Radar Filters Design in the Presence of Target Doppler Frequency and Interference Covariance Matrix Uncertainties

This paper considers the design of robust filters for radar pulse-Doppler processing when the interference is a wide sense stationary random process. The Signal-to-Interference-plus-Noise Ratio (SINR) at the filter output is considered as the figure of merit to optimize under a multitude of requirements accounting for Doppler filter sidelobes as well as uncertainties both in the received useful signal component and interference covariance matrix. The design is analytically formulated as a constrained optimization problem whose solvability is thoroughly studied. Specifically, a polynomial time solution technique to get the optimal filter is proposed exploiting the representation of non-negative trigonometric polynomials via linear matrix inequalities, the spectral factorization theorem, and the duality theory. Last but not least, a detailed analysis of the optimum filter performance is provided showing the trade-offs involved in the design and the gain achievable over some already known counterparts.