Code optimization with similarity and accuracy constraints

This paper deals with the design of coded waveforms which optimize radar performances in the presence of colored Gaussian disturbance. We focus on the class of linearly coded pulse trains and determine the radar code which maximizes the detection performance under a control on the region of achievable Doppler estimation accuracies, and imposing a similarity constraint with a pre-fixed radar code. The resulting optimization problem is non-convex and quadratic. In order to solve it, we propose a technique based on the relaxation of the original problem into a semidefinite program. Indeed the best code is determined through a rank-one decomposition of an optimal solution of the relaxed problem. At the analysis stage we assess the performance of the new encoding technique in terms of detection performance, region of achievable Doppler estimation accuracies, and ambiguity function.