Adaptive subspace detection based on two-step dimension reduction in the underwater waveguide

In the underwater waveguide, the conventional adaptive subspace detector (ASD), derived by using the generalized likelihood ratio test (GLRT) theory, suffers from a significant degradation in detection performance when the samplings of training data are deficient. This paper proposes a dimension-reduced approach to alleviate this problem. The dimension reduction includes two steps: firstly, the full array is divided into several subarrays; secondly, the test data and the training data at each subarray are transformed into the modal domain from the hydrophone domain. Then the modal-domain test data and training data at each subarray are processed to formulate the subarray statistic by using the GLRT theory. The final test statistic of the dimension-reduced ASD (DR-ASD) is obtained by summing all the subarray statistics. After the dimension reduction, the unknown parameters can be estimated more accurately so the DR-ASD achieves a better detection performance than the ASD. In order to achieve the optimal detection performance, the processing gain of the DR-ASD is deduced to choose a proper number of subarrays. Simulation experiments verify the improved detection performance of the DR-ASD compared with the ASD.