Super-Resolution Delay-Doppler Estimation for OFDM Passive Radar

In this paper, we consider the problem of joint delay-Doppler estimation of moving targets in a passive radar that makes use of orthogonal frequency-division multiplexing (OFDM) communication signals. A compressed sensing algorithm is proposed to achieve supper-resolution and better accuracy, using both the atomic norm and the $\ell_1$-norm. The atomic norm is used to manifest the signal sparsity in the continuous domain. Unlike previous works which assume the demodulation to be error free, we explicitly introduce the demodulation error signal whose sparsity is imposed by the $\ell_1$-norm. On this basis, the delays and Doppler frequencies are estimated by solving a semidefinite program (SDP) which is convex. We also develop an iterative method for solving this SDP via the alternating direction method of multipliers (ADMM) where each iteration involves closed-form computation. Simulation results are presented to illustrate the high performance of the proposed algorithm.