Differential delay/Doppler ML estimation with unknown signals

Previously published analyses on the maximum-likelihood estimation of joint frequency and time offsets between two noisy versions of a common signal have assumed a Gaussian random signal with a known power spectrum. In many applications, the common signal is not Gaussian and there may be no prior knowledge of its detailed structure. Instead, estimation of a hypothesized common signal can be construed as another element in the estimation process. The analysis is straightforward and shows that the complex ambiguity function (CAF) still represents the ML approach when the noise is Gaussian and spectrally flat. Additional interpretation shows that use of interference-rejection filtering followed by a CAF is an attractive suboptimum approach in an environment of narrowband interferers