A Modal-Domain Adaptive Subspace Detector in a Deep-Sea Environment

Dezhi Kong,Lei Xie,Mingyang Li,Xionghou Liu,Chao Sun

doi:10.1109/access.2019.2923543

Abstract

In deep-sea environments, the conventional adaptive subspace detector (ASD) is realized in the hydrophone domain by applying the generalized likelihood ratio test (GLRT), in which acoustic signals lie in lower-dimensional modal subspaces. When the number of snapshots in training data are deficient, ASD detection performance degrades significantly. This paper proposes a modal-domain ASD (MD-ASD) to alleviate the snapshot deficiency problem. In the MD-ASD procedure, the test and training data are mapped into the modal domain before proceeding to the GLRT; thus, the MD-ASD procedure is treated in a lower dimension and has a lower computational burden than the ASD procedure. Derivation of the MD-ASD distribution reveals the performance of the MD-ASD converges to that of the corresponding matched subspace detector (MSD). Utilizing the property of the acoustic signal and ambient noise lying in a common modal subspace, we demonstrate that the unknown parameters of the MD-ASD procedure achieve better estimation accuracies than the ASD procedure. The MD-ASD also obtains a larger output signal-to-noise ratio than the ASD, thus outperforming the ASD in detection performance, especially for the deficient training data case. Numerical simulations validate the improved detection performance of our proposed detector compared with the ASD.

Highlights

Detecting the presence of a signal radiating from an underwater acoustic source is a fundamental task for sonar
Where T denotes the test statistic of the detector and D[·] denotes a variance operation. It is noted in section VI.B that the detection performances of the adaptive subspace detector (ASD) and the modal-domain ASD (MD-ASD) are independent of the structures of the signal and noise covariance for a given signal-to-noise ratio (SNR)
We demonstrate that C2 is equivalent to CB, which indicates that the estimate of the location parameter in the MD-ASD procedure reaches the CramerRao lower bound (CRLB)

Summary

INTRODUCTION

Detecting the presence of a signal radiating from an underwater acoustic source is a fundamental task for sonar. The number of normal modes excited by a source is far greater than the number of hydrophones, it is quite possible that the signal still lies in a lower-dimensional subspace, called an effective modal subspace, with a dimension less than the hydrophone number [13]. The multidimensional Kelly detector, called the adaptive subspace detector (ASD) in [12], can be implemented in the deep sea where the signal subspace is the effective modal subspace. We develop a modal-domain adaptive subspace detector (MD-ASD) to alleviate the snapshot deficiency problem and reduce the computational burden.

DETECTION MODEL AND THE MSD

PERFORMANCE COMPARISON

COMPUTATIONAL COMPLEXITY

OUTPUT SNR

SIMULATION AND ANALYSIS

CONCLUSIONS