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IRS-Enhanced Wideband MU-MISO-OFDM Communication Systems

Hongyu Li, Rang Liu, Ming Li, Qian Liu

arXiv:1909.11314v1eess.SP

TL;DR

The paper addresses IRS-enhanced wideband MU-MISO-OFDM design, where a common IRS must support multiple subcarriers and users. It jointly designs beamformers and constant-amplitude IRS reflections through an MSE-based reformulation and block coordinate descent. Simulations report improved average sum-rate over random-IRS and no-IRS schemes, with low-resolution phase shifters offering efficient performance.

  • Problem

    Wideband IRS-assisted MU-MISO-OFDM design is unresolved because a common IRS serves all subcarriers while inter-user interference complicates optimization.

    Source: §I · p. 1

  • Method

    The paper reformulates sum-rate maximization as modified MSE minimization and solves the resulting problem through block coordinate descent over beamformers, IRS phases, and auxiliary variables.

    Source: §I · p. 1, A. Problem Reformulation · p. 3

  • Results

    The proposed algorithm outperforms random-IRS and no-IRS schemes across transmit-power ranges, while performance growth is marginal beyond 4-bit phase resolution.

    Source: §IV · p. 6

  • Takeaways & Limitations

    Low-resolution phase shifters can provide satisfactory performance with faster convergence, supporting practical IRS implementation for wideband wireless systems.

    Source: §IV · pp. 5–6, §V · p. 6

Abstract

from arXiv · show

Intelligent reflecting surface (IRS) is considered as an enabling technology for future wireless communication systems since it can intelligently change the wireless environment to improve the communication performance. In this paper, an IRS-enhanced wideband multiuser multi-input single-output orthogonal frequency division multiplexing (MU-MISO-OFDM) system is investigated. We aim to jointly design the transmit beamformer and the reflection of IRS to maximize the average sum-rate over all subcarriers. With the aid of the relationship between sum-rate maximization and mean square error (MSE) minimization, an efficient joint beamformer and IRS design algorithm is developed. Simulation results illustrate that the proposed algorithm can offer significant average sum-rate enhancement, which confirms the effectiveness of the use of the IRS for wideband wireless communication systems.

I. INTRODUCTION

The paper motivates IRS-assisted wideband MU-MISO-OFDM as an energy-efficient approach and formulates joint beamformer and IRS reflection design for maximizing average sum-rate under system constraints.

I. INTRODUCTION

  • IRS adaptively changes the propagation environment through passive phase shifters, improving channel or beamforming gain without additional power consumption.Source: §I · p. 1
  • Prior IRS designs mainly address narrowband SU/MU-MISO systems, while wideband MU-MISO-OFDM remains uninvestigated because one IRS must serve all subcarriers amid inter-user interference.Source: §I · p. 1
  • The proposed work jointly designs per-subcarrier beamformers and constant-amplitude IRS reflections to maximize average sum-rate across subcarriers.Source: §I · p. 1

II. SYSTEM MODEL AND PROBLEM FORMULATION

  • The system uses a BS with N_t antennas, K single-antenna users, N subcarriers, and an IRS with M phase shifters adjusted using channel state information.Source: §II · p. 2
  • Wideband channels are modeled with finite-duration impulse responses for the BS-user and BS-IRS links, while each user also has an IRS-user channel.Source: §II · p. 2
  • The optimization jointly selects beamformers W and phase shift matrix Φ to maximize average sum-rate subject to unit-modulus IRS elements and a total transmit-power constraint.Source: §II · p. 3

A. Problem Reformulation

The original sum-rate problem is reformulated as a modified MSE minimization problem, removing the complex SINR fraction from the logarithmic objective and enabling block coordinate descent.

A. Problem Reformulation

  • The original problem is difficult because its objective is complex and the IRS phase-shift constraint is non-convex.Source: A. Problem Reformulation · p. 3
  • Introducing auxiliary variables and positive weighting parameters yields an equivalent modified-MSE formulation with the SINR fraction removed from the log term.Source: A. Problem Reformulation · p. 3
  • The reformulated multivariable problem is more tractable and is solved using a block coordinate descent algorithm decomposed into four block optimizations.Source: A. Problem Reformulation · p. 3

B. Block Update

The block-update stage fixes the remaining variables and separately optimizes the IRS phase-shift matrix within the reformulated problem.

B. Block Update

  • With weighting parameters, auxiliary variables, and beamformers fixed, the phase-shift matrix Φ is optimized as its own sub-problem.Source: 1) Weighting parameter · p. 3

1) Weighting parameter

The weighting-parameter update is obtained from its sub-problem's first-order optimality condition while the other optimization variables remain fixed.

1) Weighting parameter

2) Auxiliary variable :

The auxiliary-variable subproblem is convex and yields its optimum by setting the objective's partial derivative to zero.

2) Auxiliary variable :

3) Beamformer W:

With other variables fixed, the beamformer is designed through an unconstrained subproblem and then normalized to satisfy the total transmit-power constraint.

3) Beamformer W:

  • The beamformer subproblem is formed with fixed weighting parameters, auxiliary variables, and phase-shift matrix.Source: 3) Beamformer W · p. 4
  • The objective groups terms for each user's beamformer on each subcarrier, motivating separate unconstrained beamformer design.Source: 3) Beamformer W · p. 4
  • The unconstrained beamformer has an easily obtained optimal form.Source: 3) Beamformer W · p. 4
  • The resulting beamformer is normalized to satisfy the total transmit-power constraint.Source: 3) Beamformer W · p. 4

4) Phase shift matrix

The IRS phase-shift matrix is optimized element by element under unit-modulus constraints, with iterative updates and optional low-resolution quantization.

4) Phase shift matrix

  • Because each phase shift has constant magnitude, the objective is split and each element is optimized while the others remain fixed.Source: 4) Phase shift matrix · p. 4
  • The conditionally optimal phase-shift element is updated iteratively until the phase-shift matrix converges.Source: 4) Phase shift matrix · pp. 4–5
  • Algorithm 1 initializes the beamformers and phase-shift matrix, then updates auxiliary variables, beamformers, and phase-shift quantities in sequence.Source: 4) Phase shift matrix · p. 5
  • The algorithm returns the optimized beamformers and phase-shift matrix after convergence.Source: 4) Phase shift matrix · p. 5
  • Low-resolution phase shifters are handled by quantizing phase values, with angle resolution Δ≜2π/2^b controlled by b bits.Source: 4) Phase shift matrix · p. 5

5) Summary:

The proposed procedure alternates updates across four variable blocks until convergence, producing a joint beamformer and IRS design.

5) Summary:

  • The algorithm initializes the beamformers and phase-shift matrix, then iteratively updates four variable blocks in a prespecified order until convergence.Source: 5) Summary · p. 5

C. Complexity Analysis

The proposed joint beamformer and IRS design has complexity about O(I2(NK^2NtM^2)) under stated large-system assumptions, while simulations assess convergence, phase resolution, transmit power, and IRS size. Results show convergence within 15 iterations for continuous phase shifters and 8 for low-resolution ones, with low-resolution designs remaining effective across tested settings.

C. Complexity Analysis

  • The algorithm’s total complexity is about O(I2(NK^2NtM^2)) operations when M ≫ Nt, M ≫ K, and the phase-shift update converges within limited iterations.I2 is the iteration count for Algorithm 1, while I1 denotes iterations for updating the phase-shift matrix.Source: C. Complexity Analysis · p. 5

IV. SIMULATION RESULTS

  • Continuous phase shifters converge within 15 iterations, whereas low-resolution phase shifters converge within 8 iterations.The paper therefore describes the proposed algorithm as affordable even with many phase-shift elements.Source: §IV · p. 5, Figure 2 · p. 5
  • Average sum-rate growth becomes marginal beyond b ≥4, making low-resolution phase shifters more practical and efficient in the tested system.Fig. 2(b) compares the proposed low-resolution design with random-phase IRS and the BS-user link without IRS.Source: §IV · p. 6
  • Across all transmit-power ranges, the proposed algorithm outperforms both the random-phase IRS and no-IRS schemes.With B = 3, its performance is close to that of continuous phase shifters.Source: §IV · p. 6, Figure 3 · p. 6
  • Across different numbers of phase-shift elements, the proposed algorithm achieves satisfactory performance compared with its competitors.This result supports the reported advantage of employing an IRS in wireless communication systems.Source: §IV · p. 6, Figure 4 · p. 6

V. CONCLUSIONS

  • The paper concludes that its sub-optimal joint design algorithm demonstrates the potential of IRS for wideband wireless communication systems.The design targets maximum average sum-rate with continuous and low-resolution phase shifters using sum-rate/MSE equivalence.Source: §V · p. 6
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