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

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Document pages: 16 pages

Abstract: In this paper, we consider the detection of a small change in the frequencyof sinusoidal signals, which arises in various signal processing applications.The generalized likelihood ratio test (GLRT) for this problem uses the maximumlikelihood (ML) estimator of the frequency, and therefore suffers from highcomputational complexity. In addition, the GLRT is not necessarily optimal andits performance may degrade for non-asymptotic scenarios that are characterizedby close hypotheses and small sample sizes. In this paper we propose a newdetection method, named the generalized locally most powerful unbiased (GLMPU)test, which is a general method for local detection in the presence of nuisanceparameters. A closed-form expression of the GLMPU test is developed for thedetection of frequency deviation in the case where the complex amplitudes ofthe measured signals are unknown. Numerical simulations show improvedperformance over the GLRT in terms of probability of detection performance andcomputational complexity.

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