Pareto-optimal radar waveform design

This paper deals with the problem of Pareto-optimal waveform design in the presence of colored Gaussian noise, under a similarity and an energy constraint. At the design stage, we determine the optimal radar code according to the following criterion: joint constrained maximization of the detection probability and constrained minimization of the Cramer Rao Lower Bound (CRLB) on the Doppler estimation accuracy. This is tantamount to jointly maximizing two quadratic forms under two quadratic constraints, so that the problem can be formulated in terms of a non-convex multi-objective optimization problem. In order to solve it, we resort to the scalarization technique, which reduces the vectorial problem into a scalar one using a Pareto weight defining the relative importance of the two objective functions. At the analysis stage, we assess the performance of the proposed waveform design scheme in terms of detection performance and region of achievable Doppler estimation accuracy. In particular, we analyze the role of the Pareto weight in the optimization process.