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MIMO Precoding Exploiting Extra Degrees of Freedom (DoF) in the Wavenumber Domain

Yuanbin Chen, Xufeng Guo, Tianqi Mao, Qingqing Wu, Zhaocheng Wang, Chau Yuen

Abstract

In this paper, we propose an emerging wavenumber-domain precoding scheme to break the limitations of rank-1 channels that merely supports single-stream transmission, enabling simultaneous transmission of multiple data streams. The proposed wavenumber-domain precoding scheme also breaks the Rayleigh distance demarcation, regardless of the far-field and near-field contexts. Specifically, by characterizing the channel response as the superposition of a series of Fourier harmonics specified by different wavenumbers, the degree of freedom (DoF) is dependent on the cardinality of the wavenumber support, based on which the extra DoF is presented. This representation is applicable for both far-field and near-field. Different wavenumber atoms, determined within this support, constitute the codebook for MIMO precoding, in which each atom allows for the transmission of a data stream. Then, to maximize the capacity, it is required to select the wavenumbers associated with the optimal transmission direction, and optimize its power allocation. Finally, our simulation results demonstrate the significant superiority in comparison to the conventional spatial division schemes, with the potential of approaching the theoretical performance upper bound achieved by singular value decomposition (SVD).

MIMO Precoding Exploiting Extra Degrees of Freedom (DoF) in the Wavenumber Domain

Abstract

In this paper, we propose an emerging wavenumber-domain precoding scheme to break the limitations of rank-1 channels that merely supports single-stream transmission, enabling simultaneous transmission of multiple data streams. The proposed wavenumber-domain precoding scheme also breaks the Rayleigh distance demarcation, regardless of the far-field and near-field contexts. Specifically, by characterizing the channel response as the superposition of a series of Fourier harmonics specified by different wavenumbers, the degree of freedom (DoF) is dependent on the cardinality of the wavenumber support, based on which the extra DoF is presented. This representation is applicable for both far-field and near-field. Different wavenumber atoms, determined within this support, constitute the codebook for MIMO precoding, in which each atom allows for the transmission of a data stream. Then, to maximize the capacity, it is required to select the wavenumbers associated with the optimal transmission direction, and optimize its power allocation. Finally, our simulation results demonstrate the significant superiority in comparison to the conventional spatial division schemes, with the potential of approaching the theoretical performance upper bound achieved by singular value decomposition (SVD).
Paper Structure (11 sections, 16 equations, 2 figures)

This paper contains 11 sections, 16 equations, 2 figures.

Table of Contents

  1. Introduction
  2. System Model
  3. Wavenumber-Domain DoF Enhanced Precoding
  4. DoF Achieved by the SVD Approach
  5. Wavenumber-Domain Channel Characterization
  6. Capacity Enhanced by Extra DoF in the Wavenumber Domain
  7. Solution: Maximize the Capacity in (\ref{['cap']})
  8. Step 1: Wavenumber Selection
  9. Step 2: Power Allocation to the Selected Wavenumbers
  10. Simulation Results
  11. Conclusion

Figures (2)

  • Figure 1: Illustration of the wavenumber-domain precoding.
  • Figure 2: (a) Capacity versus $N_x=N_{R,x} = N_{T,x}$ with Tx-Rx distance of $1$ meters. (b) Capacity versus $N_x=N_{R,x} = N_{T,x}$ with Tx-Rx distance of $5$ meters. (c) Capacity versus distance.