Space-Time Adaptive Detection at Low Sample Support

TL;DR

This paper introduces a new space-time adaptive detection method suitable for low sample support scenarios, where traditional estimators fail, by employing large-dimensional asymptotics to improve detection performance.

Contribution

It develops a novel covariance matrix estimator based on large-dimensional asymptotics, proven to be detection-theoretically optimal in low-sample regimes, with characterized detection and false-alarm rates.

Findings

The new estimator outperforms existing methods in detection probability.

Asymptotic detection and false-alarm rates depend only on observable data.

Monte Carlo simulations confirm the theoretical advantages of the proposed estimator.

Abstract

An important problem in space-time adaptive detection is the estimation of the large p-by-p interference covariance matrix from training signals. When the number of training signals n is greater than 2p, existing estimators are generally considered to be adequate, as demonstrated by fixed-dimensional asymptotics. But in the low-sample-support regime (n < 2p or even n < p) fixed-dimensional asymptotics are no longer applicable. The remedy undertaken in this paper is to consider the "large dimensional limit" in which n and p go to infinity together. In this asymptotic regime, a new type of estimator is defined (Definition 2), shown to exist (Theorem 1), and shown to be detection-theoretically ideal (Theorem 2). Further, asymptotic conditional detection and false-alarm rates of filters formed from this type of estimator are characterized (Theorems 3 and 4) and shown to depend only on data that is given, even for non-Gaussian interference statistics. The paper concludes with several Monte Carlo simulations that compare the performance of the estimator in Theorem 1 to the predictions of Theorems 2-4, showing in particular higher detection probability than Steiner and Gerlach's Fast Maximum Likelihood estimator.