# Downlink Training in Cell-Free Massive MIMO: A Blessing in Disguise

arXiv: https://arxiv.org/abs/1903.10046 · HTML: https://mlsanity.com/paper/1903.10046/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 24 Mar 2019.

## Built on by (most cited first, 2 of 2)

- [Self-Organizing mmWave MIMO Cell-Free Networks With Hybrid Beamforming: A Hierarchical DRL-Based Design](https://mlsanity.com/paper/2103.11823/) (2021)
- [Base Station Deployment under EMF constrain by Deep Reinforcement learning](https://mlsanity.com/paper/2601.02385/) (2025)

## Abstract (arXiv)

Cell-free Massive MIMO (multiple-input multiple-output) refers to a distributed Massive MIMO system where all the access points (APs) cooperate to coherently serve all the user equipments (UEs), suppress inter-cell interference and mitigate the multiuser interference. Recent works demonstrated that, unlike co-located Massive MIMO, the textitchannel hardening is, in general, less pronounced in cell-free Massive MIMO, thus there is much to benefit from estimating the downlink channel. In this study, we investigate the gain introduced by the downlink beamforming training, extending the previously proposed analysis to non-orthogonal uplink and downlink pilots. Assuming single-antenna APs, conjugate beamforming and independent Rayleigh fading channel, we derive a closed-form expression for the per-user achievable downlink rate that addresses channel estimation errors and pilot contamination both at the AP and UE side. The performance evaluation includes max-min fairness power control, greedy pilot assignment methods, and a comparison between achievable rates obtained from different capacity-bounding techniques. Numerical results show that downlink beamforming training, although increases pilot overhead and introduces additional pilot contamination, improves significantly the achievable downlink rate. Even for large number of APs, it is not fully efficient for the UE relying on the statistical channel state information for data decoding.