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

Li Qiao, Yueqing Wang, Hanjun Jiang, Xinhua Liu, Yixuan Xing, Yongpeng Wu, Zhen Gao

TL;DR

A blind MD-AirComp+ scheme is proposed, which takes advantage of the channel hardening effect in massive multiple-input multiple-output (MIMO) systems and provides 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.

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.

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

TL;DR

A blind MD-AirComp+ scheme is proposed, which takes advantage of the channel hardening effect in massive multiple-input multiple-output (MIMO) systems and provides 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.

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.
Paper Structure (27 sections, 21 equations, 8 figures, 2 algorithms)

This paper contains 27 sections, 21 equations, 8 figures, 2 algorithms.

Table of Contents

  1. Introduction
  2. Literature Review
  3. Analog AirComp
  4. Digital AirComp
  5. Random Access and AirComp
  6. Contributions
  7. System Model
  8. Remark 1.
  9. MD-AirComp Overview
  10. Stochastic Uniform Quantizer.
  11. Proposed MD-AirComp+ Scheme
  12. Blind Channel Mitigation
  13. LASSO-Based Sparse Signal Detection
  14. Communication and Accuracy Trade-off Analysis
  15. Step 1 — quantization error
  16. ...and 12 more sections

Figures (8)

  • Figure 1: Illustration of a typical digital AirComp scenario.
  • Figure 2: Illustration of the proposed MD-AirComp+ scheme.
  • Figure 3: Illustration of the channel hardening effect in massive MIMO system.
  • Figure 4: Convergence and MSE comparison: ISTA versus LISTA and their improved variants
  • Figure 5: (a) MSE versus the number of quantization levels $Q$, with fixed $L$ and SNR = 20 dB. (b) Optimal number of quantization levels $Q^*$ versus preamble length $L$.
  • ...and 3 more figures