Relative Entropy-Based Waveform Design for MIMO Radar Detection in the Presence of Clutter and Interference

This paper considers the waveform design problem for multiple-input multiple-output (MIMO) radars in order to improve the detection performance of the systems. We assume that target echoes are embedded in (signal-dependent) clutter as well as (colored) interference. Considering the optimal (Neyman-Pearson) detector, obtaining waveforms which maximize the detection probability for a fixed value of the probability of false alarm is intractable. Therefore, we employ relative entropy associated with the detection problem as the figure of merit for the waveform design. We devise an iterative method based on minorization-maximization (MM) technique to tackle the nonconvex design problem. This method also includes a novel trick for replacing a nonconvex constraint set (associated with an equivalent form of the design problem) with a convex one iteratively. The proposed method increases the design metric monotonically and is guaranteed to converge. We extend the devised method for using in design with peak-to-average power ratio (PAR) and similarity constraints. The method can be applied to both statistical and colocated MIMO radars. Several numerical examples are included to demonstrate the effectiveness of the proposed method.