Spectral-Based SPD Matrix Representation for Signal Detection Using a Deep Neutral Network.

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.

Spectral Convolution Feature-Based SPD Matrix Representation for Signal Detection Using a Deep Neural Network.

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.

A Phase-Coded Sequence Design Method for Active Sonar.

Phase-coded sequences are widely studied as the transmitted signals of active sonars. Recently, several design methods have been developed to generate phased-coded sequences satisfying specific aperiodic or periodic autocorrelation sidelobe level metrics. In this paper, based on the majorization-minimization strategy and the squared iterative acceleration scheme, we propose a method to generate sequences with the periodic weighted integrated sidelobe level metric. Numerical simulations illustrate that the proposed method can effectively suppress the periodic autocorrelation sidelobe levels in specific time lags. Compared with other sequence design methods satisfying the periodic weighted integrated sidelobe level metric, our method improves the computational efficiency significantly. In addition, the proposed sequence demonstrates better matched filter performance in specific range intervals compared with its counterpart. The results suggest that the method could be applied as a valid and real-time design method for transmitted signals of active sonars.

Optimal Waveform Design Using Frequency-Modulated Pulse Trains for Active Sonar.

Frequency-modulated pulse trains can be applied in active sonar systems to improve the performance of conventional transmitted waveforms. Recently, two pulse trains have been widely researched as the transmitted waveforms for active sonars. The LFM-Costas pulse train was formed by modulating the linear frequency-modulated (LFM) waveform via the Costas sequence to remove the Doppler ambiguity of LFM pulses. The generalized sinusoidal frequency-modulated (GSFM) waveform, another frequency-modulated pulse train, achieved an ideal ambiguity function shape with thumbtack mainlobe. In this paper, we focus on constructing an optimization model to optimize the LFM-Costas and GSFM pulse trains with the genetic algorithm. The pulse trains can be improved on properties of both ambiguity function and correlations between sub-pulses. The optimized pulse trains are proven to have better detection performance than those of the initial pulse trains, including the lower sidelobe levels of ambiguity function, as well as lower cross-correlation property. Moreover, it is affirmed that the reverberation suppression performance of pulse trains has also been improved through the optimization model.