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End-to-End Mobility-Aware Multi-RIS Optimization via Blockage Detection and Closed-Form Riemannian Updates

Sehyun Ryu, Seungmin Choi, Hyun Jong Yang, John M. Cioffi

arXiv:2608.25393v1eess.SPeess.SY

TL;DR

Dynamic blockages can make RIS links unavailable in mobile mmWave MU-MIMO systems, while prior work often assumes ideal RIS availability. The paper combines indexed synchronization and energy-based per-RIS detection with mobility-aware joint BS–RIS optimization using SCRPA. Simulations report over 95% active-panel detection probability with virtually no false positives, and higher end-to-end WSR than baselines across tested mobility and system configurations.

Abstract

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Millimeter-wave (mmWave) multi-user MIMO systems are highly susceptible to dynamic blockages, and reconfigurable intelligent surfaces (RIS) have been introduced as a remedy. However, RIS links can themselves be blocked, while existing studies often assume ideal availability. This paper proposes an end-to-end mobility-aware multi-RIS optimization framework that integrates per-RIS blockage detection with closed-form Riemannian updates. The base station transmits short indexed synchronization signals, enabling each user to identify blocked panels via a simple energy test. Based on the detected feasible sets, we jointly optimize the BS precoder and RIS phases using a Stochastic Closed-form Riemannian Phase Alignment (SCRPA) algorithm, which ensures unit-modulus feasibility, monotone convergence, and low complexity. Extensive simulations validate reliable blockage detection and demonstrate significant weighted sum-rate and scalability gains compared to existing baselines.

I. INTRODUCTION

The paper addresses blockage-aware multi-RIS optimization for mobile mmWave MU-MIMO systems, where RIS visibility varies by user and existing designs often assume ideal availability. It combines standard-compliant per-RIS detection with joint BS–RIS optimization under mobility and imperfect CSIT.

Motivation

  • mmWave links are highly vulnerable to blockage, motivating RIS-based propagation control but also making blocked RIS links a central concern.Weak diffraction and line-of-sight-dominated propagation can cause abrupt SNR degradation and service interruptions.Source: §I · pp. 1–2

Research gap

  • Existing multi-RIS studies commonly optimize weighted sum rate under coupled active–passive constraints, while per-RIS online detection and CSI-interval execution remain open challenges.The paper identifies RIS-wise isolation under superposed multipath and timely optimization within NR CSI update intervals as the two critical gaps.Source: §I · pp. 1–2

Blockage detection

  • The framework periodically transmits short indexed m-sequence synchronization signals, enabling each UE to classify RIS panels through per-index correlation or energy testing.Cyclic shifts aligned with 3GPP NR provide panel indexing without learning, environment replay, or signaling overhead.Source: §I · p. 2, 1) Per-RIS Indexed Synchronization… · pp. 2–3

Evaluation

  • Ray-tracing simulations report reliable detection, robustness to CSIT aging and feedback delay, improved WSR and convergence efficiency, and a detection–optimization loop compatible with the NR CSI update interval.The reported evaluation compares against representative alternating-optimization and manifold-based baselines.Source: §I · p. 2

System model

Indexed synchronization

2) Effective Per-Subcarrier Channel:

The method models delayed channel knowledge and detects each UE’s active RIS set before transmission. It accounts for per-link aging, residual uncertainty, sensing overhead, and false-alarm-constrained threshold design.

Imperfect CSIT

  • At sensing time t0, the BS obtains noisy per-link channel estimates, which differ from the true channels at t0+∆ because of control and feedback delay.The model explicitly separates sensing-time estimates from later channel realizations.Source: 3) Imperfect CSIT with Per-Link Aging… · p. 3

Channel prediction

  • First-order temporal correlation is applied on a per-link basis rather than aging the entire cascaded channel with a single scalar.This provides the predicted effective channel for a candidate RIS configuration and active set.Source: 3) Imperfect CSIT with Per-Link Aging… · p. 3

Residual uncertainty

  • The residual channel mismatch captures estimation error, CSI feedback distortion, and mobility-induced innovation through a Gauss–Markov additive complex Gaussian model.The residual covariance represents the combined uncertainty sources.Source: 3) Imperfect CSIT with Per-Link Aging… · p. 3

Blockage detection

Sensing overhead

  • The sensing duration includes useful-sequence transmission, cyclic-prefix overhead, UE processing latency, and uplink-control reporting latency.These terms are represented by Ts, Lcp, Tproc, and Tctrl in the sensing-time expression.Source: C. Problem 1: Blockage Detection · p. 3

Detector design

  • Detection thresholds are designed using a Neyman–Pearson criterion under per-panel false-alarm constraints.The criterion controls the detector design for distinguishing blocked and unblocked RIS panels.Source: C. Problem 1: Blockage Detection · p. 3

D. Problem 2: Throughput Maximization within CSI Update Interval

The throughput problem allocates the CSI update interval between sensing, optimization, and data transmission, then maximizes expected cycle-averaged sum-rate under residual CSIT uncertainty. The sensing design uses short indexed pilots and CP processing to identify active RIS panels with low overhead.

Timing and overhead

  • The detect–optimize–transmit cycle must fit within the NR CSI update interval.The timing constraint compares the BS/RIS optimization runtime with the CSI update interval.Source: D. Problem 2: Throughput Maximization… · p. 4
  • The data phase is characterized by its duration and corresponding usable-data fraction within each CSI update interval.These quantities capture the throughput cost of sensing and optimization overhead.Source: D. Problem 2: Throughput Maximization… · p. 4

Throughput objective

Sensing design

  • Short CP-assisted indexed synchronization sequences identify active RIS panels with low sensing overhead.CP removal over the useful samples preserves circular convolution and the periodic correlation structure of cyclic shifts.Source: A. RIS-Indexed Synchronization Sequences · p. 4

B. Matched Filtering Model and NP Detection Metric

After CP removal, each UE applies fixed combining and matched filtering to the received indexed sensing signal. Stacking the matched-filter outputs exposes deterministic inter-index coupling caused by the m-sequences' constant cross-correlation.

Matched filtering

  • The received sensing signal is processed after CP removal, with each UE using a fixed equal-gain combiner.The effective channel notation refers to the BS–RIS-i–UE link under the sensing configuration.Source: B. Matched Filtering Model and NP… · p. 4

Detection metric

  • Figure 3 evaluates blockage-detection performance using the Jaccard index versus SNR across UE counts, RIS-panel counts, and sequence lengths.The evaluation uses target false-alarm probability α and per-RIS blockage probability BL.Source: Figure 3 · p. 5

Matched filtering

  • Matched-filter outputs are stacked into vectors of per-index observations and pilot coefficients.The stacked representation is Zk = [Zk,1, . . . , Zk,M]T and ak = [ak,1, . . . , ak,M]T.Source: B. Matched Filtering Model and NP… · p. 5

Index coupling

  • The stacked model makes explicit deterministic inter-index coupling induced by the m-sequences' constant cross-correlation.The coupling is represented through the all-ones matrix JM.Source: B. Matched Filtering Model and NP… · p. 5

C. Decoupled Detection via Inversion of the Coupling Matrix

The framework decouples per-RIS blockage detection through coupling-matrix inversion, then optimizes robust throughput with SCRPA’s stochastic block updates. The method supports continuous or quantized RIS phases, monotone convergence, and scalable complexity.

Detection

  • Inverting the coupling matrix removes deterministic inter-panel coupling and yields unbiased per-panel estimates for energy-based blockage tests.The resulting estimates determine each UE’s active RIS set.Source: C. Decoupled Detection via Inversion… · p. 5
  • Sequence length improves post-correlation SNR, but sensing airtime must remain within the NR CSI update interval.The standard-aligned choice is ℓ= 127, while longer sequences support larger panels or stricter reliability requirements.Source: D. Sequence-Length and Latency… · p. 5
  • The detector achieves high accuracy with short sequences, improving with SNR and sequence length, and benefits from fewer RIS panels and UEs.The reported accuracy improvement is attributed to reduced multi-user and inter-RIS interference.Source: E. Empirical Evaluation of Blockage… · p. 5
  • With α = 10−3, active-RIS identification exceeds 95% probability while producing virtually no false positives across tested configurations.Avoiding false positives prevents transmission toward inactive or blocked panels and wasted resources.Source: E. Empirical Evaluation of Blockage… · p. 5

Optimization

  • SCRPA uses sample-average stochastic block MM with closed-form BS precoder and RIS phase updates under mobility-induced CSIT uncertainty.RIS updates support continuous phases and optional β-bit projection for finite-resolution hardware.Source: §IV · pp. 6–7
  • Under continuous phases, SCRPA monotonically decreases the objective and converges to a block-stationary point; finite-resolution updates converge to a discrete block-stationary point.Its complexity scales linearly with S and NRIS and cubically with Nt through the precoder solve.Source: §IV · p. 7

A. Empirical Evaluation of WSR Optimization

The evaluation compares SCRPA with AO and manifold-based baselines under imperfect, aged CSI and mobility. SCRPA maintains stable WSR, achieves higher end-to-end WSR under blockage, and converges to a substantially higher solution despite more iterations.

Evaluation setup

  • SCRPA optimizes using imperfect and aged CSI, while all WSR results are evaluated on shared true instantaneous geometry-consistent channels.The common channel realizations support fair comparison across methods.Source: A. Empirical Evaluation of WSR… · p. 8
  • SCRPA is compared against AO–SPR, RMO–LS, AO–RMCG, and WMMSE–GRAD, representing deterministic, manifold-based, and imperfect-CSI optimization baselines.The baselines differ in their CSI assumptions and RIS phase-update procedures.Source: A. Empirical Evaluation of WSR… · p. 8

WSR performance

  • At 5 km/h, SCRPA maintains stable and high WSR by predicting channels from three recent observations and modeling residual uncertainty with SAA.The method leverages temporal correlation across consecutive channel realizations.Source: A. Empirical Evaluation of WSR… · p. 8

Convergence

  • 386 iterations is SCRPA’s average time to reach 99% of converged WSR, compared with 47 for AO-SPR and 413 for RMO-LS.SCRPA reaches a substantially higher WSR despite requiring more iterations than AO-SPR.Source: A. Empirical Evaluation of WSR… · pp. 8–9

End-to-end evaluation

  • With 30% per-link blockage, SCRPA consistently achieves substantially higher WSR than baselines across pedestrian speeds and (M, K) configurations.Its performance closely approaches the Strong LP Benchmark.Source: Figure 7 · p. 9

V. NUMERICAL EXPERIMENTS

The numerical experiments include a ray-tracing-based channel-generation scene from NVIDIA Sionna. The scene illustrates the placement of the BS, multiple RIS panels, and UEs.

Numerical experiments

  • NVIDIA Sionna generates a ray-tracing-based Munich urban scene containing the BS, multiple RIS panels, and UEs.The illustrated example uses M = 8 and K = 4.Source: Figure 8 · p. 9

A. Dataset

Experiments use geometry-consistent ray-traced Munich urban microcell channels with mobility, blockage, and RIS reflections. UE speeds span 5, 10, and 15 km/h, and figures report repeated channel-realization statistics.

Dataset

  • Datasets use NVIDIA Sionna’s ray-tracing-based Munich urban scene to model mobility, blockage, and RIS-assisted reflections.The deployment follows a typical 3GPP urban microcell scenario.Source: A. Dataset · p. 9
  • At v = 10 km/h, WSR is evaluated every 5 ms while algorithms use only past channel-state information for sequential optimization.The figure reports mean and standard deviation over 50 channel realizations.Source: Figure 9 · p. 10
  • SCRPA performance at RX-SNR = 10 dB is evaluated for 10 km/h mobility with M = 16, K = 8, and 2-, 4-, or 8-bit RIS quantization.Mean WSR is computed over 50 independent channel realizations with one-standard-deviation error bars.Source: Figure 10 · p. 10
  • UEs are randomly initialized within a central urban microcell area and move along straight-line trajectories with planar receive arrays.The spatial region is on the order of 10^2 meters.Source: A. Dataset · p. 10
  • UE speeds are v ∈{5, 10, 15} km/h, representing pedestrian and low-mobility mmWave scenarios.Dominant beam directions remain stable across several samples while small-scale fading and phase variations remain non-negligible.Source: A. Dataset · p. 10

B. End-to-End Operation under Mobility

The end-to-end framework combines per-RIS blockage detection with SCRPA-based WSR optimization under mobility, imperfect CSI, and phase quantization. Simulations show high WSR, practical timing, favorable complexity, and scalability across RIS and UE configurations.

End-to-End Performance

  • 30% per-link blockage probability still yields substantially higher WSR for SCRPA than baselines across pedestrian speeds and (M, K) configurations.Performance closely approaches the Strong LP Benchmark.Source: B. End-to-End Operation under Mobility · p. 10
  • 5 ms execution preserves stable and high WSR under continuous user mobility when the detection–optimization loop completes within the CSI update interval.The algorithm is executed sequentially at 5 ms resolution while users follow prescribed trajectories.Source: B. End-to-End Operation under Mobility · p. 10

Complexity and Timing

  • SCRPA requires the third smallest FLOP count while achieving significantly higher WSR than the lower-complexity WMMSE-GRAD and AO-SPR baselines.The joint performance–complexity comparison identifies SCRPA as having the most favorable end-to-end trade-off.Source: B. End-to-End Operation under Mobility · p. 10
  • 3.869 GFLOPs is SCRPA’s total cost for M = 32 RIS panels and K = 16 UEs, requiring approximately 0.774 TFLOPs/s to meet a 5 ms budget.The reported throughput requirement is within contemporary general-purpose computing capabilities.Source: B. End-to-End Operation under Mobility · pp. 10–11

Scalability and Robustness

  • SCRPA maintains stable convergence and consistent WSR gains as the numbers of RIS panels and UEs increase, indicating scalable operation.The effective-channel and optimization dimensions grow rapidly with system size.Source: C. Robustness and Scalability · p. 11
  • The 4-bit versus 8-bit WSR gap remains within approximately 0.3%, while SCRPA consistently outperforms baselines across 2-, 4-, and 8-bit resolutions.Performance remains close to the Strong LP Benchmark under all tested quantization levels.Source: C. Robustness and Scalability · p. 11

Framework

  • The framework explicitly addresses user mobility and dynamic blockage under time-varying and imperfect CSI through standard-compliant per-RIS detection and robust WSR optimization.Indexed m-sequences identify active RIS panels, while SCRPA provides closed-form BS precoder and hardware-constrained RIS phase optimization.Source: §VI · p. 11
  • Ray-tracing simulations report spectral-efficiency gains over representative baselines under CSI uncertainty and RIS phase quantization, with favorable scaling toward dense multi-RIS deployments.Analytical complexity and timing evaluations verify practical CSI update interval requirements.Source: §VI · p. 11

APPENDIX A PROOF OF THEOREM 1

The proof analyzes SCRPA as successive receiver/weight, BS precoder, and RIS phase block updates for a fixed-ensemble SAA WMMSE objective. It establishes the update properties underlying monotonic descent for continuous and finite-resolution RIS phases.

Proof Setup

  • The objective is continuous and bounded below, while the BS precoder feasible set is compact and the RIS feasible set is compact or finite.The feasible-set properties support the convergence argument.Source: A. Preliminaries · p. 11
  • SCRPA’s full iteration successively updates receiver/weight blocks, the BS precoder, and RIS phases for a fixed Monte Carlo ensemble.The proof treats the ensemble generated at outer iteration t as fixed.Source: B. Monotonic Descent of Each Block… · p. 11, A. Preliminaries · p. 11

Block Updates

  • MMSE receiver and optimal weight updates jointly minimize each separable block subproblem for fixed BS precoder and RIS phases.The objective is separable across user and ensemble indices in these blocks.Source: B. Monotonic Descent of Each Block… · p. 11
  • The BS precoder update globally minimizes its convex quadratic subproblem under the power constraint when RIS phases and receiver/weight blocks are fixed.This block update therefore does not increase the objective.Source: B. Monotonic Descent of Each Block… · p. 12

RIS Phase Updates

  • For continuous RIS phases, SCRPA majorizes the phase subproblem quadratically and obtains a closed-form unit-modulus update by minimizing the majorizer.The parameter Li is selected to ensure majorization, for example by backtracking.Source: B. Monotonic Descent of Each Block… · p. 12
  • For finite-resolution phases, elementwise projection onto the discrete feasible set solves the discrete MM subproblem and ensures monotonic decrease of the surrogate.The resulting sequence converges to a discrete block-stationary point.Source: B. Monotonic Descent of Each Block… · p. 12

C. Convergence

The convergence proof combines the block updates into a full SCRPA iteration and applies lower-bounded block-MM arguments. Continuous phases converge to block-stationary accumulation points, while quantized phases converge to discrete block-stationary solutions.

Continuous Phases

  • Each full continuous-phase SCRPA iteration satisfies the block-MM descent conditions for the fixed-ensemble SAA objective.The convergence argument uses the combined receiver/weight, precoder, and RIS phase updates.Source: C. Convergence · p. 12
  • Since J is bounded below, the objective sequence converges, and every accumulation point is block-stationary for the fixed-ensemble SAA problem.This follows from standard block-MM convergence results.Source: C. Convergence · p. 12

Finite-Resolution Phases

  • Under quantized RIS phases, SCRPA converges to a discrete block-stationary solution where no single block update further decreases the MM surrogate.The stationarity notion is defined over the finite-resolution feasible set.Source: C. Convergence · p. 12

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