Designing (In)finite-alphabet Sequences via Shaping the Radar Ambiguity Function

In this paper, a new framework for designing the radar transmit waveform is established through shaping the radar Ambiguity Function (AF). Specifically, the AF of the phase coded waveforms are analyzed and it is shown that a continuous/discrete phase sequence with the desired AF can be obtained by solving an optimization problem promoting equality between the AF of the transmit sequence and the desired AF. An iterative algorithm based on Coordinate Descent (CD) method is introduced to deal with the resulting non-convex optimization problem. Numerical results illustrate the proposed algorithm make it possible to design sequences with remarkably high tolerance towards Doppler frequency shifts, which is of interest to the future generations of automotive radar sensors.