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Reconfigurable Intelligent Surfaces with Reflection Pattern Modulation: Beamforming Design and Performance Analysis

Shaoe Lin, Beixiong Zheng, George C. Alexandropoulos, Miaowen Wen, Marco Di Renzo, Fangjiong Chen

arXiv:2008.02555v1cs.ITeess.SP

TL;DR

RIS information transfer without transmit RF chains is challenging because passive surfaces lack signal-processing capability. This paper proposes RPM for joint passive beamforming and RIS information transfer, optimizes AP and RIS beamforming under statistical RIS-state knowledge, and analyzes outage and achievable rate. The scheme improves achievable rate over a conventional full-ON RIS system despite losing received signal strength.

  • Problem

    RISs need a low-cost way to convey their own information through reflection without transmit RF chains, but passive hardware makes this challenging.

  • Method

    The paper proposes RPM and jointly designs AP active beamforming and RIS passive beamforming, using alternating optimization for the non-convex problem.

  • Results

    The RIS-RPM scheme improves achievable rate over a conventional full-ON RIS-assisted system despite reduced received signal strength, while its asymptotic outage probability is derived in closed form.

  • Takeaways & Limitations

    Reflection pattern modulation supports dual-use passive beamforming and RIS information transfer within the considered MISO system.

Abstract

from arXiv · show

Recent considerations for reconfigurable intelligent surfaces (RISs) assume that RISs can convey information by reflection without the need of transmit radio frequency chains, which, however, is a challenging task. In this paper, we propose an RIS-enhanced multiple-input single-output system with reflection pattern modulation, where the RIS can configure its reflection state for boosting the received signal power via passive beamforming and simultaneously conveying its own information via reflection. We formulate an optimization problem to maximize the average received signal power by jointly optimizing the active beamforming at the access point (AP) and passive beamforming at the RIS for the case where the RIS's state information is statistically known by the AP, and propose a high-quality suboptimal solution based on the alternating optimization technique. We analyze the asymptotic outage probability of the proposed scheme under Rayleigh fading channels, for which a closed-form expression is derived. The achievable rate of the proposed scheme is also investigated for the case where the transmitted symbol is drawn from a finite constellation. Simulation results validate the effectiveness of the proposed scheme and reveal the effect of various system parameters on the achievable rate performance. It is shown that the proposed scheme outperforms the conventional RIS-assisted system without information transfer in terms of achievable rate performance.

I. INTRODUCTION

The paper introduces reflection pattern modulation (RPM), enabling a passive RIS to enhance AP–user communication while conveying its own information through ON/OFF reflection states. It addresses practical RIS design by jointly optimizing AP and RIS beamforming with statistically known RIS states and evaluates outage and achievable-rate performance.

  • Motivation: Without transmit RF chains, RIS information can be delivered through reflection, avoiding the higher hardware cost and energy consumption of multiple transmit RF chains.This approach remains challenging because RISs lack signal-processing capability and contain many unit cells.
  • Related work: Earlier passive beamforming and information-transfer schemes could suffer high outage probability because their number of activated elements fluctuates over time.RPM is motivated as a way to combine information transfer with controlled reflection patterns.
  • Reflection pattern modulation: RPM uses selected ON-state RIS elements to form a beam toward the receiver while encoding RIS information in their indices.The scheme provides passive beamforming and information transfer without requiring transmit RF chains at the RIS.
  • Joint beamforming design: The paper jointly optimizes AP active beamforming and RIS passive beamforming to maximize average received signal power when the AP knows RIS ON/OFF states statistically.Because the formulation is non-convex, an alternating-optimization algorithm obtains a high-quality suboptimal solution.
  • Performance analysis: The proposed scheme derives a closed-form asymptotic outage probability over Rayleigh fading and shows that phase-shift design can increase diversity gain.The analysis also considers achievable rate when transmitted symbols come from a finite constellation.
  • Performance results: RIS-RPM outperforms a conventional full-ON RIS-assisted system in achievable rate despite losing received signal strength.Varying the number of ON-state elements offers a potential trade-off between received signal power and achievable rate.

II. SYSTEM DESCRIPTION AND CHANNEL ESTIMATION

The paper models an RIS-enhanced MISO system in which an RIS supports the AP-to-user link while a controller reconfigures its elements for passive beamforming and reflection modulation. It assumes quasi-static block-fading channels whose realizations remain constant over coherence blocks and are i.i.d. across blocks.

  • System model: The system comprises an AP with N transmit antennas, an L-element RIS, and a single-antenna user.An RIS controller reconfigures element phase shifts and/or reflection amplitudes and exchanges information with the AP.
  • System model: The RIS controller uses sensors to collect environmental data, typically low-rate bursty data intended for the user.
  • Channel model: The AP-user, AP-RIS, and RIS-user links are modeled as quasi-static block-fading channels.Channels remain unchanged over a coherence block of T_c symbol sampling periods and are i.i.d. across coherence blocks.
  • Channel model: The block-fading assumption is motivated by RIS deployment for low-mobility users in their vicinity.

A. System Model

The proposed reflection pattern modulation activates selected RIS groups to both enhance the reflected signal and encode RIS information in their ON-state indices. Grouping reduces the combinatorial burden associated with selecting active elements, while ON groups use maximum reflection amplitude and configurable phase shifts.

  • Reflection pattern modulation: For each symbol duration, K of L elements are ON, equivalently K̄ of G groups are ON, yielding information through their index combinations.The paper’s construction uses K̄ ≤ G ON groups and G−K̄ OFF groups.
  • Reflection pattern modulation: Grouping addresses the enormous calculation and storage overhead caused by exponentially increasing K-combinations as the number of RIS elements grows.
  • Reflection pattern modulation: The RIS conveys information through the indices of groups randomly turned ON, while the remaining groups are deliberately turned OFF.The grouping scheme partitions L elements into G adjacent groups, each containing grouping size L̄ elements with a common reflection coefficient.
  • Reflection coefficients: ON-state groups use maximum reflection amplitude β_g = 1, while their common reflection coefficients include configurable phase shifts.The grouped reflection vector θ has K̄ nonzero entries, expressed as ||θ||_0 = K̄.
  • Signal model: The received signal combines the AP-user direct channel with the grouped cascaded AP-RIS-user channel under RIS reflection.The transmitted symbol x is drawn from an M-ary constellation, and noise is modeled as AWGN.
  • Information transmission: The RIS reflection pattern conveys information through ON/OFF states while the AP symbol conveys a separate explicitly transmitted information component.The received information therefore has an AP part represented by x and an RIS part embedded in θ.

B. Channel Estimation

Channel estimation obtains the AP-RIS and direct AP-user CSI at the AP using channel reciprocity and TDD pilot signaling. After estimating the channels, the AP jointly designs AP beamforming and RIS group phase shifts to increase received signal power under statistically known RIS state information.

  • CSI acquisition: The AP requires the AP-RIS channel H and direct AP-user channel h_d to jointly design active and passive beamforming.
  • Pilot signaling: Using channel reciprocity and TDD, the AP obtains CSI from G + 1 consecutive pilot symbols sent by the user.The RIS applies a phase-shift state during each pilot, and the AP receives the resulting pilot signal vectors.
  • Channel estimation: A DFT-based phase-shift pattern is used to estimate H and h_d from the received pilot signals.
  • Beamforming configuration: After CSI acquisition, the AP jointly optimizes its active beamforming and the RIS groups’ phase shifts, then communicates the optimized phases to the RIS controller.
  • Beamforming configuration: The subsequent design maximizes average received signal power using statistical ON/OFF state information because the instantaneous RIS state is not available to the AP.

III. BEAMFORMING DESIGN BASED ON STATISTICAL ON/OFF STATE INFORMATION

Because the AP knows only the RIS ON/OFF-state statistics, the paper designs beamforming to maximize average received signal power and thereby improve outage performance. The resulting problem is non-convex, so an alternating optimization algorithm provides a high-quality suboptimal solution by iteratively updating AP and RIS beamformers.

  • Problem formulation: The design objective is to minimize outage probability by maximizing average received signal power under statistically known RIS ON/OFF states.The AP cannot access instantaneous RIS states, so the optimization uses their covariance matrix and mean vector.
  • Problem formulation: The RIS reflection vector is represented as θ = Φs, where s contains group ON/OFF states and Φ is a diagonal phase-shift matrix.Each state entry is 1 for ON and 0 for OFF, while the RIS phase shifts satisfy unit-modulus constraints.
  • Problem formulation: The outage formulation imposes maximum AP transmit power and unit-modulus RIS reflection constraints, making direct optimization difficult.
  • Problem formulation: The formulated optimization is non-convex because its objective is non-concave in AP and RIS beamformers, the phase-shift constraint is non-convex, and the variables are mutually coupled.
  • Solution method: An alternating optimization algorithm finds a high-quality suboptimal solution by fixing one beamformer while iteratively optimizing the other.
  • Solution method: The algorithm initializes the RIS phase matrix, updates AP beamforming through a maximum-eigenvalue eigenvector, and updates RIS phases using convex optimization and Gaussian randomization.Iterations stop when the fractional objective increase falls below a threshold or the maximum iteration count is reached.

B. Joint Beamforming Design

The paper jointly designs AP active beamforming and RIS passive beamforming by alternating optimization. The phase-shift subproblem is relaxed to an SDP, while the active-beamforming update uses the maximum-eigenvalue eigenvector.

  • The active-beamforming update uses the eigenvector associated with the maximum eigenvalue of the Hermitian matrix R̃, normalized to unit norm.This gives w* = v_max/∥v_max∥.
  • The passive phase-shift update is a non-convex QCQP that is homogenized and relaxed into a convex SDP by removing the rank-one constraint.The relaxed SDP can be solved with standard convex optimization solvers, but its solution may not be rank one.
  • The recovered phase-shift vector drives passive beamforming for the selected ON-state groups, while the remaining RIS groups are switched OFF.The resulting design supports RIS reflection-pattern modulation through the selected group configuration.
  • Alternating optimization iteratively updates the active beamformer and RIS phase shifts until the objective increase falls below a threshold or the iteration limit is reached.The objective is non-decreasing and bounded by the finite transmit-power constraint, supporting convergence.
  • The overall computational complexity is O((N^3 + (G + 1)^4.5)I), combining the active-beamforming and SDP costs over I iterations.The eigenvalue step costs O(N^3), and the SDP has worst-case complexity O((G + 1)^4.5).

IV. BEAMFORMING DESIGN BASED ON INSTANTANEOUS ON/OFF STATE INFORMATION

With instantaneous RIS ON/OFF-state information available at the AP, the paper jointly optimizes active and passive beamforming to maximize received signal power. Alternating optimization yields iterative MRT and phase-shift updates with a non-decreasing objective.

  • The resulting analysis investigates outage probability for the proposed RIS-RPM scheme under the instantaneous-state beamforming setting.
  • The proposed design maximizes received signal power by jointly designing AP active beamforming and RIS passive beamforming from instantaneous ON/OFF-state information.The AP is assumed to know the RIS state exactly in real time.
  • For a fixed active beamformer, each ON-state group receives a unit-modulus phase shift chosen using the triangle inequality.The resulting phase-shift update is given for the selected group indices I.
  • The optimal active beamformer is maximum-ratio transmission, and it is alternated with the RIS phase-shift update until convergence.One variable is optimized while the other remains fixed in each iteration.
  • The alternating procedure converges because the objective value is non-decreasing and the optimal objective is finite.

A. Outage Probability

The outage analysis assumes a deterministic AP–RIS LoS link and Rayleigh RIS–user and AP–user links. Under perfect CSI, properly designed RIS phases improve diversity gain, which increases with the number of ON-state groups.

  • The channel model uses a fixed LoS AP–RIS component together with Rayleigh RIS–user and AP–user components.This corresponds to κ_AR = ∞, κ_Ru = 0, and κ_Au = 0.
  • The diversity gain k_x increases linearly with the number of ON-state groups K̄ and satisfies 1 ≤ k_x ≤ K̄ + 1, with equality only when K̄ = 0.
  • At high SNR, the asymptotic outage expression tracks the simulated outage trend well, and increasing K̄ increases the diversity gain.Figure 2 evaluates N = 1 with G = 4, R = 1, σ_r^2 = 1, and perfect CSI at the AP.
  • Properly designed RIS phase shifts provide higher diversity gain than the unit-phase-shift benchmark.The unit-phase design requires no CSI for setting RIS phase shifts and therefore avoids channel acquisition for that purpose.

B. Achievable Rate

The achievable-rate analysis treats RIS reflection patterns and finite-constellation AP symbols as jointly conveyed information. It derives rate expressions for statistical and instantaneous-state beamforming using mutual information conditioned on effective channels.

  • For finite constellations, the AP symbols are discrete and equiprobable, while RIS ON-state group combinations are also independent and equiprobable.The combination set S contains J possible ON-state realizations.
  • 1) Beamforming Design Based on Statistical ON/OFF State Information: The achievable rate for statistical-state beamforming is given by a mutual-information expression conditioned on the effective cascaded and direct channels.The user is assumed to know these effective channels, which can be acquired through downlink pilots and direct-link estimation.
  • 1) Beamforming Design Based on Statistical ON/OFF State Information: Proposition 1 gives the achievable rate for practical statistical-state beamforming, with the received-noise term modeled as a complex Gaussian variable.
  • 2) Beamforming Design Based on Instantaneous ON/OFF State Information: For instantaneous-state beamforming, the rate is conditioned on the full effective channel associated with the selected RIS state and optimized beamformers.The user is assumed to know the effective channel f(I,H,h_d).
  • 2) Beamforming Design Based on Instantaneous ON/OFF State Information: Proposition 2 provides the achievable-rate expression for the instantaneous-state beamforming design.The expression again includes a complex Gaussian noise variable.

VI. SIMULATION RESULTS AND DISCUSSIONS

Simulations evaluate Algorithm 1 and RIS-RPM against non-RIS, random-phase, full-ON, upper-bound, and PBIT benchmarks under specified channel and array settings. Algorithm 1 approaches the instantaneous-CSI upper bound with perfect CSI, while estimated CSI degrades performance at large distances.

  • A. Performance of Algorithm 1: RIS-assisted schemes significantly enhance average received power near the RIS compared with the scheme without RIS.
  • A. Performance of Algorithm 1: Algorithm 1 significantly outperforms the random phase shift scheme, while remaining upper-bounded by beamforming designed with instantaneous RIS ON/OFF information.The comparison uses average received signal power, with the instantaneous-state design serving as an upper bound.
  • A. Performance of Algorithm 1: Algorithm 1 incurs only a small received-power loss versus the no-information-transfer scheme because one RIS group is deliberately turned OFF for RIS information transmission.The benchmark keeps all RIS-element groups active for reflected-signal enhancement.
  • A. Performance of Algorithm 1: With perfect CSI, Algorithm 1 nearly matches the upper bound; with estimated CSI, performance worsens when the user is far from both AP and RIS.The degradation is attributed to lower received training-signal power and poorer channel estimation at larger distances.

B. Outage Rate Performance

The outage and achievable-rate experiments compare RIS-RPM with PBIT and conventional benchmarks across transmit power, distance, ON-state groups, and grouping ratio. Fixed ON-state counts reduce power fluctuations, while the preferred grouping depends on transmit power and trades received power against RIS information.

  • C. Achievable Rate Performance: RIS-assisted achievable rates increase as the user approaches the RIS and decrease when the user moves away from both AP and RIS.The results indicate that a nearby RIS can enhance the rate of a cell-edge user.
  • C. Achievable Rate Performance: RIS-RPM can improve achievable rate over the full-ON no-information-transfer scheme despite lower received signal power, especially at high AP transmit power.At low transmit power and K̄ = 2, the information gain may not compensate for the received-power loss; at high power, RIS-RPM is significantly superior.
  • C. Achievable Rate Performance: When AP transmit power is high, PBIT achieves the maximum achievable rate among the considered schemes.

3) Effect of RIS-elements Grouping Ratio:

RIS-elements grouping controls the balance between beamforming freedom, RIS information, and channel-estimation overhead. Larger grouping ratios improve the supported achievable rate but increase pilot overhead, while the paper’s broader design combines RPM with statistical-CSI beamforming and analyzes outage and finite-constellation rates.

  • 3) Effect of RIS-elements Grouping Ratio:: With fixed average ON-state elements, larger G achieves better achievable-rate performance because it supports both higher passive beamforming gain and more RIS information.
  • 3) Effect of RIS-elements Grouping Ratio:: Larger grouping ratios improve RIS-RPM achievable-rate performance by increasing reflection-design degrees of freedom and the additional information conveyed.
  • 3) Effect of RIS-elements Grouping Ratio:: Increasing the grouping ratio raises pilot-overhead ratio ξ, leaving less time for data transmission and reducing average achievable rate.This creates a direct overhead-related boundary on the grouping-ratio benefit.
  • VII. CONCLUSIONS: The proposed RPM scheme jointly uses RIS passive beamforming and information transfer, with statistical-CSI beamforming optimized by alternating optimization.
  • VII. CONCLUSIONS: The paper derives a closed-form asymptotic outage probability under Rayleigh fading and analyzes achievable rate for finite-constellation transmitted symbols.
  • VII. CONCLUSIONS: RIS-RPM improves achievable rate over the conventional full-ON RIS-assisted system despite losing received signal power.
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