[Paper Review] Deep learning for location based beamforming with NLOS channels

Luc Le Magoarou, Taha Yassine+2 more|arXiv (Cornell University)|Jan 26, 2022

Millimeter-Wave Propagation and ModelingEngineering32 references16 citations

TL;DR

This paper proposes a deep learning-based location-based beamforming method that maps user location directly to a precoder using a neural network with random Fourier features (RFFs), enabling accurate beamforming in both LOS and NLOS environments. The RFF-enhanced network learns high-frequency spatial variations in channel coefficients, achieving a median correlation of 0.946 with the channel, significantly outperforming classical LBB and standard MLP baselines.

ABSTRACT

Massive MIMO systems are highly efficient but critically rely on accurate channel state information (CSI) at the base station in order to determine appropriate precoders. CSI acquisition requires sending pilot symbols which induce an important overhead. In this paper, a method whose objective is to determine an appropriate precoder from the knowledge of the user's location only is proposed. Such a way to determine precoders is known as location based beamforming. It allows to reduce or even eliminate the need for pilot symbols, depending on how the location is obtained. the proposed method learns a direct mapping from location to precoder in a supervised way. It involves a neural network with a specific structure based on random Fourier features allowing to learn functions containing high spatial frequencies. It is assessed empirically and yields promising results on realistic synthetic channels. As opposed to previously proposed methods, it allows to handle both line-of-sight (LOS) and non-line-of-sight (NLOS) channels.

Motivation & Objective

• Address the limitation of classical location-based beamforming (LBB) methods that rely solely on line-of-sight (LOS) paths and fail in non-line-of-sight (NLOS) scenarios.
• Reduce or eliminate pilot overhead in massive MIMO systems by determining precoders from user location alone.
• Develop a neural network capable of learning high-frequency spatial variations in channel coefficients due to fading, which classical MLPs cannot capture.
• Enable robust beamforming in complex urban environments with both LOS and NLOS propagation conditions.
• Demonstrate that a supervised deep learning approach with RFFs can generalize well across diverse propagation environments using a labeled training database.

Proposed method

• Train a deep neural network to learn a direct mapping from user location (in 2D or 3D) to a unit-norm precoding vector.
• Use random Fourier features (RFFs) as the first layer to encode spatial frequency information, enabling the network to model high-frequency channel variations.
• The RFF layer transforms input location coordinates using random basis functions: γ(l) = [cos(2πBl), sin(2πBl)]^T, where B is a matrix of randomly sampled spatial frequencies.
• Stack the RFF output with a multilayer perceptron (MLP) of depth Q=4 and width M=512, using ReLU activations, to learn complex nonlinear mappings.
• The final layer outputs 2A real numbers representing the real and imaginary parts of the predicted precoder vector w.
• Optimize the network using stochastic gradient descent (Adam) on a labeled dataset of 10,000 training channels and locations, minimizing the negative correlation between predicted precoder and actual channel.

Experimental results

Research questions

• RQ1 Can a deep learning model trained on user location and channel data generalize to both LOS and NLOS propagation conditions?
• RQ2 Does the use of random Fourier features (RFFs) significantly improve the ability of a neural network to learn high-frequency spatial variations in channel coefficients compared to standard MLPs?
• RQ3 How does the performance of the proposed RFF-based LBB method compare to classical LBB and standard deep learning baselines in terms of precoder-channel correlation?
• RQ4 What is the required density of training data (number of training channels per unit area) for the method to achieve high performance in realistic urban environments?
• RQ5 Can the proposed method achieve high spectral efficiency without relying on pilot symbols, by leveraging location information alone?

Key findings

• The proposed RFF-based deep learning method achieves a median correlation of 0.946 between the predicted precoder and the actual channel on a test set of 10,000 synthetic channels.
• This performance significantly outperforms classical LBB (median correlation: 0.708) and a standard MLP baseline (median correlation: 0.714), especially in NLOS regions.
• Spatial performance maps show that the proposed method provides high correlation (yellow) across both LOS and NLOS areas, while classical LBB fails in NLOS regions (blue areas).
• The method begins to perform well on test data when the number of training channels exceeds 3,000, corresponding to approximately one training sample per 7 m² in the 20,520 m² area.
• The use of RFFs enables the network to learn high-frequency spatial variations in channel coefficients, which classical MLPs cannot model due to spectral bias.
• The method is robust to the absence of LOS paths and generalizes well across diverse propagation environments, demonstrating its potential for real-world deployment in urban scenarios.