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Constrained Maximum Likelihood Channel Estimation for CoFAR

This paper considers estimation of channel state information of a radar system. The underlying radar signal model considered in this paper is based on a stochastic Green’s function. In this model, clutter returns can be modeled using a channel matrix with entries computed from fundamental physics using a stochastic Green’s function based approach. We propose a maximum likelihood (ML) channel estimation algorithm which can be expressed by a constrained least squares problem under independent and identically distributed (i.i.d.) Gaussian assumption. We first show that the adjacent channel transfer functions have close relationship in terms of a squared cosine similarity measurement. Then we set up a least squares problem under the squared cosine similarity constraint. It turns out that the derived optimization problem is a non-convex quadratically constrained quadratic programming, however, the strong duality holds. We solve the optimization problem using a semidefinite relaxation approach. Numerical simulations are provided to verify the performance of the proposed method on a dataset generated using the high-fidelity modeling and simulation tool RFView®.