  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fixed-dimensional asymptotics are no longer applicable.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.
