# Unsupervised Neural Beamforming for Uplink MU-SIMO in 3GPP-Compliant Wireless Channels

## TL;DR

This paper introduces two deep learning-based beamforming models for wireless communication, comparing their performance and computational complexity in realistic and simplified scenarios.

## Contribution

The paper proposes and evaluates two unsupervised neural beamforming architectures for 3GPP-compliant wireless systems.

## Key findings

- Transformer-based NNBF outperforms in realistic conditions but has higher computational complexity.
- Simple NNBF performs better than traditional methods with lower complexity under simplified assumptions.
- The study provides a FLOPs-based complexity analysis of the proposed models and traditional beamforming techniques.

## Abstract

Beamforming is highly significant for the physical layer of wireless communication systems, for multi-antenna systems such as multiple input multiple output (MIMO) and massive MIMO, since it improves spectral efficiency and reduces interference. Traditional linear beamforming methods such as zero-forcing beamforming (ZFBF) and minimum mean square error (MMSE) beamforming provide closed-form solutions. Yet, their performance drops when they face non-ideal conditions such as imperfect channel state information (CSI), dynamic propagation environment, or high-dimensional system configurations, primarily due to static assumptions and computational limitations. These limitations have led to the rise of deep learning-based beamforming, where data-driven models derive beamforming solutions directly from CSI. By leveraging the representational capabilities of cutting-edge deep learning architectures, along with the increasing availability of data and computational resources, deep learning presents an adaptive and potentially scalable alternative to traditional methodologies. In this work, we unify and systematically compare our two unsupervised learning architectures for uplink receive beamforming: a simple neural network beamforming (NNBF) model, composed of convolutional and fully connected layers, and a transformer-based NNBF model that integrates grouped convolutions for feature extraction and transformer blocks to capture long-range channel dependencies. They are evaluated in a common multi-user single input multiple output (MU-SIMO) system model to maximize sum-rate across single-antenna user equipments (UEs) under 3GPP-compliant channel models, namely TDL-A and UMa. Furthermore, we present a FLOPs-based asymptotic computational complexity analysis for the NNBF architectures alongside baseline methods, namely ZFBF and MMSE beamforming, explicitly characterizing inference-time scaling behavior. Experiments for the simple NNBF are performed under simplified assumptions such as stationary UEs and perfect CSI across varying antenna configurations in the TDL-A channel. On the other hand, transformer-based NNBF is evaluated in more realistic conditions, including urban macro environments with imperfect CSI, diverse UE mobilities, coding rates, and modulation schemes. Results show that the transformer-based NNBF achieves superior performance under realistic conditions at the cost of increased computational complexity, while the simple NNBF presents comparable or better performance than baseline methods with significantly lower complexity under simplified assumptions.