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Analog Computing for Signal Processing and Communications -- Part II: Toward Gigantic MIMO Beamforming

Matteo Nerini, Bruno Clerckx

TL;DR

<3-5 sentence high-level summary> This paper addresses the challenge of hardware and computational complexity in gigantic MIMO beamforming by introducing MiLAC, a microwave linear analog computer that performs key linear operations entirely in the analog domain. It demonstrates how MiLAC can implement LMMSE-estimator special cases and a family of MiLAC-aided beamforming strategies that match digital performance while dramatically reducing RF chains, ADC/DAC resolution, and per-symbol computation. The work shows significant computational savings (e.g., up to 1.5×10^4 to 4.0×10^7× reductions for various operations) and validates robustness to impairments, suggesting a viable path to scalable 6G-era transceivers. Overall, MiLAC-aided beamforming emerges as a game-changing approach for massively scalable, low-complexity wireless transceiver architectures.

Abstract

Analog-domain operations offer a promising solution to accelerating signal processing and enabling future multiple-input multiple-output (MIMO) communications with thousands of antennas. In Part I of this paper, we have introduced a microwave linear analog computer (MiLAC) as an analog computer that processes microwave signals linearly, demonstrating its potential to reduce the computational complexity of specific signal processing tasks. In Part II of this paper, we extend these benefits to wireless communications, showcasing how MiLAC enables gigantic MIMO beamforming entirely in the analog domain. MiLAC-aided beamforming enables the maximum flexibility and performance of digital beamforming, while significantly reducing hardware costs by minimizing the number of radio-frequency (RF) chains and only relying on low-resolution analog-to-digital converters (ADCs) and digital-to-analog converters (DACs). In addition, it eliminates per-symbol operations by completely avoiding digital-domain processing and remarkably reduces the computational complexity of zero-forcing (ZF), which scales quadratically with the number of antennas instead of cubically. It also processes signals with fixed matrices, e.g., the discrete Fourier transform (DFT), directly in the analog domain. Numerical results show that it can perform ZF and DFT with a computational complexity reduction of up to $1.5\times 10^4$ and $4.0\times 10^7$ times, respectively, compared to digital beamforming.

Analog Computing for Signal Processing and Communications -- Part II: Toward Gigantic MIMO Beamforming

TL;DR

<3-5 sentence high-level summary> This paper addresses the challenge of hardware and computational complexity in gigantic MIMO beamforming by introducing MiLAC, a microwave linear analog computer that performs key linear operations entirely in the analog domain. It demonstrates how MiLAC can implement LMMSE-estimator special cases and a family of MiLAC-aided beamforming strategies that match digital performance while dramatically reducing RF chains, ADC/DAC resolution, and per-symbol computation. The work shows significant computational savings (e.g., up to 1.5×10^4 to 4.0×10^7× reductions for various operations) and validates robustness to impairments, suggesting a viable path to scalable 6G-era transceivers. Overall, MiLAC-aided beamforming emerges as a game-changing approach for massively scalable, low-complexity wireless transceiver architectures.

Abstract

Analog-domain operations offer a promising solution to accelerating signal processing and enabling future multiple-input multiple-output (MIMO) communications with thousands of antennas. In Part I of this paper, we have introduced a microwave linear analog computer (MiLAC) as an analog computer that processes microwave signals linearly, demonstrating its potential to reduce the computational complexity of specific signal processing tasks. In Part II of this paper, we extend these benefits to wireless communications, showcasing how MiLAC enables gigantic MIMO beamforming entirely in the analog domain. MiLAC-aided beamforming enables the maximum flexibility and performance of digital beamforming, while significantly reducing hardware costs by minimizing the number of radio-frequency (RF) chains and only relying on low-resolution analog-to-digital converters (ADCs) and digital-to-analog converters (DACs). In addition, it eliminates per-symbol operations by completely avoiding digital-domain processing and remarkably reduces the computational complexity of zero-forcing (ZF), which scales quadratically with the number of antennas instead of cubically. It also processes signals with fixed matrices, e.g., the discrete Fourier transform (DFT), directly in the analog domain. Numerical results show that it can perform ZF and DFT with a computational complexity reduction of up to and times, respectively, compared to digital beamforming.

Paper Structure

This paper contains 34 sections, 19 equations, 10 figures, 4 tables.

Table of Contents

  1. Introduction
  2. Microwave Linear Analog Computer
  3. Analog Computing for the Special Cases of the LMMSE Estimator
  4. LMMSE Estimator for Linear Observation Processes
  5. Special Cases of the LMMSE Estimator for Linear Observation Processes
  6. Generalized Least Squares
  7. Generalized Matched Filtering
  8. Regularized Least Squares
  9. Ordinary Least Squares
  10. Ordinary Matched Filtering
  11. Computing the Special Cases of the LMMSE Estimator with a MiLAC
  12. A Novel Beamforming Strategy: MiLAC-Aided Beamforming
  13. Arbitrary Beamforming
  14. LMMSE-Inspired Beamforming at the Transmitter: R-ZFBF, ZFBF, and MBF Transmitters
  15. LMMSE-Inspired Beamforming at the Receiver: MMSE, ZF, and MF Receivers
  16. ...and 19 more sections

Figures (10)

  • Figure 1: Representation of a $P$-port MiLAC with input on $N$ ports, where $P=N+M$.
  • Figure 2: MiLAC-aided beamforming at the transmitter, performing $\mathbf{x}=\mathbf{W}\mathbf{s}$ in the analog domain, where $\mathbf{s}$ is the symbol vector and $\mathbf{W}$ is an arbitrary precoding matrix.
  • Figure 3: MiLAC-aided beamforming at the receiver, performing $\mathbf{z}=\mathbf{G}\mathbf{y}$ in the analog domain, where $\mathbf{y}$ is the received signal and $\mathbf{G}$ is an arbitrary combining matrix.
  • Figure 4: (a) Digital, (b) analog, (c) hybrid, (d) RIS-aided, (e) SIM-aided, and (f) -aided beamforming at the transmitter.
  • Figure 5: Sum rate in a $4\times4$ multi-user MISO system, with digital and -aided beamforming at the transmitter.
  • ...and 5 more figures

Theorems & Definitions (4)

  • Remark 1
  • Remark 2
  • Remark 3
  • Remark 4