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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.

  • Problem

    Dynamic blockage can affect both mmWave links and RIS links, while multi-RIS designs need online per-panel detection and optimization within CSI update intervals.

  • Method

    The framework uses short indexed m-sequence signals for per-RIS energy detection, then jointly optimizes BS precoding and quantized RIS phases with stochastic SCRPA under aged, imperfect CSIT.

  • Results

    Over 95% active-panel detection probability with virtually no false positives; under 30% per-link blockage, SCRPA achieves substantially higher WSR than baselines across tested speeds and (M, K) configurations.

  • Takeaways & Limitations

    The detection–optimization–transmission loop supports mobility-aware multi-RIS operation with favorable scalability and practical CSI-update timing.

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.
  • 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.
  • 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.
  • 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.
  • System model: The detected active RIS sets determine the multi-RIS downlink model, whose passive phase vectors satisfy unit-modulus constraints for each reflecting element.The system serves K UEs with M distributed passive RIS panels, and each UE may observe a different unblocked subset.
  • Indexed synchronization: CP-assisted sensing preserves cyclic correlation structure by making multipath convolution circular over the useful samples, with longer m-sequences available when the number of RIS panels is large.The default sequence length is ℓ = 127, while lengths 255 and 511 are feasible for larger M.

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.
  • 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.
  • 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.
  • Blockage detection: Each UE performs a per-RIS energy test and reports the detected active set to the BS as an uplink-control bitmap.The detected set identifies which RIS panels are treated as available for subsequent optimization.
  • 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.
  • 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.

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.
  • Timing and overhead: 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.
  • Throughput objective: The design objective maximizes cycle-averaged sum-rate using the BS precoder and RIS control variables.The formulation defines the precoder matrix, instantaneous achievable rate, and resulting design problem.
  • Throughput objective: The objective expectation accounts for residual CSIT uncertainty.This incorporates imperfect channel-state information into the throughput formulation.
  • 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.

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.
  • 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.
  • 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.
  • 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.

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.
  • Detection: 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.
  • Detection: 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.
  • Detection: 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.
  • 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.
  • Optimization: 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.

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.
  • Evaluation setup: 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.
  • 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.
  • 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.
  • 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.

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.

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.
  • Dataset: 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.
  • Dataset: 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.
  • Dataset: 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.
  • Dataset: 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.

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.
  • End-to-End Performance: 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.
  • 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.
  • Complexity and Timing: 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.
  • 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.
  • Scalability and Robustness: 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.
  • 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.
  • Framework: 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.

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.
  • Proof Setup: 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.
  • 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.
  • Block Updates: 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.
  • 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.
  • RIS Phase Updates: 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.

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.
  • Continuous Phases: 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.
  • 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.
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