Matrix Information Geometry for Signal Detection via Hybrid MPI/OpenMP

Abstract

The matrix information geometric signal detection (MIGSD) method has achieved satisfactory performance in many contexts of signal processing. However, this method involves many matrix exponential, logarithmic, and inverse operations, which result in high computational cost and limits in analyzing the detection performance in the case of a high-dimensional matrix. To address these problems, in this paper, a high-performance computing (HPC)-based MIGSD method is proposed, which is implemented using the hybrid message passing interface (MPI) and open multiple processing (OpenMP) techniques. Specifically, the clutter data are first modeled as a Hermitian positive-definite (HPD) matrix and mapped into a high-dimensional space, which constitutes a complex Riemannian manifold. Then, the task of computing the Riemannian distance on the manifold between the sample data and the geometric mean of these HPD matrices is assigned to each MPI process or OpenMP thread. Finally, via comparison with a threshold, the signal is identified and the detection probability is calculated. Using this approach, we analyzed the effect of the matrix dimension on the detection performance. The experimental results demonstrate the following: (1) parallel computing can effectively optimize the MIGSD method, which substantially improves the practicability of the algorithm; and (2) the method achieves superior detection performance under a higher dimensional HPD matrix.