Deep Learning Based Near-Field User Localization with Beam Squint in Wideband XL-MIMO Systems

TL;DR

The paper develops a theoretical and practical framework for centimeter-level user localization in wideband XL-MIMO under near-field beam squint and spatial non-stationarity. It derives Cramér-Rao Bounds for angle and distance in the presence of controllable beam squint, proposes a CBS-BT beam-training scheme to exploit multi-subcarrier focusing, and introduces a ConvNeXt-based DL localization method that leverages CBS outputs and image-like inputs to mitigate non-stationarity and noise. The results show that CRBs decrease with more subcarriers and bandwidth, while the ConvNeXt approach achieves centimeter-level localization, outperforming existing methods in mixed LoS/NLoS scenarios. The work has practical impact for integrated sensing and communication in 6G/XL-MIMO systems by providing both theory and data-driven tools to achieve robust, high-precision localization.

Abstract

Extremely large-scale multiple-input multiple-output (XL-MIMO) is gaining attention as a prominent technology for enabling the sixth-generation (6G) wireless networks. However, the vast antenna array and the huge bandwidth introduce a non-negligible beam squint effect, causing beams of different frequencies to focus at different locations. One approach to cope with this is to employ true-time-delay lines (TTDs)-based beamforming to control the range and trajectory of near-field beam squint, known as the near-field controllable beam squint (CBS) effect. In this paper, we investigate the user localization in near-field wideband XL-MIMO systems under the beam squint effect and spatial non-stationary properties. Firstly, we derive the expressions for Cramér-Rao Bounds (CRBs) for characterizing the performance of estimating both angle and distance. This analysis aims to assess the potential of leveraging CBS for precise user localization. Secondly, a user localization scheme combining CBS and beam training is proposed. Specifically, we organize multiple subcarriers into groups, directing beams from different groups to distinct angles or distances through the CBS to obtain the estimates of users' angles and distances. Furthermore, we design a user localization scheme based on a convolutional neural network model, namely ConvNeXt. This scheme utilizes the inputs and outputs of the CBS-based scheme to generate high-precision estimates of angle and distance. More importantly, our proposed ConvNeXt-based user localization scheme achieves centimeter-level accuracy in localization estimates.

Figures (10)

• Figure 1: The wideband near-field communication scenario with a uniform linear array (ULA) at the BS in the XL-MIMO system, where UEs are single-antenna devices.
• Figure 2: Illustration of the near-field beamformeing architectures and their corresponding normalized beamforming gains. The sub-figure (a) and (c) depict beamforming architectures based on PSs and TTDs, respectively. Meanwhile, the sub-figure (b) and (d) depict the normalized beamforming gains corresponding to the sub-figure (a) and (c), respectively. In sub-figure (b) and (d), blue represents the minimum gain, red represents the maximum gain, and other colors transition between these two extremes. These representations are depicted considering a bandwidth of $B=6$ GHz, a central carrier frequency of $f_c=100$ GHz, the utilization of $M=5$ subcarriers, and an array comprising $N=512$ antennas. The location of the UE is set as $(7, -7)$.
• Figure 3: The near-field beam trajectories based on the controllable beam squint. Parameters for these trajectories include a a bandwidth of $B=6$ GHz, a central carrier frequency of $f_c=100$ GHz, the utilization of $M=20$ subcarriers, and an array comprising $N=512$ antennas. Taking trajectory $2$ as an example, when we set ${r_s} = {r_e} = 20$$\text{m}$, ${\theta _s} = 60^\circ$, and ${\theta _e} = 0^\circ$ in \ref{['7']}, the $1$-st and the $20$-th subcarrier beams would be directed to $(20$$\text{m}, 60^\circ)$ and $(20$$\text{m}, 0^\circ)$, respectively. In this scenario, the focus of the $m$-th subcarrier beam can be determined by \ref{['8']} and \ref{['9']}. For instance, the focus of the $5$-th and $16$-th subcarrier beams is $(26.21$$\text{m}, 42.45^\circ)$ and $(22.83$$\text{m}, 10.01^\circ)$, respectively. These focal points corresponding to $M$ subcarriers can be connected to form a trajectory, covering a specific angle or distance range.
• Figure 4: The normalized signal power of the angle estimation stage and the distance estimation stage of the scheme in [3] under both spatial stationary channel and spatial non-stationary channel conditions, where the UE is located at $(15$${\rm m}, 0^\circ)$, $M =2048$, $f_c = 100$ GHz, $N =512$, and $B =6$ GHz. We assume that there is no noise for illustration.
• Figure 5: The proposed ConvNeXt based user localization scheme. It is worth noting that the proposed ConvNeXt based method is suitable for multi-user localization scenarios. Without loss of generality, Fig. 5 only takes user $k$ as an example.