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Downlink Pilots are Essential for Cell-Free Massive MIMO with Multi-Antenna Users

Eren Berk Kama, Junbeom Kim, Emil Björnson

TL;DR

This work addresses the downlink performance of cell-free massive MIMO when users have multiple antennas, where the conventional hardening bound with no downlink CSI underestimates achievable SE. It introduces a pilot-based downlink channel estimation scheme using LMMSE on the effective downlink channel and employs ZF combining at the receiver to mitigate non-Gaussian residuals. The authors derive SE expressions for no-CSI, perfect-CSI, and pilot-estimated CSI cases and show, through simulations, that downlink pilots substantially boost SE for multi-antenna users, approaching the genie-aided bound as the AP count or power allocation improves. The results demonstrate the practical value of downlink CSI acquisition in multi-antenna user scenarios and quantify how SE scales with the numbers of APs, users, and antennas.

Abstract

We consider a cell-free massive MIMO system with multiple antennas on the users and access points. In previous works, the downlink spectral efficiency (SE) has been evaluated using the hardening bound that requires no downlink pilots. This approach works well when having single-antenna users. In this paper, we show that much higher SEs can be achieved if downlink pilots are sent since the effective channel matrix does not harden when having multi-antenna users. We propose a pilot-based downlink estimation scheme and derive a new SE expression that utilizes zero-forcing combining. We show numerically how the number of users and user antennas affects the SE.

Downlink Pilots are Essential for Cell-Free Massive MIMO with Multi-Antenna Users

TL;DR

This work addresses the downlink performance of cell-free massive MIMO when users have multiple antennas, where the conventional hardening bound with no downlink CSI underestimates achievable SE. It introduces a pilot-based downlink channel estimation scheme using LMMSE on the effective downlink channel and employs ZF combining at the receiver to mitigate non-Gaussian residuals. The authors derive SE expressions for no-CSI, perfect-CSI, and pilot-estimated CSI cases and show, through simulations, that downlink pilots substantially boost SE for multi-antenna users, approaching the genie-aided bound as the AP count or power allocation improves. The results demonstrate the practical value of downlink CSI acquisition in multi-antenna user scenarios and quantify how SE scales with the numbers of APs, users, and antennas.

Abstract

We consider a cell-free massive MIMO system with multiple antennas on the users and access points. In previous works, the downlink spectral efficiency (SE) has been evaluated using the hardening bound that requires no downlink pilots. This approach works well when having single-antenna users. In this paper, we show that much higher SEs can be achieved if downlink pilots are sent since the effective channel matrix does not harden when having multi-antenna users. We propose a pilot-based downlink estimation scheme and derive a new SE expression that utilizes zero-forcing combining. We show numerically how the number of users and user antennas affects the SE.
Paper Structure (12 sections, 3 theorems, 27 equations, 3 figures)

This paper contains 12 sections, 3 theorems, 27 equations, 3 figures.

Table of Contents

  1. Introduction
  2. System Model
  3. Uplink Channel Estimation
  4. Downlink Data Transmission
  5. Hardening Bound Without CSI at the Receiver
  6. Capacity Bound with Perfect CSI at the Receiver
  7. Estimation of the Effective Downlink Channel
  8. Capacity Bound with Estimate Channel at the Receiver
  9. Numerical Results
  10. Conclusions
  11. Appendix
  12. Proof of Theorem \ref{['th:mainresult']}

Key Result

Lemma 1

In the absence of CSI, an achievable SE at user $k$ is where $| \cdot |$ denotes the determinant.

Figures (3)

  • Figure 1: Achievable per user SE as a function of the number of AP antennas with $M=1$.
  • Figure 2: Achievable per user SE as a function of the number of AP antennas with $M=2$.
  • Figure 3: Achievable per user SE as a function of the number of users and user antennas.

Theorems & Definitions (3)

  • Lemma 1
  • Lemma 2
  • Theorem 1