Lie Group-Based Detector for Signal Detection

This article assumes geometric characteristics of covariance matrices and applies certain group structures treating the entire covariance matrix as a Lie group. The feature relationship between signals and noise is established by leveraging the geometric features of Lie groups. Initially, all signal covariance matrices are considered as a manifold, and this manifold is transformed into a Lie group by introducing a specific algebraic structure. The mean of the clutter covariance matrix is then computed using the mean calculation method on the Lie group. After incorporating the echo signal, the Log Euclidean distance(LED) between the tested unit and the mean of other clutter units is calculated. This distance serves as the detection statistic for target detection. Through Monte Carlo simulation, the threshold is determined, and the detection statistics are compared to this threshold. Evaluation criteria are formulated to ascertain the presence or absence of the signal, resulting in the design of a Lie group distance detector. Simulation results indicate that the LED detector exhibits superior detection performance.