The cross-ambiguity function (CAF) is commonly used to analyze the delay-Doppler characteristics of signals in radar, sonar, and communication systems. Accordingly, a CAF relates to the correlation processing of signals in the presence of delays and Doppler shifts. In this paper, we use a metaheuristic approach to address the CAF synthesis problem by jointly designing a pair of waveforms. The CAF ofwaveforms designed in this way, approximates a desired pre-defined CAF. It turns out that the waveforms designed by this approach have the benefit of low peak-to-average power ratios. Numerical examples are presented to show that nature-inspired metaheuristic algorithms can be used as an effective tool to synthesize different types of CAFs.
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