Analysis of a simple, effective frequency estimator based on Prony's method

In a recent paper by Tufts and Fiore a low-complexity frequency estimator based on Prony's method was proposed. The estimate is formed from two sample correlations (r) over cap(L1) and (r) over cap(L2), where 1 less than or equal to L-1 < L-2 less than or equal to N - 1 and N is the number of samples. For a correct phase unwrapping it is required that L-1 and L-2 are relatively prime. In this paper, a slight modification of the original algorithm is presented, and an expression for its asymptotic variance is derived. It is shown that the error variance is minimized for L-1 = 3N/5 and L-2 = 4N/5 for which the quotient of the error variance and the Cramer-Rao bound tends to 25/24 approximate to 1.042. Suboptimal settings of L-1 and L-2 are shown to exist, resulting in a lowered SNR-threshold while retaining the asymptotic efficiency. Simulation results which lend support to the theoretical findings are included.