Optimizing radar waveforms using generalized alternating projections

The radar ambiguity function, described as an autocorrelation of shifts in time and frequency, is useful for determining a waveform's accuracy at detecting targets in certain range-Doppler combinations. An algorithm is proposed which uses a generalized method of alternating projections to synthesize waveforms with desired ambiguity function properties. In practice, it is often desirable to minimize the magnitude of the ambiguity function at range-Doppler combinations where targets other than the detection are likely to cause interference. The algorithm alternates between projections in the time, frequency, and range-Doppler domains until an optimal solution which fits desired ambiguity function properties is found. This work provides a computationally intelligent methodology to dynamically optimize detection in radar applications and a foundation for future work in joint circuit optimization for spectral compliance.