Model-driven deep neural network for enhanced direction finding with commodity 5G gNodeB

TL;DR

This work addresses accurate AoA-based positioning in 5G networks where hardware impairments undermine ideal-model estimators. It introduces MoD-DNN, a three-module framework combining a frequency-diverse multi-task autoencoder beamformer, a coarray spectrum generator, and a model-driven spectrum reconstruction module (MoDL-SSR) that iteratively calibrates angular-dependent phase errors using a CNN and a sparse conjugate gradient solver. The approach demonstrates automatic calibration and high-resolution AoA estimation through numerical simulations and real-world experiments in anechoic and indoor environments, outperforming conventional methods such as MUSIC, DeepMUSIC, and pure CNN baselines, while maintaining real-time complexity. The results highlight the viability of hybrid data-and-model-driven direction finding on commodity 5G gNodeB, with strong implications for mobile positioning in future 5G-Advanced and 6G networks.

Abstract

Pervasive and high-accuracy positioning has become increasingly important as a fundamental enabler for intelligent connected devices in mobile networks. Nevertheless, current wireless networks heavily rely on pure model-driven techniques to achieve positioning functionality, often succumbing to performance deterioration due to hardware impairments in practical scenarios. Here we reformulate the direction finding or angle-of-arrival (AoA) estimation problem as an image recovery task of the spatial spectrum and propose a new model-driven deep neural network (MoD-DNN) framework. The proposed MoD-DNN scheme comprises three modules: a multi-task autoencoder-based beamformer, a coarray spectrum generation module, and a model-driven deep learning-based spatial spectrum reconstruction module. Our technique enables automatic calibration of angular-dependent phase error thereby enhancing the resilience of direction-finding precision against realistic system non-idealities. We validate the proposed scheme both using numerical simulations and field tests. The results show that the proposed MoD-DNN framework enables effective spectrum calibration and accurate AoA estimation. To the best of our knowledge, this study marks the first successful demonstration of hybrid data-and-model-driven direction finding utilizing readily available commodity 5G gNodeB.

Figures (5)

• Figure 1: Antenna array of a commodity gNodeB for 5G communications. a, We design and fabricate a four-element ULA as RRU antennas. Two antennas at both sides are dummy elements to guarantee the same boundaries seen by the central four elements. b, Measured phase errors of the antennas by selecting the first antenna as reference. Within the AoA ranges spanning from $-30^{\circ}$ to $0^{\circ}$ and from $0^{\circ}$ to $30^{\circ}$, the phase errors demonstrate a relatively stable level of fluctuation, remaining below $20^{\circ}$. However, beyond these subregions, i.e., beyond $-30^{\circ}$ and $30^{\circ}$, the phase errors noticeably escalate while maintaining a consistent slope. c, Comparison of spatial spectrum generated by Coarray DBF (CDBF) and SCG algorithms within the phase errors. Black dashed line denotes the truth. When the AoA is $-15^{\circ}$, the half-power beam width (HPBW) of CDBF is $13.4^{\circ}$, while that of SCG is $0.7^{\circ}$.
• Figure 2: Network framework of MoD-DNN for AoA estimation using gNodeB. a, Multi-task autoencoder. We first rearrange the input CSI matrix $\mathbf{H}$ to real-value vectors-form $\mathbf{h}(k)$. Then, we apply a group of multi-task autoencoders to filter the input into $P$ subregions and enhance the consistency of hardware impairments within each subregion. b, Coarray spectrum generation module. We vectorize sampled covariance matrix $\hat{\mathbf{R}}_p$ calculated from the CSI $\mathbf{H}_{p}$ to obtain the coarray signal $\mathbf{y}_p$. The signal is then transformed to the image of the coarray spatial spectrum $\hat{\boldsymbol{\eta}}_p$ by utilizing the coarray DBF technique. c, Model-driven deep learning-based spatial spectrum reconstruction. We integrate deep learning and signal processing methods to design a module with the ability of spectrum reconstruction and enhance the AoA estimation.
• Figure 3: Illustration of proposed iteration for MoDL-SSR module. a, Overall iteration in MoDL-SSR module. We leverage 1D-CNN to calibrate the input coarray spectrum and obtain a calibrated version $\mathbf{z}$. We then design a SCG algorithm with sparsity modification in CG method. Coarray spectrum is fed into iterations between 1D-CNN and SCG algorithm to reconstruct sparse spatial spectrum. b, Alternative optimization between CNN-based calibrator and inverse problem-based SSR. We apply the same 1D-CNN at each iteration to share the weights among the CNNs in different iterations.
• Figure 4: Performance comparison based on dataset for numerical experiments. a, Amplitude responses of Autoencoder I. b, Phase responses of Autoencoder I. c, Amplitude responses of Autoencoder II. d, Phase responses of Autoencoder II. e, Comparison of spatial spectrum results at different AoA. Black dashed lines denote the truth. f--h, Performance comparison between different methods. f, RMSE versus SNR. g, RMSE performance comparison versus degree of impairment $\rho$. h, SD performance comparison versus number of epoch. i, RMSE performance of MoD-DNN in different channels.
• Figure 5: Experiment in an anechoic chamber and real-world test in an indoor environment. a, Setups for anechoic chamber experiments. Error performance of different methods in an anechoic chamber in terms of b, CDF and c, boxplots for 4 subregions. d, Setups for real-world test in an indoor experiment. Real-world error performance of different methods in terms of e, CDF and f, boxplots for 4 subregions.