MD-AirComp+: Adaptive Quantization for Blind Massive Digital Over-the-Air Computation

TL;DR

This paper introduces MD-AirComp+ which enhances over-the-air computation in massive MIMO systems by using adaptive quantization and blind detection, improving robustness and reducing complexity without channel pre-equalization.

Contribution

It proposes a blind MD-AirComp+ scheme leveraging channel hardening, with an optimal quantization strategy and a low-complexity deep unfolding detection algorithm.

Findings

Effective in federated learning scenarios

Optimal quantization improves accuracy

Low-complexity detection reduces computational load

Abstract

Recent research has shown that unsourced massive access (UMA) is naturally well-suited for over-the-air computation (AirComp), as it does not require knowledge of each individual signal, as demonstrated by the massive digital AirComp (MD-AirComp) scheme proposed in prior work. The MD-AirComp scheme has proven effective in federated edge learning and is highly compatible with current digital wireless networks. However, it depends on channel pre-equalization, which may amplify computation errors in the presence of channel estimation inaccuracies, thus limiting its practical use. In this paper, we propose a blind MD-AirComp+ scheme, which takes advantage of the channel hardening effect in massive multiple-input multiple-output (MIMO) systems. We provide an upper bound on the computation mean square error, analyze the trade-off between computation accuracy and communication overhead, and determine the optimal quantization level. Additionally, we introduce a deep unfolding algorithm to reduce the computational complexity of solving the underdetermined detection problem formulated as a least absolute shrinkage and selection operator optimization problem. Simulation results confirm the effectiveness of the proposed MD-AirComp+ framework, the optimal quantization selection strategy, and the low-complexity detection algorithm.