# Performance Analysis of Joint Antenna Selection and Precoding Methods in Multi-user Massive MISO

arXiv: https://arxiv.org/abs/2409.04924 · HTML: https://mlsanity.com/paper/2409.04924/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 7 Sep 2024.

## Built on by (most cited first, 1 of 1)

- [Asymptotic Analysis of One-bit Quantized Box-Constrained Precoding in Large-Scale Multi-User Systems](https://mlsanity.com/paper/2502.02953/) (2025)

## Abstract (arXiv)

This paper presents a performance analysis of two distinct techniques for antenna selection and precoding in downlink multi-user massive multiple-input single-output systems with limited dynamic range power amplifiers. Both techniques are derived from the original formulation of the regularized-zero forcing precoder, designed as the solution to minimizing a regularized distortion. Based on this, the first technique, called the ℓ1-norm precoder, adopts an ℓ1-norm regularization term to encourage sparse solutions, thereby enabling antenna selection. The second technique, termed the thresholded ℓ1-norm precoder, involves post-processing the precoder solution obtained from the first method by applying an entry-wise thresholding operation. This work conducts a precise performance analysis to compare these two techniques. The analysis leverages the Gaussian min-max theorem which is effective for examining the asymptotic behavior of optimization problems without explicit solutions. While the analysis of the ℓ1-norm precoder follows the conventional Gaussian min-max theorem framework, understanding the thresholded ℓ1-norm precoder is more complex due to the non-linear behavior introduced by the thresholding operation. To address this complexity, we develop a novel Gaussian min-max theorem tailored to these scenarios. We provide precise asymptotic behavior analysis of the precoders, focusing on metrics such as received signal-to-noise and distortion ratio and bit error rate. Our analysis demonstrates that the thresholded ℓ1-norm precoder can offer superior performance when the threshold parameter is carefully selected. Simulations confirm that the asymptotic results are accurate for systems equipped with hundreds of antennas at the base station, serving dozens of user terminals.