Frequency Estimation for Closely Spaced Sinsoids: Simple Approximations to the Cramer-Rao Lower Bound
D.N. Swingler · IEEE Transactions on Signal Processing · 1993
Simple approximate formulas for the evaluation of the Cramer-Ran lower bound (CRLB) of unbiased frequency estimates for the deterministic and stochastic cases of multiple snapshots of two closely spaced cisoids in complex noise are introduced. These are based on general expressions recently published by Stoica and Nehorai. Also explored, along the same lines, is the case of a single snapshot com- prising either one real sinusoid in real noise or two cisoids in complex noise. These formulas, though simple, are accurate to within a few percent where the number of data points per snapshot is greater than about 6. It is felt that they add insight into the behavior of the CRLB, and cover many of the situations commonly cited in the literature.