The symmetric positive definite (SPD) matrix has attracted much attention in classification problems because of its remarkable performance, which is due to the underlying structure of the Riemannian manifold with non-negative curvature as well as the use of non-linear geometric metrics, which have a stronger ability to distinguish SPD matrices and reduce information loss compared to the Euclidean metric. In this paper, we propose a spectral-based SPD matrix signal detection method with deep learning that uses time-frequency spectra to construct SPD matrices and then exploits a deep SPD matrix learning network to detect the target signal. Using this approach, the signal detection problem is transformed into a binary classification problem on a manifold to judge whether the input sample has target signal or not. Two matrix models are applied, namely, an SPD matrix based on spectral covariance and an SPD matrix based on spectral transformation. A simulated-signal dataset and a semi-physical simulated-signal dataset are used to demonstrate that the spectral-based SPD matrix signal detection method with deep learning has a gain of 1.7–3.3 dB under appropriate conditions. The results show that our proposed method achieves better detection performances than its state-of-the-art spectral counterparts that use convolutional neural networks.

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.

Convolutional neural networks have powerful performances in many visual tasks because of their hierarchical structures and powerful feature extraction capabilities. SPD (symmetric positive definition) matrix is paid attention to in visual classification, because it has excellent ability to learn proper statistical representation and distinguish samples with different information. In this paper, a deep neural network signal detection method based on spectral convolution features is proposed. In this method, local features extracted from convolutional neural network are used to construct the SPD matrix, and a deep learning algorithm for the SPD matrix is used to detect target signals. Feature maps extracted by two kinds of convolutional neural network models are applied in this study. Based on this method, signal detection has become a binary classification problem of signals in samples. In order to prove the availability and superiority of this method, simulated and semi-physical simulated data sets are used. The results show that, under low SCR (signal-to-clutter ratio), compared with the spectral signal detection method based on the deep neural network, this method can obtain a gain of 0.5–2 dB on simulated data sets and semi-physical simulated data sets.

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