17-03-2014, 06:08 PM
ABSTRACT
In this study, a general approach to the detection problem
of unknown-amplitude coherent signals in some practical
groups of non-Gaussian and/or correlated clutters is investigated.
Since there exist no closed-form analytical probability
distributions in these contributions, an optimal likelihood
ratio test is not applicable and we instead utilize the characteristic
function and its estimate in order to perform the
estimation and detection. We also extend this idea to the case
of correlated K-distributed clutter observations. We assess
the performance of the proposed detectors and make some
comparisons through Monte-Carlo simulations.
Index Terms— Characteristic function, Detection in non-
Gaussian clutters, Estimation, Radar.
1. INTRODUCTION
Coherent radar detection in a mixture of thermal Gaussian
noise and clutters has received considerable attention in
the last few decades. In this regard, many conventionallydesigned
detectors from the landmarkGLRT detector of Kelly
[1] to the very robust detection scheme in non-homogeneous
colored noise proposed by Bidon, Besson and Tourneret [2],
do assume a Gaussian behavior for the noise or clutters of
interest. However, research shows that in various detection
applications this type of clutter modeling is not as realistic
and non-Gaussian probability density distribution (PDF)
models are to be applied [3, 4]. As a matter of fact, there
are situations for which a specific and predefined PDF would
not exist at all and one of the most common are the mixtures
of Gaussian noise and non-Gaussian clutters which has not
been particularly investigated before. Therefore, an analytical
optimal PDF-based detection structure cannot be obtained in
these scenarios.
The basic motivation of our work in this paper is to
employ the definement and properties of the characteristic
function (CF) and its classical unbiased estimation, empirical
characteristic function (ECF), to design and implement novel
detectors for detection in a few practical non-Gaussian clutters
added to Gaussian noise. In this connection, J. Ilow and
D. Hatzinakos [5] introduced a flexible, yet simple, detection
strategy on the basis of the CF and ECF rather than the PDF.
Their method requires a predefined formalism for the CF, i.e.
the Fourier transform of the PDF, which in turn may not always
exist, and is quite sensitive to the estimated parameters
of the unknown CF. In addition, it is applicable only in the
case of independent identically distributed (iid) data observations.
We provide new approaches to both omit the need for
prior CF formulations and cover the detection task in correlated
clutters. We also provide a novel method of estimation
of unknown coherent signals without the necessity of having
any PDF at hand. The remainder of the paper is organized
as follows. In section II, a novel approach to the estimation
of coherent signal amplitudes in non-Gaussian perturbations
is introduced. The detection structures is derived in section
III. Section IV is devoted to performance assessment of
the proposed detectors and some further results. Section V
concludes.
In this study, a general approach to the detection problem
of unknown-amplitude coherent signals in some practical
groups of non-Gaussian and/or correlated clutters is investigated.
Since there exist no closed-form analytical probability
distributions in these contributions, an optimal likelihood
ratio test is not applicable and we instead utilize the characteristic
function and its estimate in order to perform the
estimation and detection. We also extend this idea to the case
of correlated K-distributed clutter observations. We assess
the performance of the proposed detectors and make some
comparisons through Monte-Carlo simulations.
Index Terms— Characteristic function, Detection in non-
Gaussian clutters, Estimation, Radar.
1. INTRODUCTION
Coherent radar detection in a mixture of thermal Gaussian
noise and clutters has received considerable attention in
the last few decades. In this regard, many conventionallydesigned
detectors from the landmarkGLRT detector of Kelly
[1] to the very robust detection scheme in non-homogeneous
colored noise proposed by Bidon, Besson and Tourneret [2],
do assume a Gaussian behavior for the noise or clutters of
interest. However, research shows that in various detection
applications this type of clutter modeling is not as realistic
and non-Gaussian probability density distribution (PDF)
models are to be applied [3, 4]. As a matter of fact, there
are situations for which a specific and predefined PDF would
not exist at all and one of the most common are the mixtures
of Gaussian noise and non-Gaussian clutters which has not
been particularly investigated before. Therefore, an analytical
optimal PDF-based detection structure cannot be obtained in
these scenarios.
The basic motivation of our work in this paper is to
employ the definement and properties of the characteristic
function (CF) and its classical unbiased estimation, empirical
characteristic function (ECF), to design and implement novel
detectors for detection in a few practical non-Gaussian clutters
added to Gaussian noise. In this connection, J. Ilow and
D. Hatzinakos [5] introduced a flexible, yet simple, detection
strategy on the basis of the CF and ECF rather than the PDF.
Their method requires a predefined formalism for the CF, i.e.
the Fourier transform of the PDF, which in turn may not always
exist, and is quite sensitive to the estimated parameters
of the unknown CF. In addition, it is applicable only in the
case of independent identically distributed (iid) data observations.
We provide new approaches to both omit the need for
prior CF formulations and cover the detection task in correlated
clutters. We also provide a novel method of estimation
of unknown coherent signals without the necessity of having
any PDF at hand. The remainder of the paper is organized
as follows. In section II, a novel approach to the estimation
of coherent signal amplitudes in non-Gaussian perturbations
is introduced. The detection structures is derived in section
III. Section IV is devoted to performance assessment of
the proposed detectors and some further results. Section V
concludes.