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MIMO with Analogue 1-bit Phase Shifters: A Quantum Annealing Perspective

Ioannis Krikidis

TL;DR

This letter studies the analogue pre/post-coding vector design for a point-to-point multiple-input multiple-input multiple-output (MIMO) system with 1-bit phase shifters and proposes two classical computation heuristics.

Abstract

In this letter, we study the analogue pre/post-coding vector design for a point-to-point multiple-input multiple-output (MIMO) system with 1-bit phase shifters. Specifically, we focus on the signal-to-noise ratio (SNR) maximization problem which corresponds to a combinatorial NP-hard due to the binary phase resolution. Two classical computation heuristics are proposed i.e., i) an 1-bit real-valued approximation of the optimal digital designs, and ii) an alternating optimization where a Rayleigh quotient problem is solved at each iteration. An iterative quantum annealing (QA)-based heuristic is also investigated, which outperforms classical counterparts and achieves near-optimal performance while ensuring polynomial time complexity. Experimental results in a real-world D-WAVE QA device validate the efficiency of the proposed QA approach.

MIMO with Analogue 1-bit Phase Shifters: A Quantum Annealing Perspective

TL;DR

This letter studies the analogue pre/post-coding vector design for a point-to-point multiple-input multiple-input multiple-output (MIMO) system with 1-bit phase shifters and proposes two classical computation heuristics.

Abstract

In this letter, we study the analogue pre/post-coding vector design for a point-to-point multiple-input multiple-output (MIMO) system with 1-bit phase shifters. Specifically, we focus on the signal-to-noise ratio (SNR) maximization problem which corresponds to a combinatorial NP-hard due to the binary phase resolution. Two classical computation heuristics are proposed i.e., i) an 1-bit real-valued approximation of the optimal digital designs, and ii) an alternating optimization where a Rayleigh quotient problem is solved at each iteration. An iterative quantum annealing (QA)-based heuristic is also investigated, which outperforms classical counterparts and achieves near-optimal performance while ensuring polynomial time complexity. Experimental results in a real-world D-WAVE QA device validate the efficiency of the proposed QA approach.
Paper Structure (10 sections, 1 theorem, 12 equations, 4 figures, 1 table, 3 algorithms)

This paper contains 10 sections, 1 theorem, 12 equations, 4 figures, 1 table, 3 algorithms.

Table of Contents

  1. Introduction
  2. System model
  3. Exhaustive search (ES)- Benchmark
  4. Design $1$-bit analogue pre/post-coding vectors
  5. SVD-based design
  6. Rayleigh quotient-based design
  7. QA-based design
  8. QA background
  9. An iterative QA algorithm
  10. Evaluation

Key Result

Proposition 1

The $1$-bit analogue pre/post-coding vectors that minimize the MSE expressions in obj1 are given by where the operator $\textrm{sign}(\cdot)$ returns the sign of its argument.

Figures (4)

  • Figure 1: Point-to-point MIMO with $N_T$ transmit antennas, $N_R$ receive antennas and analogue $1$-bit pre/post-coding.
  • Figure 2: Average SNR performance for the proposed vector designs; [top] MIMO with $N_T=N_R=8$, [bottom] MIMO with $N_T=N_R=10$.
  • Figure 3: D-WAVE performance for a single iteration and channel realization with $N_T=N_R=8$; ES benchmark (dashed line). [top] SNR performance of the returned solutions in descending order, [bottom] Occurrence probability of the returned solutions.
  • Figure 4: D-WAVE performance for a single iteration and channel realization with $N_T=N_R=10$; ES benchmark (dashed line). [top] SNR performance of the returned solutions in descending order, [bottom] Occurrence probability of the returned solutions.

Theorems & Definitions (2)

  • Proposition 1
  • proof