The Cramer-Rao bound on frequency estimates of signals closely spaced in frequency (original) (raw)

This paper examines the Cramer-Rao (CR) lower bound on the variance of frequency estimates for the problem of n signals closely spaced in frequency. The dependence of the bound upon maximum frequency separation (6w), the signal-to-noise ratio (SNR), and the number N of data vectors (or snapshots), bears importantly upon the performance of highresolution techniques for spectrum analysis. Previously these dependences have been explored via simulation due to the complexity of the Fisher information matrix. The main results presented herein are simple analytic expressions for the CR bound in terms of 80, SNR and N valid for small 6w. The results are applicable to the conditional (deterministic) signal model.