K-PHD Tek-Ton Frekans Kestiricisinin Bir Kesin Değişinti İfadesi: Rasgele Faz Durumu

Betofe Mboyo Keyta,Erdoğan Di̇laveroğlu,Sevim Hazal Uz

doi:10.17482/uumfd.559986

Betofe Mboyo Keyta, Erdoğan Di̇laveroğlu + Show 1 more

Open Access

https://doi.org/10.17482/uumfd.559986

Copy DOI

Abstract

The k-PHD method, a generalization of the well-known Pisarenko harmonic decomposition (PHD) method, is considered for frequency estimation of a single real random-phased sinusoid in noise. With the use of a simple variance analysis technique, an exact expression of the k-PHD frequency variance is derived. An approximate k-PHD variance formula for sufficiently large data lengths and signal-to-noise ratios is also given. Computer simulations are included to validate the theoretical development.

Highlights

The problem of estimating the frequency of a single real tone in noise has been frequently studied in the signal processing literature due to its wide range of applications
In Chan and So (2003), an exact variance expression of the Piseranko harmonic decomposition (PHD) frequency estimator has been derived, which holds for moderate data lengths and/or signal-tonoise ratios (SNRs)
By utilizing the variance analysis technique employed in Chan and So (2003), and taking into account that the phase is a random variable, we derive an exact closed-form expression for the frequency variance of the k-PHD method

Summary

INTRODUCTION

The problem of estimating the frequency of a single real tone in noise has been frequently studied in the signal processing literature due to its wide range of applications. In Chan and So (2003), an exact variance expression of the PHD frequency estimator has been derived, which holds for moderate data lengths and/or signal-tonoise ratios (SNRs). A variance expression of the k-PHD frequency estimator has been given in De Sabata et al (2007). By utilizing the variance analysis technique employed in Chan and So (2003) (and in De Sabata et al, 2007), and taking into account that the phase is a random variable, we derive an exact closed-form expression for the frequency variance of the k-PHD method. The variance expressions derived in this paper can be adapted to the PHD estimator for the random-phased sinusoid case.

EXACT VARIANCE DEVELOPMENT

NUMERICAL EXAMPLES

CONCLUSIONS