Massive Synchrony in Distributed Antenna Systems

TL;DR

This work analyzes over-the-air phase calibration in distributed antenna systems for reciprocity-based coherent beamforming. It develops a graph-based, least-squares framework to estimate per-antenna phase sums $\boldsymbol{\phi}$ from pairwise measurements, and shows that it is optimal to compute a single global calibration, even as the network scales. The results reveal topology-dependent behavior: some topologies (e.g., line, ring, LIS) can cause the estimation variance $\mathsf{Var\{\hat{\phi}_n\}}$ to grow unbounded with $N$, while the complete graph yields massive synchrony with vanishing variance, implying different scalability limits. The findings guide design choices for large distributed antenna systems and quantify the trade-offs between global versus local calibration strategies for beamforming performance.

Abstract

Distributed antennas must be phase-calibrated (phase-synchronized) for certain operations, such as reciprocity-based joint coherent downlink beamforming, to work. We use rigorous signal processing tools to analyze the accuracy of calibration protocols that are based on over-the-air measurements between antennas, with a focus on scalability aspects for large systems. We show that (i) for some who-measures-on-whom topologies, the errors in the calibration process are unbounded when the network grows; and (ii) despite that conclusion, it is optimal -- irrespective of the topology -- to solve a single calibration problem for the entire system and use the result everywhere to support the beamforming. The analyses are exemplified by investigating specific topologies, including lines, rings, and two-dimensional surfaces.

Figures (7)

• Figure 1: Line topology, where antennas perform calibration measurements on their immediate neighbors. Two users A and B are also shown.
• Figure 2: Example of ${{\mathcal{G}}}$, ${{{\mathcal{G}}}_\Omega}$, $\Omega$, and $\bar{\Omega}$. Here $N=16$, $N_\Omega=6$, $M=25$ and $M_\Omega=7$.
• Figure 3: ${ \mathsf{Var} \{ \hat{\phi}_n \} }$ as function of antenna index $n$, for different total numbers of antennas, $N$, for the line (radio stripe) topology in Figure \ref{['fig:lrs']}, for ${{\boldsymbol{Q}} =10^{-4}\cdot{\boldsymbol{I}}}$. Note the logarithmic scale; the minimum occurs when $n=N/2$.
• Figure 4: Ring topology, where every antenna performs measurements on its two neighbors.
• Figure 5: Large-intelligent-surface topology, where each antenna performs measurements on its north-south, east-west, southeast-northwest and southwest-northeast closest neighbors.