Performance bounds for polynomial phase parameter estimation with nonuniform and random sampling schemes

Estimating the parameters of a cisoid with an unknown amplitude and polynom ial phase using uniformly spaced samples can result in ambiguous estimates due to Nyquist sampling limitations. It has been shown previously that nonu niform sampling has the advantage of unambiguous estimates beyond the Nyqui st frequency; however, the effect of sampling on the Cramer-Rao bounds is n ot well known, This paper first derives the maximum likelihood estimators and Cramer-Rao b ounds for the parameters with known, arbitrary sampling times, It then outl ines two methods for incorporating random sampling times into the lower var iance bounds, describing one in detail. It is then shown that for a signal with additive white, Gaussian noise the bounds for the estimation with nonuniform sampling tend toward those of uni form sampling, Thus, nonuniform sampling overcomes the ambiguity problems o f uniform-sampling without incurring the penalty of an increased variance i n parameter estimation.