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An Efficient Interference-Aware Constrained Massive MIMO Beamforming for mm-Wave JSDM

Murat Bayraktar, Gokhan Muzaffer Guvensen

TL;DR

Simulation results verify the superiority of the proposed interference-aware constrained design over existing approaches in terms of beampattern, spectral efficiency, outage capacity, bit-error rate (BER), and channel estimation accuracy.

Abstract

Low-complexity beamformer design with practical constraints is an attractive research area for hybrid analog/digital systems in mm-wave massive multiple-input multiple-output (MIMO). This paper investigates interference-aware pre-beamformer (analog beamformer) design for joint spatial division and multiplexing (JSDM) which is a user-grouping based two-stage beamforming method. Single-carrier frequency domain equalization (SC-FDE) is employed in uplink frequency-selective channels. First, unconstrained slowly changing statistical analog beamformer of each group, namely, generalized eigenbeamformer (GEB) which has strong interference suppression capability is designed where the mutual information in reduced dimension is maximized. Then, constant-modulus constrained approximations of unconstrained beamformer are obtained by utilizing alternating minimization algorithms for fully connected arrays and fixed subarrays. In addition, a dynamic subarray algorithm is proposed where the connections between radio frequency (RF) chains and antennas are changed with changing channel statistics. Convergence of the proposed alternating minimization-based algorithms are provided along with their complexity analysis. It is observed that additional complexity of proposed algorithms is insignificant for the overall system design. Although most of the interference is suppressed with the help of proposed constrained beamformers, there may be some residual interference after the analog beamforming stage. Therefore, linear minimum mean square error (LMMSE) type digital beamformers, which take the residual interference in reduced dimension into account, are proposed instead of zero-forcing (ZF) type. Simulation results verify the superiority of the proposed interference-aware constrained design over existing approaches in terms of beampattern, spectral efficiency, outage capacity and channel estimation accuracy.

An Efficient Interference-Aware Constrained Massive MIMO Beamforming for mm-Wave JSDM

TL;DR

Simulation results verify the superiority of the proposed interference-aware constrained design over existing approaches in terms of beampattern, spectral efficiency, outage capacity, bit-error rate (BER), and channel estimation accuracy.

Abstract

Low-complexity beamformer design with practical constraints is an attractive research area for hybrid analog/digital systems in mm-wave massive multiple-input multiple-output (MIMO). This paper investigates interference-aware pre-beamformer (analog beamformer) design for joint spatial division and multiplexing (JSDM) which is a user-grouping based two-stage beamforming method. Single-carrier frequency domain equalization (SC-FDE) is employed in uplink frequency-selective channels. First, unconstrained slowly changing statistical analog beamformer of each group, namely, generalized eigenbeamformer (GEB) which has strong interference suppression capability is designed where the mutual information in reduced dimension is maximized. Then, constant-modulus constrained approximations of unconstrained beamformer are obtained by utilizing alternating minimization algorithms for fully connected arrays and fixed subarrays. In addition, a dynamic subarray algorithm is proposed where the connections between radio frequency (RF) chains and antennas are changed with changing channel statistics. Convergence of the proposed alternating minimization-based algorithms are provided along with their complexity analysis. It is observed that additional complexity of proposed algorithms is insignificant for the overall system design. Although most of the interference is suppressed with the help of proposed constrained beamformers, there may be some residual interference after the analog beamforming stage. Therefore, linear minimum mean square error (LMMSE) type digital beamformers, which take the residual interference in reduced dimension into account, are proposed instead of zero-forcing (ZF) type. Simulation results verify the superiority of the proposed interference-aware constrained design over existing approaches in terms of beampattern, spectral efficiency, outage capacity and channel estimation accuracy.

Paper Structure

This paper contains 33 sections, 1 theorem, 60 equations, 9 figures, 2 tables, 4 algorithms.

Table of Contents

  1. Introduction
  2. Related Work
  3. Contributions
  4. System Model
  5. Wideband SC-FDE Uplink Transmission
  6. Two-Stage Beamforming Concept
  7. Unconstrained Hybrid Massive MIMO Beamformer Design
  8. Optimal Analog Beamformer Design: Generalized Eigenbeamformer (GEB)
  9. Digital Beamformer Design
  10. ZF Type Digital Beamformer
  11. LMMSE Type Digital Beamformer
  12. Constrained Analog Beamformer Design
  13. Fully Connected Array
  14. DFT Beamformer
  15. Phase Extraction (PE)
  16. ...and 18 more sections

Key Result

Lemma 1

Using $\textbf{S}^{(g)} \textbf{A}$ instead of $\textbf{S}^{(g)}$ does not change the cost function where $\textbf{A} \in \mathbb{C}^{D_g \times D_g}$ is any invertible matrix.

Figures (9)

  • Figure 1: Block diagram of the overall system design with constrained analog beamformers
  • Figure 2: Angle-delay map of groups with $\phi = 15^\circ$
  • Figure 3: Beampatterns of Group-1 for fully connected array structures with $\phi = 10^\circ$, $D_1 = 4$ and $E_s^{(g)} = 40$ dB for $\forall g$
  • Figure 4: Average spectral efficiency of Group-1 vs. $E_s^{(1)}$ for fully connected array structures with $E_s^{(g')} = 40$ dB for $g' \neq 1$
  • Figure 5: CDF of spectral efficiency of Group-1 for fully connected array structures with $E_s^{(g)} = 40$ dB for $\forall g$
  • ...and 4 more figures

Theorems & Definitions (4)

  • Lemma 1
  • Remark 1
  • Remark 2
  • Remark 3