Asymptotically optimal narrowband signal detection using uniform linear array antenna

This paper addresses the detection of a narrowband signal in Gaussian noise with unknown parameters. Assuming unknown direction-of-arrival (DoA), amplitude, frequency, phase and noise variance, two Separating Function Estimation Tests (SFETs) and a Generalized Likelihood Ratio Test (GLRT) are proposed to detect the signal. These SFETs are estimates of a proposed Separating Function (SF). This proposed SF provides asymptotically optimal detectors using Maximum Likelihood Estimation (MLE) and is derived by the decomposition of Fisher information function of the induced maximal invariant. We propose two estimators MLE and Outlier Processed MLE (OPMLE) for estimation of the SF. It is shown that, the MLE of frequency and DoA are obtained by an exhaustive search to maximize the absolute of the two-dimensional discrete Fourier transform (DFT) of the received signals. We propose OP-MLE as an MLE based estimator by first eliminating the outliers from the DFT of the received signal using a pre-estimation of DoA and frequency. The simulation results show that the omission of outliers results in considerable improvement. Similarly, the resulting SFET using OP-MLE provides a higher probability of detection comparing with SFET using MLE and GLRT.