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Performance Analysis on RIS-Aided Wideband Massive MIMO OFDM Systems with Low-Resolution ADCs

Xianzhe Chen, Hong Ren, Cunhua Pan, Zhangjie Peng, Kangda Zhi, Yong Liu, Xiaojun Xi, Ana Garcia Armada, Cheng-Xiang Wang

TL;DR

This paper derives the closed-form approximate expression of the uplink achievable rate, based on which the asymptotic system performance is analyzed when the number of the antennas at the base station and the number of reflecting elements at the RIS grow to infinity.

Abstract

This paper investigates a reconfigurable intelligent surface (RIS)-aided wideband massive multiple-input multiple-output (MIMO) orthogonal frequency division multiplexing (OFDM) system with low-resolution analog-to-digital converters (ADCs). Frequency-selective Rician fading channels are considered, and the OFDM data transmission process is presented in time domain. This paper derives the closed-form approximate expression of the uplink achievable rate, based on which the asymptotic system performance is analyzed when the number of the antennas at the base station and the number of reflecting elements at the RIS grow to infinity. Besides, the power scaling laws of the considered system are revealed to provide energy-saving insights. Furthermore, this paper proposes a gradient ascent-based algorithm to design the phase shifts of the RIS for maximizing the minimum user rate. Finally, numerical results are presented to verify the correctness of analytical conclusions and draw insights.

Performance Analysis on RIS-Aided Wideband Massive MIMO OFDM Systems with Low-Resolution ADCs

TL;DR

This paper derives the closed-form approximate expression of the uplink achievable rate, based on which the asymptotic system performance is analyzed when the number of the antennas at the base station and the number of reflecting elements at the RIS grow to infinity.

Abstract

This paper investigates a reconfigurable intelligent surface (RIS)-aided wideband massive multiple-input multiple-output (MIMO) orthogonal frequency division multiplexing (OFDM) system with low-resolution analog-to-digital converters (ADCs). Frequency-selective Rician fading channels are considered, and the OFDM data transmission process is presented in time domain. This paper derives the closed-form approximate expression of the uplink achievable rate, based on which the asymptotic system performance is analyzed when the number of the antennas at the base station and the number of reflecting elements at the RIS grow to infinity. Besides, the power scaling laws of the considered system are revealed to provide energy-saving insights. Furthermore, this paper proposes a gradient ascent-based algorithm to design the phase shifts of the RIS for maximizing the minimum user rate. Finally, numerical results are presented to verify the correctness of analytical conclusions and draw insights.
Paper Structure (21 sections, 7 theorems, 467 equations, 6 figures, 1 table, 1 algorithm)

This paper contains 21 sections, 7 theorems, 467 equations, 6 figures, 1 table, 1 algorithm.

Table of Contents

  1. Introduction
  2. System Model
  3. Channel Model: Channel Impulse Response
  4. Data Transmission
  5. Uplink Rate Analysis
  6. RIS Phase Shift Design
  7. Numerical Results
  8. Conclusion
  9. Derivation of $\mathbb{E} \left\{ \left| \mathbf{g}_{\mathrm{u},nt}^{H}\mathbf{\Phi }^H\mathbf{G}_{\mathrm{b}}^{H}\mathbf{G}_{\mathrm{b}}\mathbf{\Phi g}_{\mathrm{u},nt} \right|^2 \right\}$
  10. Derivation of $\mathbb{E} \left\{ \left| \mathbf{g}_{\mathrm{u},nt}^{H}\mathbf{\Phi }^H\mathbf{G}_{\mathrm{b}}^{H}\mathbf{G}_{\mathrm{b}}\mathbf{\Phi g}_{\mathrm{u},ut} \right|^2 \right\}$ and $\mathbb{E} \left\{ \left\| \mathbf{g}_{\mathrm{u},nt}^{H}\mathbf{\Phi }^H\mathbf{G}_{\mathrm{b}}^{H} \right\| ^2 \right\}$
  11. Derivation of $\mathbb{E} \left\{ \mathbf{g}_{\mathrm{u},nt}^{H}\mathbf{\Phi }^H\mathbf{G}_{\mathrm{b}}^{H}\left( \mathbf{I}_{N_{\mathrm{b}}}\otimes \mathbf{F} \right) \mathbf{R}_{\mathbf{z}_{\mathrm{q}}}\left( \mathbf{I}_{N_{\mathrm{b}}}\otimes \mathbf{F}^H \right) \mathbf{G}_{\mathrm{b}}\mathbf{\Phi g}_{\mathrm{u},nt} \right\}$
  12. The $\mathbf{\Upsilon }_{1112}$ and $\mathbf{\Upsilon }_{2111}$-Related Expectations
  13. The $\mathbf{\Upsilon }_{1121}$ and $\mathbf{\Upsilon }_{1211}$-Related Expectations
  14. The $\mathbf{\Upsilon }_{1122}$ and $\mathbf{\Upsilon }_{2211}$-Related Expectations
  15. The $\mathbf{\Upsilon }_{1212}$ and $\mathbf{\Upsilon }_{2121}$-Related Expectations
  16. ...and 6 more sections

Key Result

Theorem 1

With MRC processing, the approximate expression for the uplink achievable rate of User $n$ in an RIS-aided multi-user wideband massive MIMO OFDM system with low-resolution ADCs under Rician fading channels can be expressed as where $\varpi _n$, $\eta _{n,u}$, $\xi _n$, and $\epsilon _n$ are respectively defined in omega_bar_n, eta_n_u, xi_n, and epsilon_n in Appendix app_A.

Figures (6)

  • Figure 1: System Model
  • Figure 2: The Minimum User Rate versus $N_{\mathrm{b}}$
  • Figure 3: The Minimum User Rate versus The Rician Factors
  • Figure 4: The Minimum User Rate versus The Quantization Bit of ADC
  • Figure 5: The Power Scaling Law Related to $N_{\mathrm{b}}$
  • ...and 1 more figures

Theorems & Definitions (8)

  • Theorem 1
  • Remark 1
  • Corollary 1
  • Corollary 2
  • Corollary 3
  • Corollary 4
  • Lemma 1
  • Lemma 2