Analyzing the FD-MIMO sparse imaging under carrier frequency offsets from the perspective of point spread function

In this paper, we address the problem of the frequency diverse multiple-input-multiple-output (FD-MIMO) radar sparse imaging with imperfect carrier frequency synchronization. From the perspective of classical point spread function (PSF) in range-angle plane, we get to know that the different scatterers in the interested scene would no longer share the same PSF. Instead, the scatterers located in different range bins would have distinct PSFs. Furthermore, for different sources to produce carrier frequency offsets, we find that those who are relevant to the receivers would result in more severe impact on the PSF due to the caused cross-interference between the range-angle dimensions. We further present a non-rigorous threshold of the carrier frequency offsets to suggest the boundary beyond which the resulting PSF would be totally distorted. Correspondingly, we propose to iteratively compensate the effect of carrier frequency offsets after sparse reconstruction when those offsets are controllable. Simulations demonstrate the reasonable results inferred from the analytical derivation and verify the effectiveness of the proposed algorithm.