Iterative Procedure for Real Single-tone Frequency Estimation

In many situations, a signal consisting of a single tone corrupted by additive white noise is available, and the frequency of the tone must be estimated. This problem has applications in communications, radar, sonar, measurements, adaptive control, speech processing etc [1], and it belongs to the wider class of spectrum estimation problems [2]. Both complex and real signals have been considered in the literature. As maximum likelihood (ML) estimators perform very well but are not computationally efficient [3, 4], various estimation algorithms have been proposed (see [5−11] for the complex case and [4, 12, 13, 14, 15] for the real case). The Pisarenko harmonic decomposer (PHD) [12, 13, 16, 17,], and the reformed Pisarenko harmonic decomposer (RPHD) [15, 18, 19] are among the algorithms that perform well and are computationally efficient in the real case, when the signal consists of a real sinusoid and an additive, white noise. The theory for both the above mentioned algorithms assumes a white noise. In the present paper we report an iterative method designed to improve the performance of the RPHD such that frequency error variances close to the Cramer-Rao lower bound (CRLB) are obtained for signal-to-noise ratios (SNR) as low as 3 dB in a few iterations. An iteration consists of filtering the initial data sequence with a frequency selective filter whose maximum of the frequency response is at the