51. Space-Time Adaptive Detection at Low Sample Support
- Author
-
Benjamin Robinson, Robert Malinas, and Alfred O. Hero
- Subjects
Signal Processing (eess.SP) ,Asymptotic analysis ,Covariance matrix ,Space time ,Maximum likelihood ,Monte Carlo method ,Estimator ,020206 networking & telecommunications ,02 engineering and technology ,Type (model theory) ,Signal Processing ,FOS: Electrical engineering, electronic engineering, information engineering ,0202 electrical engineering, electronic engineering, information engineering ,Applied mathematics ,Ideal (order theory) ,Limit (mathematics) ,Electrical Engineering and Systems Science - Signal Processing ,Electrical and Electronic Engineering ,Random variable ,Mathematics - 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 p) fixed-dimensional asymptotics are no longer applicable.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., 13 pages, 3 figures
- Published
- 2021