sampling rate of the proposed method is only 3.8% of the carrier frequency, and much less than the Nyquist sampling rate of the signal. Finally, we analyze the effect of noise and present a robust reconstruction algorithm. Simulation results show that the proposed method exhibits better noise robustness than previous approaches.