The paper addresses channel state information estimation for a cognitive radar system. The underlying radar signal model considered in this paper is based on a stochastic Green's function approach. In the radar model, the clutter returns can be expressed as a convolution of the stochastic Green's function impulse response with the transmit radar waveform. The paper proposes and solves constrained channel estimation algorithms that exploit the cosine similarity constraint and the inner product

more »

... nstraint to improve conventional least squares solutions. Using the fact that adjacent channel transfer functions have a close relationship in terms of a cosine similarity metric, the cosine similarity constraint can be exploited in the least squares problem. It turns out that the derived optimisation problem under the cosine similarity constraint is non-convex. However, since strong duality holds for the non-convex optimisation problem, it can be solved using the semi-definite relaxation (SDR) approach. The paper also proposes a new optimisation problem with an additional inner product constraint, which results in a convex second-order cone programming (SOCP) and is robust to the signal-to-noise ratio (SNR) in terms of the cosine similarity measurement. Numerical simulations are provided to verify the performance of the proposed methods on a challenge dataset generated using the high-fidelity modelling and simulation tool, RFView ® .