Radar Waveform Sidelobe Level Optimality and Sampling

Radar waveforms are often optimized to achieve minimal sidelobes in the ambiguity function. We show that sampling rate can affect the optimality of the sidelobe level, so the sampling rate should be considered already at the optimization phase. We develop a theorem showing that for narrowband waveforms with amplitude and phase coding, the peaks of the ambiguity function cannot increase due to oversampling. Nevertheless, it is shown that it is possible for oversampling to cause an increased sidelobe level. Numerical examples demonstrating the validity of the results are provided.