Automatic modulation recognition (AMR) is a significant technology in noncooperative wireless communication systems. This paper proposes a deep complex network that cascades the bidirectional long short-term memory network (DCN-BiLSTM) for AMR. In view of the fact that the convolution operation of the traditional convolutional neural network (CNN) loses the partial phase information of the modulated signal, resulting in low recognition accuracy, we first apply a deep complex network (DCN) to extract the features of the modulated signal containing phase and amplitude information. Then, we cascade bidirectional long short-term memory (BiLSTM) layers to build a bidirectional long short-term memory model according to the extracted features. The BiLSTM layers can extract the contextual information of signals well and address the long-term dependence problems. Next, we feed the features into a fully connected layer. Finally, a softmax classifier is used to perform classification. Simulation experiments show that the performance of our proposed algorithm is better than that of other neural network recognition algorithms. When the signal-to-noise ratio (SNR) exceeds 4 dB, our model’s recognition rate for the 11 modulation signals can reach 90%.

Direction of arrival (DOA) estimation is widely used in the field of array signal processing. The model-based algorithms rely on domain knowledge and assumptions, facing limitations in estimating coherent sources and running on few snapshots etc. In contrast, deep learning approaches can learn from data, offering a promising alternative for DOA estimation. In this paper, a novel end-to-end model-based deep learning DOA estimation architecture (MD-DOA) is proposed to estimate the DOAs of multiple narrowband signals captured by a uniform linear array. Specifically, the multi-branch convolutional recurrent neural network with a residual link (MBCR2net) is developed to extract multi-scale features and learn correlation in received temporal signals. Subsequently, the weighted noise subspace network (WNSnet) is proposed to learn a more representative noise subspace from the one obtained by eigenvalue decomposition (EVD), developing the more precise subspace division. The matrix reshape process (MRP) then generates the pseudo covariance matrix (PCM) and captures the correlation in the weighted noise subspace. Notably, EVD and MRP are the model-based modules to preserve the interpretability. Finally, the PCM-based DOA-finding network (PDFnet) estimates the desired DOAs. MD-DOA integrates the model-based and data-driven advantages. It inherits the overall framework of the subspace-based methods while using the network to augment the covariance matrix estimation, subspace division and peak-finding process. Our proposed architecture can operate successfully in the presence of array mismatch, low signal-to-noise ratios (SNRs), and few snapshots. It is also applicable to real-world measurements and demonstrates superior performance compared with other existing algorithms in this field.

Spherical arrays have been widely used in direction-of-arrival (DOA) estimation in recent years, and the high-resolution estimation of signal parameter via rotational invariance technique (ESPRIT) was developed in the spherical harmonics domain. However, the spherical harmonics ESPRIT (SHESPRIT) cannot estimate the DOA when the elevation approaches 90°. To solve this problem, we present a two-step SHESPRIT (TS-SHESPRIT) based on two new recurrence relations of complex spherical harmonics. Furthermore, we develop a real-valued two-step SHESPRIT (RTS-SHESPRIT) that exploits a unitary matrix to obtain a real-valued relation between the signal subspace and the steering matrix to further reduce the computational complexity. However, the number of sources that are estimated by RTS-SHESPRIT is limited. Therefore, we propose the semi-RTS-SHESPRIT method, which reduces the computational complexity associated with eigenvalue decomposition (EVD) and avoids the limitations of RTS-SHESPRIT. Relative to SHESPRIT and TS-SHESPRIT, RTS-SHESPRIT and semi-RTS-SHESPRIT reduce the computational burden by 75% during EVD. Furthermore, we derive the mean square errors (MSEs) of the above algorithms and significantly simplify the MSE expressions. Different expressions for the MSEs are due to different recurrence relations used by different SHESPRIT-type algorithms. All proposed two-step SHESPRIT-type algorithms have higher accuracy than traditional SHESPRIT. The simulation results demonstrate the satisfactory performance of our methods.

Spherical microphone arrays have been used for source localization in three-dimensional space recently. In this paper, a two-stage algorithm is developed to localize mixed far-field and near-field acoustic sources in free-field environment. In the first stage, an array signal model is constructed in the spherical harmonics domain. The recurrent relation of spherical harmonics is independent of far-field and near-field mode strengths. Therefore, it is used to develop spherical estimating signal parameter via rotational invariance technique (ESPRIT)-like approach to estimate directions of arrival (DOAs) for both far-field and near-field sources. In the second stage, based on the estimated DOAs, simple one-dimensional MUSIC spectrum is exploited to distinguish far-field and near-field sources and estimate the ranges of near-field sources. The proposed algorithm can avoid multidimensional search and parameter pairing. Simulation results demonstrate the good performance for localizing far-field sources, or near-field ones, or mixed field sources.

A tensor is used to describe head-related transfer functions (HRTFs) depending on frequencies, sound directions, and anthropometric parameters. It keeps the multi-dimensional structure of measured HRTFs. To construct a multi-linear HRTF personalization model, an individual core tensor is extracted from the original HRTFs using high-order singular value decomposition (HOSVD). The individual core tensor in lower-dimensional space acts as the output of the multi-linear model. Some key anthropometric parameters as the inputs of the model are selected by Laplacian scores and correlation analyses between all the measured parameters and the individual core tensor. Then, the multi-linear regression model is constructed by high-order partial least squares (HOPLS), aiming to seek a joint subspace approximation for both the selected parameters and the individual core tensor. The numbers of latent variables and loadings are used to control the complexity of the model and prevent overfitting feasibly. Compared with the partial least squares regression (PLSR) method, objective simulations demonstrate the better performance for predicting individual HRTFs especially for the sound directions ipsilateral to the concerned ear. The subjective listening tests show that the predicted individual HRTFs are approximate to the measured HRTFs for the sound localization.