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Alternating Minimization for Wideband Multiuser IRS-aided MIMO Systems under Imperfect CSI

Darian Pérez-Adán, Michael Joham, Óscar Fresnedo, José P. González-Coma, Luis Castedo, Wolfgang Utschick

TL;DR

This work tackles the joint design of wideband IRS-aided multiuser MIMO systems under imperfect CSI by formulating an MMSE minimization problem and solving it with a BC-MAC duality-based alternating algorithm. The approach simultaneously designs frequency-dependent BS precoders/receivers and a frequency-flat IRS phase-shift matrix, while exploiting the statistics of channel estimation errors to enhance robustness. Key contributions include a robust alternating MSE minimization framework, convergence and complexity analyses, and extensive simulations showing substantial sum-rate and MSE gains over baselines, with only modest losses when IRS phase shifts are discretized. The results demonstrate the practical viability of deploying passive IRSs in wideband MU MIMO settings and offer design insights for IRS phase quantization and deployment under imperfect CSI.

Abstract

This work focuses on wideband intelligent reflecting surface (IRS)-aided multiuser MIMO systems. One of the major challenges of this scenario is the joint design of the frequency-dependent base station (BS) precoder and user filters, and the IRS phase-shift matrix which is frequency flat and common to all the users. In addition, we consider that the channel state information (CSI) is imperfect at both the transmitter and the receivers. A statistical model for the imperfect CSI is developed and exploited for the system design. A minimum mean square error (MMSE) approach is followed to determine the IRS phase-shift matrix, the transmit precoders, and the receiving filters. The broadcast (BC)- multiple access channel (MAC) duality is used to solve the optimization problem following an alternating minimization approach. Numerical results show that the proposed approach leads to substantial performance gains with respect to baseline strategies that neglect the inter-user interference and do not optimize the IRS phase-shift matrix. Further performance gains are obtained when incorporating into the system design the statistical information of the channel estimation errors.

Alternating Minimization for Wideband Multiuser IRS-aided MIMO Systems under Imperfect CSI

TL;DR

This work tackles the joint design of wideband IRS-aided multiuser MIMO systems under imperfect CSI by formulating an MMSE minimization problem and solving it with a BC-MAC duality-based alternating algorithm. The approach simultaneously designs frequency-dependent BS precoders/receivers and a frequency-flat IRS phase-shift matrix, while exploiting the statistics of channel estimation errors to enhance robustness. Key contributions include a robust alternating MSE minimization framework, convergence and complexity analyses, and extensive simulations showing substantial sum-rate and MSE gains over baselines, with only modest losses when IRS phase shifts are discretized. The results demonstrate the practical viability of deploying passive IRSs in wideband MU MIMO settings and offer design insights for IRS phase quantization and deployment under imperfect CSI.

Abstract

This work focuses on wideband intelligent reflecting surface (IRS)-aided multiuser MIMO systems. One of the major challenges of this scenario is the joint design of the frequency-dependent base station (BS) precoder and user filters, and the IRS phase-shift matrix which is frequency flat and common to all the users. In addition, we consider that the channel state information (CSI) is imperfect at both the transmitter and the receivers. A statistical model for the imperfect CSI is developed and exploited for the system design. A minimum mean square error (MMSE) approach is followed to determine the IRS phase-shift matrix, the transmit precoders, and the receiving filters. The broadcast (BC)- multiple access channel (MAC) duality is used to solve the optimization problem following an alternating minimization approach. Numerical results show that the proposed approach leads to substantial performance gains with respect to baseline strategies that neglect the inter-user interference and do not optimize the IRS phase-shift matrix. Further performance gains are obtained when incorporating into the system design the statistical information of the channel estimation errors.
Paper Structure (17 sections, 59 equations, 10 figures, 6 tables, 1 algorithm)

This paper contains 17 sections, 59 equations, 10 figures, 6 tables, 1 algorithm.

Table of Contents

  1. Introduction
  2. Contributions and organization
  3. Notation
  4. System Model
  5. Channel estimation
  6. Channel model
  7. Achievable sum-rate
  8. MMSE Approach
  9. Proposed Solution
  10. Alternating MSE minimization algorithm
  11. Convergence Analysis
  12. Convergence of the sequences $\lbrace \text{MSE}^{\text{UL}}({{\mathbf{T}}},\underline{\boldsymbol{\nu}}^{(i)})\rbrace$
  13. Convergence of the sequences $\lbrace \text{MSE}^{\text{UL}}(\underline{{\mathbf{T}}}^{(i)},\boldsymbol{\tilde{\nu}}^{(i)})\rbrace$
  14. Convergence of the sequences $\lbrace \text{MSE}^{\text{UL}}(\underline{{\mathbf{T}}}^{(i)},\boldsymbol{\nu}^{(i)})\rbrace$
  15. Computational Complexity Analysis
  16. ...and 2 more sections

Figures (10)

  • Figure 1: Block diagram of the multistream wideband downlink MU IRS-aided mmWave MIMO system.
  • Figure 2: Multistream wideband downlink MU IRS-aided mmWave MIMO system at subcarrier $\ell$.
  • Figure 3: Multistream wideband dual uplink MU IRS-aided mmWave MIMO system model at subcarrier $\ell$.
  • Figure 4: Sum-rate $(\text{bit}/\text{s}/\text{Hz})$ vs $\text{SNR\;(dB)}$ for $K=3$ users, $N_{\text{r}}=4$, $N_{\text{t}}=9$, $L=32$, $N=25$, and $N_{\text{s},k}[\ell]=2,\forall k,\ell$.
  • Figure 5: Sum-rate $(\text{bit}/\text{s}/\text{Hz})$ vs $\text{SNR\;(dB)}$ for $K=3$ users, $N_{\text{r}}=4$, $N_{\text{t}}=9$, $L=32$, $N=25$, $N_{\text{s},k}[\ell]=2,\forall k,\ell$ and discrete phase shifts (2 and 3 bits).
  • ...and 5 more figures