Sub-Nyquist sampling with independent measurements

Abstract

This paper presents an efficient sub-Nyquist pulse-Doppler radar system via quadrature compressive sampling (QuadCS) in fast-time domain. QuadCS is a bandpass variant of random demodulation and inserts randomness into the measurement matrix by employing a random chipping signal. Different from conventional sub-Nyquist radars using fixed measurement matrices in all pulse repetition intervals (PRIs), namely the same chipping signals for our system, we utilizes independent chipping signals in each PRI. Hence we obtain a sequence of independent measurement matrices in a coherent processing interval, and the resulting sensing matrix has better restricted isometry property than that with fixed measurement. Theoretical analysis indicates that our system can further reduce the sampling rate or can identify more number of targets than that with fixed measurement. Moreover, the sampling rate and the number of transmitted pulses are exchangeable, thus providing more flexibility for the design of sub-Nyquist radars. The main challenge of independent measurement is that the computational efficient decoupled processing of fast-time and slow-time domains cannot be applied directly. We thus develop a first-order fast target recovery algorithm by exploiting the factorization of the proposed sensing matrix suitable for fast matrix-vector products. Numerical results validate the efficiency of the proposed system.