Optimal waveform design for range-Doppler processing in colored noise

The problem of radar waveform design for moving target detection in the presence of radio frequency interference (RFI) is considered. The transmit waveform is assumed to be a coherent train of uniform pulses, and the RFI is modeled as a wide-sense stationary random process with a known power spectral density. Both pulse-Doppler processing and matched filter bank processing are considered. For each case, it is shown that a constant modulus pulse can be found that locally maximizes the signal-to-noise ratio while respecting user-specified ambiguity function constraints. It is also shown that under certain conditions approximations can be made that result in identical waveform design problems for both processing schemes. The modulus and ambiguity function constraints render the waveform design problem analytically intractable, but numeric techniques can be employed. Simulation results are provided to demonstrate the efficacy of the approach.