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Learning-Accelerated Joint AP/RIS Optimization for Low-Latency Indoor mmWave XR Networks

Ali Elghariani, Mohammed Elbamby, Anis Elgabli

arXiv:2610.33945v1cs.NI

TL;DR

Indoor XR requires high-rate, predictable low-latency service, but mmWave links are vulnerable to blockage and multi-AP interference remains insufficiently explored for shared-RIS systems. The paper jointly optimizes AP precoders and RIS phases with centralized AO, then uses supervised learning to initialize AO. The learned warm start approaches converged AO performance with fewer refinement iterations, while AO converges monotonically to a coordinate-wise locally optimal solution for the discretized problem.

  • Problem

    Indoor mmWave XR links face blockage, and the impact of inter-AP interference in multi-AP RIS-assisted systems remains insufficiently explored.

    Source: §I · p. 1

  • Method

    The paper jointly designs AP precoders and RIS phases with centralized AO, and trains a supervised model on offline AO solutions to initialize online optimization.

    Source: §I · pp. 1–2

  • Results

    With only a few refinement iterations, NN+AO closely approaches converged AO performance across the tested N values and percentiles.

    Source: B. Numerical Results · p. 5

  • Takeaways & Limitations

    The hybrid model-based and learning-driven framework lowers online optimization time while preserving near-optimal performance.

    Source: §V · pp. 5–6

    ZF is a heuristic rather than an exact solution to the continuous precoder subproblem, though the acceptance rule ensures monotonic improvement and empirical convergence stability.

    Source: B. Convergence Analysis · p. 3

Abstract

from arXiv · show

This paper studies a reconfigurable intelligent surface (RIS)-assisted indoor architecture for extended reality (XR) applications, where multiple access points (APs) simultaneously serve multiple users over a shared frequency channel under a centralized AP controller. We formulate a non-convex sum-rate maximization problem with coupled AP precoders and RIS phase shifts, and develop a centralized alternating optimization (AO) framework for joint design. We rigorously prove that the proposed AO guarantees monotonic improvement of the sum rate that converges to a coordinate-wise stationary point, despite the non-convexity of the resulting subproblems. Although AO provides reliable performance, its iterative nature limits real-time applicability as the system dimension grows. To overcome this limitation, we propose a supervised learning-assisted approach that leverages AO-generated solutions to significantly accelerate convergence. Simulation results demonstrate that the proposed framework achieves near-optimal performance with substantially fewer AO iterations, which makes it well-suited for latency-critical RIS-assisted XR deployments.

I. INTRODUCTION

Indoor XR needs high-rate, predictable low-latency links, but mmWave connections are vulnerable to blockage. The paper studies joint AP and RIS design for coordinated multi-AP service and uses learning to accelerate AO for this setting.

I. INTRODUCTION

  • XR demands multi-gigabit rates and low, predictable latency, while indoor mmWave links can be interrupted by blockage.Walls, furniture, and human bodies are identified as potential blockers.Source: §I · p. 1
  • Prior RIS work has considered single-cell optimization and cooperative multi-cell sensing, while inter-AP interference in multi-AP RIS systems remains insufficiently explored.The authors identify this as the gap motivating their study.Source: §I · p. 1
  • The target architecture has multiple APs serving multiple users on one frequency channel under a centralized controller, with blocked direct links and one shared RIS.The RIS must support users associated with different APs while helping useful transmission and controlling inter-AP interference.Source: §I · p. 1
  • The design question is whether one RIS can coordinate reflected paths for simultaneous multi-AP, multi-user service while keeping interference manageable.The RIS phases must be designed jointly with AP precoders because a reflected path may help one user and harm another.Source: §I · p. 1
  • The paper formulates joint AP-precoder and RIS-phase optimization under a zero-forcing constraint and applies centralized AO to update the two variable blocks in turn.The stated problem is non-convex because active and passive beamforming are coupled.Source: §I · pp. 1–2
  • A learned initialization from offline AO solutions is used to reduce online AO iterations while retaining a high-quality joint-design starting point.The model predicts an initialization from the network state.Source: §I · p. 2

II. SYSTEM MODEL

The system is a centralized indoor mmWave network in which multiple APs serve an equal number of users through a shared RIS, with direct AP–UE links assumed blocked. Its channel model and signal description specify the reflected links, transmission, and centralized CSI coordination.

II. SYSTEM MODEL

  • The model assumes J = K, one user served per AP at a time, and completely blocked direct AP–UE links to isolate the shared-RIS interference-coordination problem.APs have M antennas each; the RIS has N passive elements in a uniform planar array.Source: §II · p. 2
  • Propagation follows the Saleh–Valenzuela model, representing a finite number of dominant clusters with multiple rays and their gains, delays, and angular parameters.The passage describes this model as suitable for sparse mmWave propagation and as capturing large- and small-scale effects.Source: §II · p. 2
  • The RIS reflection matrix is diagonal, with each element set by a phase shift; AP-to-user communication is represented through the cascaded AP–RIS–UE channel.Each AP precoder has a per-AP power constraint, and the received signal includes inter-user interference and noise.Source: §II · p. 2
  • A common AP controller coordinates the APs and uses CSI for all AP–RIS and RIS–UE links, aggregated after uplink pilot training and local channel estimation.The passage describes centralized CSI aggregation for beamforming and RIS optimization.Source: §II · p. 2

III. PROBLEM FORMULATION

The paper formulates network sum-rate maximization over the AP precoders and RIS phase shifts. Coupling between these variables and the RIS unit-modulus constraints makes the joint problem non-convex.

III. PROBLEM FORMULATION

  • For a given RIS configuration, the controller computes a centralized zero-forcing precoder and normalizes each AP precoder to meet its per-AP power constraint.The implementation uses a Moore–Penrose pseudoinverse or regularized ZF to avoid numerical instability when the effective channel is ill-conditioned.Source: §III · pp. 2–3
  • The objective jointly optimizes active AP precoders and the passive RIS phase-shift matrix to maximize network sum rate.The formulation uses cascaded channel information collected into an effective channel matrix.Source: §III · pp. 2–3
  • The joint problem is non-convex because the precoders and RIS phases are coupled through cascaded effective channels and the RIS elements have unit-modulus constraints.The passage characterizes direct joint optimization as intractable.Source: §III · p. 3

A. Alternating Optimization Framework

The centralized AO framework alternates between updating AP precoders and RIS phases, accepting updates that do not reduce sum rate. RIS phases are searched sequentially over a discrete set until convergence or an iteration limit.

A. Alternating Optimization Framework

  • With RIS phases fixed, AP precoders are updated using the ZF solution, and the update is accepted only if sum rate does not decrease.This step mitigates inter-user interference through centralized precoding.Source: A. Alternating Optimization Framework · p. 3
  • With AP precoders fixed, the RIS phases are optimized sequentially by discrete coordinate descent, updating each element over a discrete phase set.The phase resolution is denoted by L.Source: A. Alternating Optimization Framework · p. 3
  • AO stops when relative sum-rate improvement meets its convergence criterion or when the maximum iteration count is reached.The passage specifies these as alternative stopping conditions.Source: A. Alternating Optimization Framework · p. 3
  • The proposed AO framework guarantees monotonic convergence because each subproblem fixes the other variable block and each update is non-decreasing in sum rate.This is the stated guarantee for the alternating framework.Source: A. Alternating Optimization Framework · p. 3

B. Convergence Analysis

The AO algorithm increases sum rate monotonically and, for a discretized RIS phase set, terminates at a coordinate-wise locally optimal solution. Its ZF precoder update is heuristic, but an acceptance rule preserves monotonic improvement and empirical convergence stability.

B. Convergence Analysis

  • AO monotonically increases system sum rate despite the problem's non-convexity, through monotonic ZF acceptance and discrete coordinate-descent RIS updates.The ZF precoder is a heuristic rather than an exact solution to the continuous precoder subproblem; its acceptance rule ensures monotonic improvement and empirical convergence stability.Source: B. Convergence Analysis · p. 3
  • For the discretized RIS phase set, AO converges in finitely many iterations to a coordinate-wise locally optimal solution with non-decreasing sum-rate values.Each RIS phase element is searched over the finite set, and the finite feasible configurations limit strictly improving updates.Source: B. Convergence Analysis · p. 3
  • Each coordinate update strictly increases or maintains the objective until no single RIS-coordinate update can further improve it.This finite-update argument establishes coordinate-wise, not global, optimality.Source: B. Convergence Analysis · p. 3

C. Learning-Assisted Online Approximation of AO

To reduce the online latency of iterative AO, the paper trains a supervised model using converged AO solutions. The model predicts RIS phase indices and AP beamformers from channel features, providing a direct configuration or an AO warm start for lightweight refinement.

C. Learning-Assisted Online Approximation of AO

  • The learning-assisted approach addresses the online computational latency of AO, which is costly when AP, user, and RIS dimensions grow.Rapid updates matter in XR settings where channels and user positions may change frequently and RIS updates have stringent delay requirements.Source: C. Learning-Assisted Online… · pp. 3–4
  • A supervised model trained on offline AO solutions predicts RIS phase indices and AP beamformers from real and imaginary channel features.The training data sample channel realizations and AP/user geometries, then use converged joint beamforming and RIS optimization solutions as labels.Source: C. Learning-Assisted Online… · p. 4
  • Online, the model's estimate can be used directly for very low latency or as an AO warm start followed by a small number of refinement iterations.The learned initialization is intended to approximate the converged AO solution, with lightweight refinement available to recover remaining performance gap.Source: C. Learning-Assisted Online… · p. 4
  • The online algorithm can initialize from predicted phase indices and beamformers, then apply up to the specified refinement budget of AO iterations.The algorithm supports a zero-refinement direct-output mode as well as iterative refinement from the learned initialization.Source: C. Learning-Assisted Online… · p. 4

D. Complexity Analysis

The learning-assisted warm start reduces the number of costly AO iterations, with the RIS phase-update stage dominating runtime for large surfaces.

D. Complexity Analysis

  • Each AO iteration has complexity O((JM)^3 + NLK), combining ZF precoding and RIS phase updates.The respective operation counts are O((JM)^3) and O(NLK).Source: D. Complexity Analysis · p. 4
  • Learning-assisted refinement reduces total complexity from O(Tmax((JM)^3 + NLK)) to O(Tref((JM)^3 + NLK)), where Tref < Tmax.The reduction comes from using fewer AO iterations after the learned warm start.Source: D. Complexity Analysis · p. 4
  • For large RIS sizes, phase updates dominate runtime because their complexity grows linearly with the number of RIS elements and phase-grid resolution.The phase-update term is O(NLK).Source: D. Complexity Analysis · p. 4

A. Learning Model Architecture and Training

The learning model uses channel features to predict RIS phase choices and AP beamformers through a shared-encoder MLP with two task-specific output heads. Training combines classification and regression losses, with hidden-layer widths scaled to RIS size.

A. Learning Model Architecture and Training

  • The SharedEncoderMLP input concatenates real and imaginary parts of AP–RIS matrices and RIS–UE vectors, with dimension 2(JNM + KN).Separate channel-feature encoders feed a shared two-layer trunk with BatchNorm, GELU activations, and dropout.Source: A. Learning Model Architecture and… · p. 4
  • The model has two output heads: an N × L classifier for each RIS element's discrete phase and a beamformer head encoding AP beamformers in 2JM real values.These heads predict phase choices and AP beamforming vectors, respectively.Source: A. Learning Model Architecture and… · pp. 4–5
  • Training combines cross-entropy for discrete phase classification and MSE for beamformer regression, using AdamW, cosine annealing, and early stopping.Hidden-layer widths scale with N to accommodate different RIS sizes; key parameters are listed in Table I.Source: A. Learning Model Architecture and… · p. 5, Table I · p. 5

B. Numerical Results

The simulations compare joint AP/RIS optimization and learning-assisted modes across network sizes, RIS sizes, and transmit powers. The learning-assisted warm start approaches converged AO performance with fewer iterations, while joint optimization outperforms the TDM and random-phase benchmarks in the reported cases.

Evaluation setup

  • The evaluation uses 1,000 channel and user-location realizations; learning modes include direct prediction and prediction followed by a few AO refinements.The indoor setup uses N=32, 64, or 128, with J∈{2, 4} APs and K∈{2, 4} users; training uses offline converged AO solutions.Source: B. Numerical Results · p. 5

Network size and benchmarks

  • For (J, K)=(2, 2) and (4, 4), joint optimization outperforms TDM and random RIS phases; the 4-AP case achieves higher sum rate than the 2-AP case.The comparison is at 30 dBm and N=128.Source: B. Numerical Results · p. 5

RIS size

Transmit power

  • With J=K=4, sum rate increases with transmit power, and the improvement becomes more pronounced above 10 dBm.Source: B. Numerical Results · p. 5

AO convergence

  • Randomly initialized AO requires approximately 10–12 iterations at the 50th percentile, highlighting its online-iteration burden for latency-sensitive XR.Source: B. Numerical Results · p. 5

Learning-assisted convergence

  • At N=16–128, NN+AO uses ∼0.1–4.7 iterations versus AO’s ∼1.6–10.2 while achieving nearly identical sum rate; NN+AO takes 98 ms versus 220 ms for AO-only at N=128.NN-only takes 0.5 ms at N=128 and approximates the AO-only CDF reasonably well, particularly at moderate N.Source: B. Numerical Results · p. 5

V. CONCLUSION

The conclusion presents joint AP precoding and RIS phase design through AO for a shared single-RIS, multi-AP XR architecture. It also proposes a supervised initialization strategy that accelerates convergence while preserving near-optimal performance.

Conclusion

  • The shared single-RIS, multi-AP XR architecture is formulated as a sum-rate maximization problem and solved through AO for joint AP precoding and RIS phase design.Source: §V · p. 5
  • A supervised learning-assisted initialization strategy accelerates convergence while preserving near-optimal performance, reducing online optimization time.Source: §V · p. 6
  • Fig. 6 tracks iterations and sum rate across different RIS sizes N.Source: Figure 6 · p. 6
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