Probabilistically Robust Design of Radar Waveform-Filter for Extended Target Detection in the Presence of Clutter

Assuming the stochastic model of Target Impulse Response (TIR), we address the radar waveform-filter design for extended targets with the recently proposed probabilistically robust detection criterion. The waveform-filter design is formulated as a non-convex fractional programming problem. We devise the Block Coordinate Descent (BCD) based algorithm to tackle this problem, where the waveform codes and filter are optimized alternately. It is shown that the waveforms can be optimized by sequentially checking the feasibility of a polynomial system based on the bisection method. The filter can be designed based on Semi-Definite Relaxation (SDR) and the Dinkelbach's transform. The proposed algorithm has guaranteed convergence. Numerical experiments are conducted to verify the effectiveness of the proposed algorithm. Results highlight that the designed waveform-filter is able to behave adaptively according to the ambient and more robust than that designed by the competing algorithm.