A signal detection method based on matrix information geometric dimensionality reduction

Traditional signal detection methods have achieved satisfactory performance in many contexts of signal processing. However, these methods based on mathematical statistics show a drawback in dealing with the low SNR cases, which limits their practicability. To this end, inspired by image processing techniques, we first make use of the short time Fourier transform to generate sufficient 2-D spectrograms of the received data. Then we extract high dimensional features of these spectrogram to construct high dimensional covariance matrices, transforming into a binary classification problem lying on a symmetric positive definite (SPD) manifold. In addition, by reducing the dimensionality directly on the SPD manifold, these spectrograms are mapped into a more discriminative SPD manifold, which improves the separability between the two classes. The simulation experiment results demonstrate that our method achieve satisfactory signal detection performance in the task of signal detection under K distribution data, even in the case of SNR = -10.