Optimization of radar phase-coded signals for multiple target detection

• The weighted average signal-to-noise ratio (SNR) maximization is combined with the similarity, detection and constant envelop constraint.
• This combination improves the practical requirements of radar system.
• The accurate approximation to the optimal solution can be obtained after performing the rank-one decomposition.
• The trade-off between the detection performance and the constraints on the signal can be further enhanced.

We address the design of radar phase-coded signals for the detection of multiple targets in the presence of a coloured Gaussian disturbance with a similarity constraint and a detection constraint. The weighted average signal-to-noise ratio (SNR), which characterises the overall level of multiple targets detection performance, is used as the cost function for the optimization of the radar waveform with a constraint on the degree of similarity with a prefixed radar signal and a constraint on the minimal SNR threshold for every target. We formulate the optimization problem in terms of a non-convex quadratically constrained quadratic program (QCQP) that is NP-hard. Hence, we propose a similarity and detection constrained signal (SDCS) design algorithm relying on both the semidefinite relaxation (SDR) technique and the randomization technique to obtain an accurate approximation of the optimal solution for the case with a continuous phase alphabet and the case with a finite phase alphabet. Finally, the results of extensive simulations demonstrate that the phase-coded signals generated with our approach are accurate approximations of the optimal signals and that a trade-off exists between the detection performance and the requirements on the signal similarity and the minimal SNR threshold.