Space-Time Adaptive Detection of Distributed Targets in Homogeneous Environment

E. Conte, A. DeMaio and

G. Ricci*

Dipartimento di Ingegneria Elettronica e delle Telecomunicazioni

Università degli Studi di Napoli Federico II

Via Claudio, 21, I-80125 Napoli, Italy.

Email: a.demaio@unina.it

* Università degli Studi di Lecce

**Abstract**** **
We address the problem of detecting distributed targets (with
unknown amplitudes) in Gaussian noise with unknown covariance matrix. Precisely, we assume
that data are collected from n sensors and deal with the problem of detecting the presence
of a target across H range cells. It is also assumed that a secondary data set is
available and that each of such snapshots does not contain any useful target echo. All of
data vectors possess one and the same covariance matrix.

Detectors based upon the Generalized Likelihood Ratio Test (GLRT) are designed and assessed. In particular, we derive a decision strategy which implements the GLRT over the entirety of data, referred to in the following as one-step GLRT detector, and receivers based upon a two-step procedure: for this case we first assume that the covariance matrix (or its structure only) is known and design the GLRT based upon the cells under test; then, in order to come up with completely adaptive structures we plug the sample covariance matrix, based upon secondary data, into the test in place of the unknown matrix.

Proposed detectors ensure the Constant False Alarm Rate Property with respect to the
covariance matrix and achieve comparable performances. In particular, two-step detectors
are to be preferred due to their simplified structures and to possible performance gains
as *H* increases (for medium/high probabilities of detection). Finally, the
comparison of the newly introduced detectors with a receiver assuming knowledge of the
covariance matrix confirms their suitability for operating in real radar scenarios.