Multitarget Joint Delay and Doppler-Shift Estimation in Bistatic Passive Radar

We study the problem of jointly estimating the delays and Doppler shifts of multiple targets in a bistatic passive radar system when the unknown signal from the illuminator of opportunity (IO) is modeled as a correlated stochastic process. We treat all the delays and Doppler shifts as continuous-valued parameters to avoid straddle loss due to discretization. A computationally efficient method based on the expectation maximization (EM) algorithm is proposed, which breaks up the complex multidimensional maximum likelihood estimation problem into several separate optimization problems, one optimization per target. The algorithm provides estimates of all the targets' delays and Doppler shifts along with the estimate of the IO signal and each target's component signal in the surveillance channel. The Cramer-Rao lower bound (CRLB) is also derived. Simulation results are presented, where we compare the proposed algorithm with the conventional cross-correlation (CC) estimator, modified CC (MCC) estimator, EM with successive interference cancellation (EM-SIC) estimator, and CRLB. It is shown that when the targets are well separated on the delay-Doppler shift plane, the proposed method outperforms all the estimators. Moreover, when the targets are close in this plane, the CC and EM-SIC estimators fails to distinguish the targets, whereas the proposed method successfully estimates the delays and Doppler shifts and outperforms the MCC in this case as well. Finally as the signal-To-noise ratio increases, the performance of the proposed method approaches that of the CRLB.