Radar-centric design of waveforms with disjoint spectral support

Radar designers seek transmit waveforms that have an acceptable time envelope (modulus), power spectral density, and ambiguity function. However, these three waveform properties are often derived from different sources, which can result in requirement inconsistency. This paper re-examines the design of radar waveforms with disjoint spectral support (also known as sparse frequency or thinned spectrum waveform design) from the perspective of these waveform properties. The conventional multi-objective optimization approach is discarded in favor of constrained nonlinear programming, which can accommodate firm constraints on the waveform modulus and ambiguity function when minimizing transmission energy in specified stop-bands. A novel autocorrelation sequence masking method is used to satisfy the ambiguity constraints. This affords more precise control over range sidelobes than does the more common approach of penalizing integrated sidelobe level. Numeric examples are presented that demonstrate the efficacy of the approach.