Logo
ScienceStack
Table of Contents
Fetching ...
Sign In

Hybrid Precoder Design for Angle-of-Departure Estimation with Limited-Resolution Phase Shifters

Huiping Huang, Musa Furkan Keskin, Henk Wymeersch, Xuesong Cai, Linlong Wu, Johan Thunberg, Fredrik Tufvesson

TL;DR

This paper investigates the hybrid precoder design problem for angle-of-departure (AoD) estimation, and proposes a two-step strategy where the fully digital precoder is obtained that minimizes the angle error bound and the quantization error upper bound is derived.

Abstract

Hybrid analog-digital beamforming stands out as a key enabler for future communication systems with a massive number of antennas. In this paper, we investigate the hybrid precoder design problem for angle-of-departure (AoD) estimation, where we take into account the practical constraint on the limited resolution of phase shifters. Our goal is to design a radio-frequency (RF) precoder and a base-band (BB) precoder to estimate AoD of the user with a high accuracy. To this end, we propose a two-step strategy where we first obtain the fully digital precoder that minimizes the angle error bound, and then the resulting digital precoder is decomposed into an RF precoder and a BB precoder, based on the alternating optimization and the alternating direction method of multipliers. Besides, we derive the quantization error upper bound and analyse the convergence behavior of the proposed algorithm. Numerical results demonstrate the superior performance of the proposed method over state-of-the-art baselines.

Hybrid Precoder Design for Angle-of-Departure Estimation with Limited-Resolution Phase Shifters

TL;DR

This paper investigates the hybrid precoder design problem for angle-of-departure (AoD) estimation, and proposes a two-step strategy where the fully digital precoder is obtained that minimizes the angle error bound and the quantization error upper bound is derived.

Abstract

Hybrid analog-digital beamforming stands out as a key enabler for future communication systems with a massive number of antennas. In this paper, we investigate the hybrid precoder design problem for angle-of-departure (AoD) estimation, where we take into account the practical constraint on the limited resolution of phase shifters. Our goal is to design a radio-frequency (RF) precoder and a base-band (BB) precoder to estimate AoD of the user with a high accuracy. To this end, we propose a two-step strategy where we first obtain the fully digital precoder that minimizes the angle error bound, and then the resulting digital precoder is decomposed into an RF precoder and a BB precoder, based on the alternating optimization and the alternating direction method of multipliers. Besides, we derive the quantization error upper bound and analyse the convergence behavior of the proposed algorithm. Numerical results demonstrate the superior performance of the proposed method over state-of-the-art baselines.
Paper Structure (31 sections, 4 theorems, 49 equations, 13 figures, 4 tables, 1 algorithm)

This paper contains 31 sections, 4 theorems, 49 equations, 13 figures, 4 tables, 1 algorithm.

Table of Contents

  1. Introduction
  2. System Model
  3. Proposed Method
  4. CRB-Based Performance Metric
  5. Problem Formulation for Optimal Precoder Design
  6. Two-Step Strategy for Solving Problem \ref{['OptPrecoder_problem']}
  7. Computational Complexity Analysis
  8. Analysis of Error Bounds and Convergence
  9. Analysis of Quantization Error Bound
  10. Convergence Analysis
  11. Numerical Results
  12. Scenario, Performance Metric, and Benchmark
  13. Results and Discussion of Scenario I
  14. DecpErr as a Function of $N_{\text{RF}}$
  15. DecpErr as a Function of $B$
  16. ...and 16 more sections

Key Result

Theorem 1

The augmented Lagrangian function value sequence $\left\{\mathcal{L}\left( {\bf{\tilde{F}}}_{\text{RF}}^{(k)}, {\bf F}_{\text{RF}}^{(k)}, {\bf U}^{(k)} \right) | k = 0 , 1, 2, \cdots \right\}$ produced by the proposed ADMM algorithm converges if Furthermore, as $k \to \infty$, we have ${\bf F}_{\text{RF}}^{(k+1)} = {\bf F}_{\text{RF}}^{(k)}$, ${\bf{\tilde{F}}}_{\text{RF}}^{(k+1)} = {\bf{\tilde{F

Figures (13)

  • Figure 1: Illustration of a mmWave downlink positioning scenario, where the single-antenna UE receives the pilot signals transmitted from the BS (consisting of a BB precoder, an RF precoder, and an arbitrary array of multiple antennas).
  • Figure 2: Decomposition error upper bound versus number of quantization bits of phase shifter.
  • Figure 3: Decomposition error versus number of RF chains with different bits of the phase shifter, by the proposed method.
  • Figure 4: Decomposition error versus number of RF chains with $B = 2$ bits, among different algorithms.
  • Figure 5: Decomposition error versus number of bits of the phase shifter with different numbers of RF chains, by the proposed method.
  • ...and 8 more figures

Theorems & Definitions (9)

  • Remark 1
  • Remark 2
  • Remark 3
  • Theorem 1
  • proof
  • Theorem 2
  • proof
  • Lemma 1
  • Lemma 2