Low-Complexity Detection of Small Frequency Changes by the Generalized LMPU Test

TL;DR

This paper introduces the GLMPU test for detecting small frequency changes in sinusoidal signals, offering improved detection performance and lower computational complexity compared to the traditional GLRT, especially in non-asymptotic scenarios.

Contribution

The paper proposes a new GLMPU detection method with a closed-form expression for unknown amplitudes, enhancing detection accuracy and reducing computational load.

Findings

GLMPU outperforms GLRT in detection probability.

GLMPU has lower computational complexity.

Performance improves in small sample and close hypothesis scenarios.

Abstract

In this paper, we consider the detection of a small change in the frequency of sinusoidal signals, which arises in various signal processing applications. The generalized likelihood ratio test (GLRT) for this problem uses the maximum likelihood (ML) estimator of the frequency, and therefore suffers from high computational complexity. In addition, the GLRT is not necessarily optimal and its performance may degrade for non-asymptotic scenarios that are characterized by close hypotheses and small sample sizes. In this paper we propose a new detection method, named the generalized locally most powerful unbiased (GLMPU) test, which is a general method for local detection in the presence of nuisance parameters. A closed-form expression of the GLMPU test is developed for the detection of frequency deviation in the case where the complex amplitudes of the measured signals are unknown. Numerical simulations show improved performance over the GLRT in terms of probability of detection performance and computational complexity.