Transmit Code Design for Detection of an Extended Target Embedded in Signal-Dependent Interference

We consider the problem of transmit code design to enhance the detection performance of an extended target embedded in clutter. We model the target impulse response (TIR) in two frameworks, either via the product of a deterministic TIR with an unknown reflection factor or as a Gaussian random vector (with known covariance). For both frameworks, we impose either the peak-to-average-power ratio or the similarity constraints on the sought code, separately. In the former framework, the performance of the generalized likelihood-ratio test depends monotonically on the signal-to-interference-plus-noise ratio (SINR) of the detector. Hence, we cope with the code design, maximizing the SINR. The resulting optimization problem is non-convex, and we propose a novel approach to tackle it. In the latter, dependence of the optimal detector’s performance on the metrics is too complex for code design. Consequently, we employ the mutual information between the TIR ensemble and the received echo as the design metric. We devise an iterative method based on majorization-minimization technique to deal with the resulting non-convex constrained problem. We make the proposed method robust to deal with uncertainties about prior knowledge of clutter and interference. Numerical analyses highlight the effectiveness of the proposed methods comparing to their counterparts.