Logo
ScienceStack
Table of Contents
Fetching ...
Sign In

Location Information Assisted Beamforming Design for Reconfigurable Intelligent Surface Aided Communication Systems

Zhe Xing, Rui Wang, Xiaojun Yuan, Jun Wu

TL;DR

A novel relaxed alternating optimization process (RAOP) is developed by utilizing various optimization tools, such as the Lagrange multiplier, the matrix inversion lemma, the semidefinite relaxation, as well as the branch-and-bound (BnB), which performs better and shows strong robustness against the location-error-related CSI uncertainty.

Abstract

In reconfigurable intelligent surface (RIS) aided millimeter-wave (mmWave) communication systems, in order to overcome the limitation of the conventional channel state information (CSI) acquisition techniques, this paper proposes a location information assisted beamforming design without the requirement of the conventional channel training process. First, we establish the geometrical relation between the channel model and the user location, based on which we derive an approximate CSI error bound based on the user location error by means of Taylor approximation, triangle and power mean inequalities, and semidefinite relaxation (SDR). Second, for combating the uncertainty of the location error, we formulate a worst-case robust beamforming optimization problem. To solve the problem efficiently, we develop a novel iterative algorithm by utilizing various optimization tools such as Lagrange multiplier, matrix inversion lemma, SDR, as well as branch-and-bound (BnB). Additionally, we provide sufficient conditions for the SDR to output rank-one solutions, and modify the BnB algorithm to acquire the phase shift solution under an arbitrary constraint of possible phase shift values. Finally, we analyse the algorithm convergence and complexity, and carry out simulations to validate the theoretical derivation of the CSI error bound and the robustness of the proposed algorithm. Compared with the existing non-robust approach and the robust beamforming techniques based on S-procedure and penalty convex-concave procedure (CCP), our method can converge more quickly and achieve better performance in terms of the worst-case signal-to-noise ratio (SNR) at the receiver.

Location Information Assisted Beamforming Design for Reconfigurable Intelligent Surface Aided Communication Systems

TL;DR

A novel relaxed alternating optimization process (RAOP) is developed by utilizing various optimization tools, such as the Lagrange multiplier, the matrix inversion lemma, the semidefinite relaxation, as well as the branch-and-bound (BnB), which performs better and shows strong robustness against the location-error-related CSI uncertainty.

Abstract

In reconfigurable intelligent surface (RIS) aided millimeter-wave (mmWave) communication systems, in order to overcome the limitation of the conventional channel state information (CSI) acquisition techniques, this paper proposes a location information assisted beamforming design without the requirement of the conventional channel training process. First, we establish the geometrical relation between the channel model and the user location, based on which we derive an approximate CSI error bound based on the user location error by means of Taylor approximation, triangle and power mean inequalities, and semidefinite relaxation (SDR). Second, for combating the uncertainty of the location error, we formulate a worst-case robust beamforming optimization problem. To solve the problem efficiently, we develop a novel iterative algorithm by utilizing various optimization tools such as Lagrange multiplier, matrix inversion lemma, SDR, as well as branch-and-bound (BnB). Additionally, we provide sufficient conditions for the SDR to output rank-one solutions, and modify the BnB algorithm to acquire the phase shift solution under an arbitrary constraint of possible phase shift values. Finally, we analyse the algorithm convergence and complexity, and carry out simulations to validate the theoretical derivation of the CSI error bound and the robustness of the proposed algorithm. Compared with the existing non-robust approach and the robust beamforming techniques based on S-procedure and penalty convex-concave procedure (CCP), our method can converge more quickly and achieve better performance in terms of the worst-case signal-to-noise ratio (SNR) at the receiver.

Paper Structure

This paper contains 24 sections, 5 theorems, 100 equations, 9 figures, 1 table, 1 algorithm.

Table of Contents

  1. Introduction
  2. System Model and Problem Formulation
  3. Channel and Received Signal Models
  4. CSI Error Model
  5. Problem Formulation
  6. Derivation of the CSI Error Bound
  7. Derivation of $\epsilon_{\mathrm{RU}}^{\mathrm{LoS}}$
  8. Determination of $\epsilon_{\Delta \mathbf{h}_{\mathrm{RU}}}$
  9. Robust Transmit and Passive Beamforming
  10. Proposed Iterative Optimization Approach
  11. Overall Algorithm Design
  12. Convergence Analysis
  13. Computational Complexity Analysis
  14. Simulation Results
  15. System Parameters and Performance Metric
  16. ...and 9 more sections

Key Result

Lemma 1

When $\|\Delta\mathbf{p}\|_2\leq \epsilon_{\Delta\mathbf{p}}$, the approximate upper bound of the maximum of $\Omega\left(\Delta\mathbf{p}\right)$, denoted by $\Omega^{\mathrm{Upp}}_{\mathrm{max}}$, can be derived as from the solution of the following convex problem: where $\mathbf{S}$ and $\mathbf{R}$ are expressed as in which $\mathbf{G}_{\alpha}$, $\mathbf{G}_{\frac{\alpha}{2}}$ and $\mathbf

Figures (9)

  • Figure 1: The considered RIS-aided wireless communication system in a 3D propagation environment. The user location $\widehat{\mathbf{p}}$, acquired from the existing localization systems, is adopted to reconstruct the LoS channel from the RIS to the UE. The actual user location $\mathbf{p}$ is assumed to be within a spherical region with radius of $\epsilon_{\Delta\mathbf{p}}$ and center of $\widehat{\mathbf{p}}$.
  • Figure 2: The flowchart of the modified BnB in our algorithm.
  • Figure 3: The CSI error bounds as functions of $N$ with different $\epsilon_{\Delta\mathbf{p}}$.
  • Figure 4: The CSI error bounds as functions of user coordinates with $\epsilon_{\Delta\mathbf{p}}=0.5$ m and different $N$.
  • Figure 5: Worst-case SNRs at the UE with respect to $N$ when $\mathcal{S}=[0,2\pi]$.
  • ...and 4 more figures

Theorems & Definitions (11)

  • Lemma 1
  • proof
  • Proposition 1
  • proof
  • Proposition 2
  • proof
  • Remark 1
  • Proposition 3
  • proof
  • Proposition 4
  • ...and 1 more