Super resolution DOA estimation based on deep neural network

Direction-of-arrival (DOA) estimation is crucial in various applications, including wireless communications and source localization. Traditional subspace-based methods like MUSIC and ESPRIT, while offering high resolution, suffer from high computational complexity and are not suitable for real-time implementation. Machine learning approaches using artificial neural networks (ANNs) provide a faster alternative. Early attempts utilized Radial Basis Function (RBF) networks and Support Vector Regression (SVR), but their performance was limited. Multilayer Perceptron (MLP) networks offered improvements, but deep learning (DL) holds the promise of even greater accuracy and generalization. Recent research has explored DNNs for DOA estimation, but these often rely on prior knowledge of the signal number, assume a constant SNR, or require large intersignal angular distances, limiting their applicability. This paper addresses these limitations by proposing a novel DNN architecture that achieves superior resolution and generalization capabilities.

Existing literature demonstrates the potential of DNNs in DOA estimation. Huang et al. achieved a location error of 0.1° but required prior knowledge of the signal number. Liu et al. proposed a two-stage DNN with a multitask autoencoder and parallel classifiers, achieving an error of 0.5° but only for two-signal scenarios and suffering from reduced accuracy at subregion edges. Most prior DNN approaches used coarse grids (5° or 10° spacing) and restricted training to large angular distances and uniform SNRs, hindering their generalization. This paper builds upon these studies, addressing their limitations with a deeper and more robust DNN architecture.

The proposed DNN architecture is designed for direction classification, handling unknown signal numbers. The data model considers a linear array of L omnidirectional antenna elements receiving P narrowband uncorrelated signals. The received signal is modeled using a steering vector and added noise. The spatial covariance matrix R is calculated from snapshots, and its upper right part is transformed into a real vector Z, which serves as input to the DNN. The DNN comprises three residual blocks with increasing dimensionality (180D, 360D, 720D), each containing ResNet layers. Linear transformations and dropout layers are used between blocks to enhance robustness and prevent overfitting. The output layer consists of 180 neurons with sigmoid activations, representing the probability of a signal at each angle from -90° to 90°. The loss function is the mean squared error (MSE) between the DNN output and smoothed one-hot vectors representing the true signal angles. The network is trained using stochastic gradient descent (SGD) with a dynamic learning rate strategy. Weight initialization and layer normalization are employed to improve training stability. The training process uses a dataset generated from an 8-element uniform linear array with random signal angles and SNRs. Millions of samples are used for training, employing a batch size of 800 and 2000k iterations. A smooth label technique is used for training to further improve the accuracy.

The proposed DNN demonstrates superior performance in several scenarios. In a scenario with a fixed number of signals and equal SNR (Case A), increasing the ResNet block depth improves precision, recall, and F-score. In a scenario with a random number of signals and equal SNR (Case B), the DNN performs well, even with varying signal numbers, achieving high F-scores (above 0.99). Performance degrades slightly as the number of signals increases. The impact of SNR is evaluated (Figure 3a) with the expected result that higher SNR leads to better performance. A test on six signals (Figure 3b) shows excellent direction estimation accuracy. In a scenario with a fixed number of signals and random SNR (Case C), the model performs acceptably, with performance decreasing as expected. An amplitude interpolation method is used to improve the resolution of direction estimation, reducing the average absolute estimation error to 0.1° with a standard deviation of 0.06°. The relationship between estimation error and deviation from integer angles is analyzed (Figure 4), revealing a sharp drop in performance when the error approaches the midpoint between integer angles. A comparison with existing methods (Table 4) highlights the superiority of the proposed DNN in terms of handling random signal numbers, random SNRs, and achieving high resolution with a smaller number of antenna elements. The DNN achieves state-of-the-art performance.

The study's findings demonstrate the efficacy of the proposed DNN model for super-resolution DOA estimation. The superior performance compared to previous approaches stems from the deep architecture, which allows for better representation of the complex mapping between the input spatial covariance matrix and the output signal directions. The ability to handle random signal numbers and SNRs significantly enhances the model's applicability to real-world scenarios. However, limitations exist. The performance degrades with increasing signal numbers, especially when signals are close together, because of signal fusion and splitting. Performance also decreases with increasing SNR differences, as stronger signals tend to dominate, and at larger angles, because of the limitations of the mapping function. The limitations identified suggest avenues for future research, including exploring advanced architectures like stacked autoencoders, restricted Boltzmann machines, or convolutional neural networks (CNNs) to enhance signal denoising and feature extraction.

This paper introduces a high-resolution DNN-based DOA estimation model surpassing previous methods by handling random signal numbers and SNRs. While limitations exist, the results demonstrate the model's applicability and its potential for further improvement. Future work could focus on integrating more advanced architectures to address the identified limitations and improve performance in challenging scenarios.

The current model's performance degrades when dealing with a large number of signals, particularly when signals are close together or when there are significant SNR differences. The mapping function's limitations at large angles also affect performance. These aspects limit the model's performance in complex scenarios and suggest avenues for future improvement.