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Analysis and Optimization of RIS-Assisted Cell-Free Massive MIMO NOMA Systems

Malay Chakraborty, Ekant Sharma, Himal A. Suraweera, Hien Quoc Ngo

TL;DR

The RIS-assisted link is more advantageous at lower transmit power regions where the direct link between AP and user is weak, NOMA outperforms orthogonal multiple access schemes in terms of SE, and the proposed joint optimization framework significantly improves the sum SE of the system.

Abstract

We consider a reconfigurable intelligent surface (RIS) assisted cell-free massive multiple-input multiple-output non-orthogonal multiple access (NOMA) system, where each access point (AP) serves all the users with the aid of the RIS. We practically model the system by considering imperfect instantaneous channel state information (CSI) and employing imperfect successive interference cancellation at the users end. We first obtain the channel estimates using linear minimum mean square error approach considering the spatial correlation at the RIS and then derive a closed-form downlink spectral efficiency (SE) expression using the statistical CSI. We next formulate a joint optimization problem to maximize the sum SE of the system. We first introduce a novel successive Quadratic Transform (successive-QT) algorithm to optimize the transmit power coefficients using the concept of block optimization along with quadratic transform and then use the particle swarm optimization technique to design the RIS phase shifts. Note that most of the existing works on RIS-aided cell-free systems are specific instances of the general scenario studied in this work. We numerically show that i) the RIS-assisted link is more advantageous at lower transmit power regions where the direct link between AP and user is weak, ii) NOMA outperforms orthogonal multiple access schemes in terms of SE, and iii) the proposed joint optimization framework significantly improves the sum SE of the system.

Analysis and Optimization of RIS-Assisted Cell-Free Massive MIMO NOMA Systems

TL;DR

The RIS-assisted link is more advantageous at lower transmit power regions where the direct link between AP and user is weak, NOMA outperforms orthogonal multiple access schemes in terms of SE, and the proposed joint optimization framework significantly improves the sum SE of the system.

Abstract

We consider a reconfigurable intelligent surface (RIS) assisted cell-free massive multiple-input multiple-output non-orthogonal multiple access (NOMA) system, where each access point (AP) serves all the users with the aid of the RIS. We practically model the system by considering imperfect instantaneous channel state information (CSI) and employing imperfect successive interference cancellation at the users end. We first obtain the channel estimates using linear minimum mean square error approach considering the spatial correlation at the RIS and then derive a closed-form downlink spectral efficiency (SE) expression using the statistical CSI. We next formulate a joint optimization problem to maximize the sum SE of the system. We first introduce a novel successive Quadratic Transform (successive-QT) algorithm to optimize the transmit power coefficients using the concept of block optimization along with quadratic transform and then use the particle swarm optimization technique to design the RIS phase shifts. Note that most of the existing works on RIS-aided cell-free systems are specific instances of the general scenario studied in this work. We numerically show that i) the RIS-assisted link is more advantageous at lower transmit power regions where the direct link between AP and user is weak, ii) NOMA outperforms orthogonal multiple access schemes in terms of SE, and iii) the proposed joint optimization framework significantly improves the sum SE of the system.
Paper Structure (30 sections, 4 theorems, 49 equations, 8 figures, 3 algorithms)

This paper contains 30 sections, 4 theorems, 49 equations, 8 figures, 3 algorithms.

Table of Contents

  1. Introduction
  2. System Model
  3. Channel Model
  4. Uplink Training
  5. Downlink Data Transmission Phase
  6. Achievable Downlink Spectral Efficiency
  7. Intuitive Insights from the Derived Closed-Form SINR Expression in Theorem-\ref{['Theorem 1']}
  8. Effect of imperfect SIC
  9. Impact of spatial correlation
  10. Impact of pilot power and pilot length
  11. Special cases
  12. Spectral Efficiency Maximization with joint power and phase optimization
  13. Successive QT-based Power Allocation Optimization
  14. PSO-based RIS Phase Optimization for SE Maximization
  15. Computational Complexity
  16. ...and 15 more sections

Key Result

Proposition 1

For a RIS-assisted cell-free mMIMO NOMA system, the linear minimum mean square error (LMMSE)The effective channel $z_{mk}$ is the sum of many random variables, and hence, its distribution is very close to the Gaussian distribution (due to the central limit theorem). As a result, using LMMSE estimati where $c_{mk}$ is given as Here the constant $\delta_{mkn} = \beta_{mkn} + \text{Tr}\left(\mathbf

Figures (8)

  • Figure 1: RIS-assisted cell-free mMIMO NOMA system.
  • Figure 2: a) Spectral efficiency versus AP transmit power, b) Spectral efficiency versus the total number of users, c) Spectral efficiency comparison of cell-free NOMA versus cell-free OMA.
  • Figure 3: a) Impact of APs and RIS elements on the spectral efficiency, b) Spectral efficiency versus AP transmit power with the proposed algorithm, c) Spectral efficiency versus AP transmit power with optimization for different scenarios.
  • Figure 4: a) Cell-free NOMA versus cell-free OMA with and without optimization, b) Spectral efficiency versus RIS elements with random and optimal phase shifts.
  • Figure 5: a) Spectral efficiency versus AP transmit power for different direct path scenarios, b) Spectral efficiency versus AP transmit power for different user distribution scenarios, c) SE versus number of iterations for Algorithm $3$.
  • ...and 3 more figures

Theorems & Definitions (9)

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