An Analytical and Experimental Study of Distributed Uplink Beamforming in the Presence of Carrier Frequency Offsets

TL;DR

This work addresses the challenge of distributed uplink beamforming under residual carrier frequency offsets (CFO) across distributed APs. It develops an analytical framework to derive a conditional SINR that accounts for CFO statistics via moments of the CFO-induced complex gain, and validates the theory with Monte Carlo simulations and extensive experiments on the RENEW massive MIMO testbed. The study finds that CFO-induced phase rotation and ICI degrade SINR and EVM, with degradation increasing for more users and longer uplink slots, yet the CFO-aware model remains accurate in practical CFO ranges. It also provides a large, publicly available dataset of uplink pilots and data to enable future research on CFO compensation and distributed beamforming system design.

Abstract

Realizing distributed multi-user beamforming (D-MUBF) in time division duplex (TDD)-based multi-user MIMO (MU-MIMO) systems faces significant challenges. One of the most fundamental challenges is achieving accurate over-the-air (OTA) timing and frequency synchronization among distributed access points (APs), particularly due to residual frequency offsets caused by local oscillator (LO) drifts. Despite decades of research on synchronization for MU-MIMO, there are only a few experimental studies that evaluate D-MUBF techniques under imperfect frequency synchronization among distributed antennas. This paper presents an analytical and experimental assessment of D-MUBF methods in the presence of frequency synchronization errors. We provide closed-form expressions for signal-to-interference-plus-noise ratio (SINR) as a function of channel characteristics and statistical properties of carrier frequency offset (CFO) among AP antennas. In addition, through experimental evaluations conducted with the RENEW massive MIMO testbed, we collected comprehensive datasets across various experimental scenarios. These datasets comprise uplink pilot samples for channel and CFO estimation, in addition to uplink multi-user data intended for analyzing D-MUBF techniques. By examining these datasets, we assess the performance of D-MUBF in the presence of CFO and compare the analytical predictions with empirical measurements. Furthermore, we make the datasets publicly available and provide insights on utilizing them for future research endeavors.

Figures (10)

• Figure 1: Illustration of the reference network architecture, including two regions each with multiple dAPs connected to a central server (CS).
• Figure 2: The conditional SINR expression in \ref{['eq:sinr_closed_form']} versus STD of the normalized CFO in \ref{['eq:eps_def']}, distributed as a (a) normal and (b) uniform random variable. There are $N=16$ antennas per dAP and $K=2$ users, and CBF is applied.
• Figure 3: (a) Simulated SINR values (Sim) and analytical SINR estimates based on \ref{['eq:sinr_closed_form']} (Anlt) for conjugate beamforming (CBF). (b) Corresponding EVM results (in percentage) obtained from the same simulation setup.
• Figure 4: (a) Simulated and analytical SINR and (b) simulated EVM results for $\beta = \{1\%, 2\%\}$ values, as functions of the OFDM symbol index $n$.
• Figure 5: Block diagram of the proposed framework for evaluating the impact of CFO on beamforming performance. Blue arrows indicate comparison points.