Compact Cramer-Rao bound expressions for frequency estimation of sinusoidal signals in unknown colored noise

Compact expressions of the Cramer-Rao bound matrix for estimating the frequencies of a number of superimposed sinusoidal signals in colored Gaussian noise are presented for both complex and real data cases. The expressions are given for the most general case in which all the signal parameters (the frequencies, amplitudes, and phases of the sinusoids) are unknown and the covariance function of the noise is parameterized in some unspecified way. We then specialize our results for the important case where the noise samples come from an autoregressive noise process.