Detection of broadband planewaves in the presence of Gaussian noise of unknown covariance: asymptotically optimum tests using the 2-D autoregressive noise model

This paper addresses the problem of detecting a broadband planewave in noise of unknown spatial and temporal covariance at a linear array of sensors. Results of asymptotic detection theory are applied to derive detectors that approach optimal performance for large data records. A parametric approach is used to model the statistics of the data. A 2-D autoregressive (2DAR) model is chosen to model the noise process. Two broadband planewave signal models are considered. Both models represent the signal as a sum of monochromatic planewaves. In the Gaussian model, the amplitudes are assumed to be Gaussian with a single variance parameter, whereas in the deterministic assumption, they are individual unknown parameters. Detectors based on asymptotic theory are derived for both models. As part of the development of the asymptotically (AS) optimum detector, the Fisher information matrix (FIM) is derived. A proof of the locally asymptotic normal (LAN) property is provided for the Gaussian model probability density function (PDF). Both detectors, however, are AS equivalent to the generalized likelihood ratio test (GLRT), are AS of constant false alarm rate (CFAR), and perform AS as well as the GLRT constructed with full knowledge of the noise statistics. The performance of both detectors are compared with each other and to a standard spatially normalized beamformer in a computer simulation