Detection of Signals in Additive Cauchy Noise with Unknown Parameters

Abstract

Detection of signals in impulsive additive noise is important in many applications. When the channel is nonstationary, unknown parameters in test statistic need to be periodically estimated and updated in the detection procedure. For impulsive noise environments modeled with a Cauchy prior, the maximum likelihood (ML) equations are intractable and ML estimates may be obtained via numerical solving. Consequently, the generalized likelihood ratio test (GLRT) is computationally intensive and is not suitable for real-time applications. In this work we study the modified maximum likelihood (MML) estimation procedure and investigate performance of MML estimators for Cauchy distribution. We propose MML estimation based detection of signals in Cauchy noise with unknown but deterministic parameters. We provide extensive simulation results to show that the performance loss of proposed detector is very small compared to GLRT. We also show that the proposed detector outperforms GLRT in presence of model uncertainties. Since MML estimators are explicit functions of a few central order statistics, complexity of the proposed detector is significantly lower than GLRT and is suitable for real-time applications.