In this paper, we propose a cognitive approach to design phase-only modulated waveforms sharing a desired ambiguity function. We formulate the problem as a quartic order polynomial optimization problem with a constant modulus constraint on each variable. Thus, we devise an optimization procedure based on the Maximum Block Improvement (MBI) approach. At the analysis stage, we assess the performance of the proposed technique showing its capability to properly shape the ambiguity function of the transmitted waveform.