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DNN based Two-stage Compensation Algorithm for THz Hybrid Beamforming with imperfect Hardware

Wenqi Zhao, Chong Han, Ho-Jin Song, Emil Björnson

Abstract

Terahertz (THz) communication is envisioned as a key technology for 6G and beyond wireless systems owing to its multi-GHz bandwidth. To maintain the same aperture area and the same link budget as the lower frequencies, ultra-massive multi-input and multi-output (UM-MIMO) with hybrid beamforming is promising. Nevertheless, the hardware imperfections particularly at THz frequencies, can degrade spectral efficiency and lead to a high symbol error rate (SER), which is often overlooked yet imperative to address in practical THz communication systems. In this paper, the hybrid beamforming is investigated for THz UM-MIMO systems accounting for comprehensive hardware imperfections, including DAC and ADC quantization errors, in-phase and quadrature imbalance (IQ imbalance), phase noise, amplitude and phase error of imperfect phase shifters and power amplifier (PA) nonlinearity. Then, a two-stage hardware imperfection compensation algorithm is proposed. A deep neural network (DNN) is developed in the first stage to represent the combined hardware imperfections, while in the second stage, the digital precoder in the transmitter (Tx) or the combiner in the receiver (Rx) is designed using NN to effectively compensate for these imperfections. Furthermore, to balance the performance and network complexity, three slimming methods including pruning, parameter sharing, and removing parts of the network are proposed and combined to slim the DNN in the first stage. Numerical results show that the Tx compensation can perform better than the Rx compensation. Additionally, using the combined slimming methods can reduce parameters by 97.2% and running time by 39.2% while maintaining nearly the same performance in both uncoded and coded systems.

DNN based Two-stage Compensation Algorithm for THz Hybrid Beamforming with imperfect Hardware

Abstract

Terahertz (THz) communication is envisioned as a key technology for 6G and beyond wireless systems owing to its multi-GHz bandwidth. To maintain the same aperture area and the same link budget as the lower frequencies, ultra-massive multi-input and multi-output (UM-MIMO) with hybrid beamforming is promising. Nevertheless, the hardware imperfections particularly at THz frequencies, can degrade spectral efficiency and lead to a high symbol error rate (SER), which is often overlooked yet imperative to address in practical THz communication systems. In this paper, the hybrid beamforming is investigated for THz UM-MIMO systems accounting for comprehensive hardware imperfections, including DAC and ADC quantization errors, in-phase and quadrature imbalance (IQ imbalance), phase noise, amplitude and phase error of imperfect phase shifters and power amplifier (PA) nonlinearity. Then, a two-stage hardware imperfection compensation algorithm is proposed. A deep neural network (DNN) is developed in the first stage to represent the combined hardware imperfections, while in the second stage, the digital precoder in the transmitter (Tx) or the combiner in the receiver (Rx) is designed using NN to effectively compensate for these imperfections. Furthermore, to balance the performance and network complexity, three slimming methods including pruning, parameter sharing, and removing parts of the network are proposed and combined to slim the DNN in the first stage. Numerical results show that the Tx compensation can perform better than the Rx compensation. Additionally, using the combined slimming methods can reduce parameters by 97.2% and running time by 39.2% while maintaining nearly the same performance in both uncoded and coded systems.

Paper Structure

This paper contains 28 sections, 54 equations, 10 figures, 3 tables.

Table of Contents

  1. Introduction
  2. Related Work
  3. Contributions
  4. System Model
  5. Hardware Imperfection Model
  6. Imperfect DAC and ADC Model
  7. IQ Imbalance Model
  8. Phase Noise Model
  9. Imperfect Phase Shifter Model
  10. Nonlinear PA Model
  11. Signal Model with All Imperfect Hardware
  12. Compensation Problem Formulation
  13. Two-stage Hardware Imperfection Compensation Algorithm With DNN
  14. Stage 1: DNN for Hardware Imperfection Representation
  15. Stage 2: Compensation Scheme with NN
  16. ...and 13 more sections

Figures (10)

  • Figure 1: THz UM-MIMO system with imperfect hardware.
  • Figure 2: Constellations for different situations. (The red arrows indicate the distortion in the constellation points, illustrating the effects of expansion, displacement, and rotation caused by hardware imperfections.)
  • Figure 3: The structure of the proposed DNN in the first stage.
  • Figure 4: The structure of the proposed NN in the second stage.
  • Figure 5: Three methods of network slimming.
  • ...and 5 more figures