# Large System Analysis of Power Normalization Techniques in Massive MIMO

## TL;DR

This paper uses large system analysis to compare the effects of matrix and vector normalization on the performance of different precoding schemes in Massive MIMO systems, revealing their impact on sum rate and fairness.

## Contribution

It provides the first comprehensive large system analysis of power normalization techniques in Massive MIMO, considering realistic system impairments and multiple precoding schemes.

## Key findings

- ZF with VN maximizes sum rate
- MN provides fairness among users
- Interference and noise often limit performance more than pilot contamination

## Abstract

Linear precoding has been widely studied in the context of Massive multiple-input-multiple-output (MIMO) together with two common power normalization techniques, namely, matrix normalization (MN) and vector normalization (VN). Despite this, their effect on the performance of Massive MIMO systems has not been thoroughly studied yet. The aim of this paper is to fulfill this gap by using large system analysis. Considering a system model that accounts for channel estimation, pilot contamination, arbitrary pathloss, and per-user channel correlation, we compute tight approximations for the signal-to-interference-plus-noise ratio and the rate of each user equipment in the system while employing maximum ratio transmission (MRT), zero forcing (ZF), and regularized ZF precoding under both MN and VN techniques. Such approximations are used to analytically reveal how the choice of power normalization affects the performance of MRT and ZF under uncorrelated fading channels. It turns out that ZF with VN resembles a sum rate maximizer while it provides a notion of fairness under MN. Numerical results are used to validate the accuracy of the asymptotic analysis and to show that in Massive MIMO, non-coherent interference and noise, rather than pilot contamination, are often the major limiting factors of the considered precoding schemes.