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Adaptive Bit Partitioning for Reconfigurable Intelligent Surface Assisted FDD Systems with Limited Feedback

Weicong Chen, Chao-Kai Wen, Xiao Li, Shi Jin

TL;DR

An upper bound on ergodic rate loss with maximum ratio transmission is derived and the rate loss can be cut down by optimizing the feedback bit allocation during codebook generation and an adaptive bit partitioning strategy is proposed that is adaptive to diverse environment and system parameters is proposed.

Abstract

In frequency division duplexing systems, the base station (BS) acquires downlink channel state information (CSI) via channel feedback, which has not been adequately investigated in the presence of RIS. In this study, we examine the limited channel feedback scheme by proposing a novel cascaded codebook and an adaptive bit partitioning strategy. The RIS segments the channel between the BS and mobile station into two sub-channels, each with line-of-sight (LoS) and non-LoS (NLoS) paths. To quantize the path gains, the cascaded codebook is proposed to be synthesized by two sub-codebooks whose codeword is cascaded by LoS and NLoS components. This enables the proposed cascaded codebook to cater the different distributions of LoS and NLoS path gains by flexibly using different feedback bits to design the codeword structure. On the basis of the proposed cascaded codebook, we derive an upper bound on ergodic rate loss with maximum ratio transmission and show that the rate loss can be cut down by optimizing the feedback bit allocation during codebook generation. To minimize the upper bound, we propose a bit partitioning strategy that is adaptive to diverse environment and system parameters. Extensive simulations are presented to show the superiority and robustness of the cascaded codebook and the efficiency of the adaptive bit partitioning scheme.

Adaptive Bit Partitioning for Reconfigurable Intelligent Surface Assisted FDD Systems with Limited Feedback

TL;DR

An upper bound on ergodic rate loss with maximum ratio transmission is derived and the rate loss can be cut down by optimizing the feedback bit allocation during codebook generation and an adaptive bit partitioning strategy is proposed that is adaptive to diverse environment and system parameters is proposed.

Abstract

In frequency division duplexing systems, the base station (BS) acquires downlink channel state information (CSI) via channel feedback, which has not been adequately investigated in the presence of RIS. In this study, we examine the limited channel feedback scheme by proposing a novel cascaded codebook and an adaptive bit partitioning strategy. The RIS segments the channel between the BS and mobile station into two sub-channels, each with line-of-sight (LoS) and non-LoS (NLoS) paths. To quantize the path gains, the cascaded codebook is proposed to be synthesized by two sub-codebooks whose codeword is cascaded by LoS and NLoS components. This enables the proposed cascaded codebook to cater the different distributions of LoS and NLoS path gains by flexibly using different feedback bits to design the codeword structure. On the basis of the proposed cascaded codebook, we derive an upper bound on ergodic rate loss with maximum ratio transmission and show that the rate loss can be cut down by optimizing the feedback bit allocation during codebook generation. To minimize the upper bound, we propose a bit partitioning strategy that is adaptive to diverse environment and system parameters. Extensive simulations are presented to show the superiority and robustness of the cascaded codebook and the efficiency of the adaptive bit partitioning scheme.

Paper Structure

This paper contains 21 sections, 4 theorems, 97 equations, 8 figures.

Table of Contents

  1. Introduction
  2. System Model
  3. Channel Model
  4. Ergodic Rate
  5. Cascade Codebook Design and Performance Analysis
  6. Cascaded Codebook Design for Path Gain Feedback
  7. Ergodic Rate Loss Analysis
  8. Quantization Error Analysis
  9. Adaptive Bit Partitioning
  10. Bit Partitioning for LoS Paths Between BS--RIS and RIS--MS
  11. Bit Partitioning for NLoS Paths Between BS--RIS and RIS--MS
  12. Case 1
  13. Case 2
  14. Bit Partitioning for LoS and NLoS Paths
  15. Numerical Results
  16. ...and 6 more sections

Key Result

Lemma 1

In the RIS-assisted system, when the MRT and optimal reflection phase design eq:optimal_phase are adopted at the BS and RIS, respectively, the expected received signal power contributed by the cascaded LoS channel can be expressed as

Figures (8)

  • Figure 1: RIS-assisted FDD system where downlink CSI is fed back to the BS via feedback link.
  • Figure 2: Theoretical upper bound and Monte Carlo result of ergodic rate loss as a function of $N_{\rm R}$ for $E=0$ dB, $b=10$, $L_{\rm B}=3$, $L_{\rm M}=10$, $(K_{\rm B}, K_{\rm M})\in \{(-5,-5),(0,0),(10,10)\}$.
  • Figure 3: Theoretical upper bound and Monte Carlo result of ergodic rate loss as a function of transmit power under different bit allocation schemes (our proposal (Pro.); equally partitioned scheme (Equ.)) for $b=20$, $N_{\rm R}=12\times 20$, $L_{\rm B}=3$, $L_{\rm M}=17$, $(K_{\rm B}, K_{\rm M})\in \{(-10,-10),(0,-10),(0,0)\}$.
  • Figure 4: Ergodic rate and bit partitioning results versus $K_{\rm B}$ when path numbers are equal for $K_{\rm M}=-30$ dB, $E=0$ dB, $L_{\rm B}=L_{\rm M}=6$, $N_{\rm R}=3\times 5$.
  • Figure 5: Ergodic rate and bit partitioning results versus $K_{\rm B}$ when path numbers are equal for $K_{\rm M}=0$ dB, $E=0$ dB, $L_{\rm B}=L_{\rm M}=6$, $N_{\rm R}=3\times 5$.
  • ...and 3 more figures

Theorems & Definitions (4)

  • Lemma 1
  • Lemma 2
  • Theorem 1
  • Theorem 2