Detection of weak transient broadband signals: Subspace and likelihood ratio test approaches

We investigate the detection of a weak transient broadband signal, and compare a polynomial subspace detection approach to a likelihood ratio test. The former is based on an analytic eigenvalue decomposition of the array data in order to derive a subspace projection away from stronger stationary sources that obscure the transient signal. An energy detection in the noise-only subspace has been demonstrated to work well in a number of broadband array applications. In this contribution, we aim to explore its comparison to a statistically optimum test, the likelihood ratio test (LRT). The LRT requires more information about the scenario than the subspace test — namely the data covariance due to the transient signal — but can still serve as a suitable benchmark. Somewhat surprisingly, simulation results show that the more dispersive the propagation environment and the weaker the transient signal is compared to any stationary sources, the better it is to base a test — either the LRT or even a simple energy criterion — on the data in the noise-only subspace. This is due to the reduced matrix dimensions and enhanced condition numbers of the involved space-time covariance matrices.