Pareto-optimal radar waveform design

This study deals with the problem of Pareto-optimal waveform design in the presence of coloured Gaussian noise, under a similarity and an energy constraint. At the design stage, the authors, determine the optimal radar code according the following criterion: constrained maximisation of the detection performance and constrained minimisation of the Cramer-Rao lower bound (CRLB) on the Doppler estimation accuracy. This is tantamount to jointly maximising two quadratic forms under two quadratic constraints, so that the problem can be formulated in terms of a non-convex multi-objective optimisation problem. In order to solve it, the authors resort to the scalarisation 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, the authors assess the performance of the proposed waveform design scheme in terms of detection performance, region of achievable Doppler estimation accuracy and ambiguity function. In particular, the authors analyse the role of the Pareto weight in the optimisation process.