Large System Analysis of the Energy Consumption Distribution in Multi-User MIMO Systems with Mobility

TL;DR

This paper analyzes the energy consumption distribution in large multi-user MIMO systems with mobile users, providing formulas for power, energy fluctuations, and practical implications for energy management and cell design.

Contribution

It introduces a large system analysis framework for energy consumption in multi-user MIMO with mobility, including closed-form expressions and a CLT for fluctuations.

Findings

Asymptotic formulas for transmit power and energy consumption.

Central limit theorem for energy fluctuations.

Guidelines for cell radius and energy outage probability.

Abstract

In this work, we consider the downlink of a single-cell multi-user MIMO system in which the base station (BS) makes use of $N$ antennas to communicate with $K$ single-antenna user equipments (UEs). The UEs move around in the cell according to a random walk mobility model. We aim at determining the energy consumption distribution when different linear precoding techniques are used at the BS to guarantee target rates within a finite time interval $T$. The analysis is conducted in the asymptotic regime where $N$ and $K$ grow large with fixed ratio under the assumption of perfect channel state information (CSI). Both recent and standard results from large system analysis are used to provide concise formulae for the asymptotic transmit powers and beamforming vectors for all considered schemes. These results are eventually used to provide a deterministic approximation of the energy consumption and to study its fluctuations around this value in the form of a central limit theorem. Closed-form expressions for the asymptotic means and variances are given. Numerical results are used to validate the accuracy of the theoretical analysis and to make comparisons. We show how the results can be used to approximate the probability that a battery-powered BS runs out of energy and also to design the cell radius for minimizing the energy consumption per unit area. The imperfect CSI case is also briefly considered.