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Fluid Reconfigurable Intelligent Surfaces: Joint On-Off Selection and Beamforming with Discrete Phase Shifts

Han Xiao, Xiaoyan Hu, Kai-Kit Wong, Hanjiang Hong, George C. Alexandropoulos, Chan-Byoung Chae

arXiv:2503.14601v1cs.ITmath.IT

TL;DR

Conventional RIS faces channel-estimation complexity, pilot overhead, and multiplicative fading. This letter proposes joint selection of FRIS element positions and discrete phase shifts using CEO, and reports a performance gain over conventional RIS in simulations.

  • Problem

    Conventional RIS faces channel-estimation complexity and high pilot overhead as passive element density grows, as well as multiplicative fading across the transmitter–RIS–receiver link.

    Source: §I · p. 1

  • Method

    An iterative CEO-based algorithm jointly optimizes FRIS element positions and discrete phase shifts to maximize achievable rate.

    Source: §I · p. 2

  • Results

    With M = 14 × 14, FRIS achieves a 40% performance gain over conventional RIS under identical conditions.

    Source: §IV · pp. 4–5

  • Takeaways & Limitations

    In the simulated SU-SISO setting, the proposed FRIS significantly outperforms its conventional RIS counterpart.

    Source: §V · p. 5

Abstract

from arXiv · show

This letter proposes a fluid reconfigurable intelligent surface (FRIS) paradigm, extending the conventional reconfigurable intelligent surface (RIS) technology to incorporate position reconfigurability of the elements. In our model, a `fluid' element is realized by a dense matrix of subelements over a given space and dynamically selecting specific elements for signal modulation based on channel conditions. Specifically, we consider a FRIS-assisted single-user single-input single-output (SU-SISO) system and formulate an optimization problem that can jointly optimize element selection and their discrete phase shifts to maximize the achievable rate. To address this problem efficiently, we propose an iterative algorithm based on the cross-entropy optimization (CEO) framework. Simulation results reveal that FRIS achieves significant performance gains over traditional RIS.

I. INTRODUCTION

Conventional RIS faces channel-estimation complexity, pilot overhead, and multiplicative fading; this letter proposes a port-based FRIS framework with discrete phase shifts and a CEO algorithm for joint design. It evaluates the framework against conventional RIS.

I. INTRODUCTION

  • RIS channel-estimation complexity and pilot overhead rise with element density, while multiplicative fading compounds the transmitter–RIS and RIS–receiver path losses.The paper frames additional degrees of freedom as a strategy for improving RIS-based systems without significant hardware complexity.Source: §I · p. 1
  • FAS adds shape and position flexibility, while earlier FRIS approaches raised concerns about physical movement or assumed perfect phase shifters [15], [16].The paper describes switched ports without physical movement in [16], alongside concerns about the practicality of perfect phase shifters.Source: §I · p. 1
  • The proposed FRIS uses densely distributed ports, spaced well below half a wavelength, and gives each activated fluid element a discrete phase shifter.The dense ports provide position reconfigurability within the available RIS surface.Source: §I · p. 1
  • The paper presents a signal-transmission model, formulates achievable-rate maximization with practical constraints, and proposes CEO to jointly optimize element positions and discrete phase shifts.The stated performance comparison is against conventional RIS.Source: §I · p. 2

II. SYSTEM MODEL

The system model is a FRIS-assisted SU-SISO link with on-off reflecting elements and a blocked direct path. It accounts for spatial correlation and represents the selected elements and their phase coefficients in the reflected link.

II. SYSTEM MODEL

  • The FRIS has M = My × Mz uniformly distributed on-off reflecting elements, with inter-element spacing d smaller than λ/2.The system is a SU-SISO link between a fixed-position-antenna base station and a single-fixed-position-antenna user.Source: §II · p. 2
  • Elements operate in ‘off’ mode without modulating the incident signal or ‘on’ mode to modify its electromagnetic properties; the direct BS–user link is assumed blocked.The paper treats an element as a port within a fluid element.Source: §II · p. 2
  • The model accounts for spatial correlation between closely spaced elements using Jake’s model and defines the channel fading vectors for the FRIS–BS and FRIS–user links.The fading-vector entries are circularly symmetric complex Gaussian with zero mean and unit variance.Source: §II · p. 2
  • For the received signal, cM elements are active; the selection matrix chooses distinct locations, while the reflected-coefficient matrix holds their phase coefficients.The model also specifies the BS power budget and additive white Gaussian noise.Source: §II · p. 2

A. Problem Formulation

The problem maximizes achievable rate through joint FRIS element selection and discrete phase-shift design. Its coupled non-convex and discrete constraints motivate a CEO-based optimization algorithm.

A. Problem Formulation

  • The objective maximizes achievable rate while jointly selecting FRIS elements and their discrete phase shifts.The formulation includes constant-modulus reflection coefficients, discrete phase shifts, element-selection choices, and a constraint that selected elements differ.Source: A. Problem Formulation · pp. 2–3
  • The objective and coupled constraints make the problem difficult for traditional optimization algorithms.The stated challenges include non-convexity, constant-modulus and discrete-variable constraints, element selection, and strong interdependence among variables.Source: A. Problem Formulation · p. 3
  • The proposed CEO-based algorithm optimizes all variables without resorting to alternative strategies.The authors propose CEO to address the formulation's combined optimization challenges.Source: A. Problem Formulation · p. 3

B. Algorithm Design

The CEO framework iteratively samples candidate solutions and updates a probability distribution using the best-performing solutions. It stops when consecutive optimal objective values differ by no more than a predetermined threshold.

B. Algorithm Design

  • CEO is a probabilistic learning method that iteratively generates and evaluates candidate solutions.The candidates are evaluated by their objective-function values.Source: B. Algorithm Design · p. 3
  • Sampling continues until the difference between consecutive iterations' optimal objective values reaches a predetermined threshold.The process begins with a sampling model characterized by tilting parameters based on variable characteristics.Source: B. Algorithm Design · p. 3
  • The sampling distribution is adjusted by minimizing cross-entropy against a reference distribution derived from the best-performing solutions.The adjusted parameters are used to generate new samples in subsequent iterations.Source: B. Algorithm Design · p. 3

1) Sampling distribution model for reflection coefficients:

The phase-shift sampling model represents each reflection coefficient with a discrete phase and assigns probabilities to its candidate values. Independent per-element sampling and a uniform random draw implement the specified distribution.

1) Sampling distribution model for reflection coefficients:

  • Each reflection coefficient is set to e^jφ, with each phase drawn from a discrete candidate set P.The constant-modulus condition is satisfied by this representation.Source: 1) Sampling distribution model for… · p. 3
  • The probabilities for an element's phase choices sum to one, and independence defines the joint distribution for generating φ.The probability matrix records the per-element probabilities for the candidate phase values.Source: 1) Sampling distribution model for… · p. 3
  • A uniform draw z in [0, 1] maps through cumulative probability intervals to a phase choice, yielding the designated sampling distribution.The text states that the generation rule produces phase values following their designated distribution.Source: 1) Sampling distribution model for… · p. 3

2) Sampling distribution model for element selection:

Element selection is sampled as a binary vector whose entries represent on or off states. The sampled vector is then adjusted to satisfy the required number of selected elements.

2) Sampling distribution model for element selection:

  • The binary selection vector ξ marks each element as on (1) or off (0).An on element reflects signals; an off element is inactive, and ξ determines the element-selection matrix.Source: 2) Sampling distribution model for… · p. 3
  • Each entry's probability g_m is the probability that the entry equals 1, defining the sampling distribution for ξ.The text applies the discrete-phase sampling approach to generate ξ.Source: 2) Sampling distribution model for… · p. 3
  • If the sampled active-element count differs from cM, lowest-probability active entries are turned off or highest-probability inactive entries turned on until it matches.The procedure corrects samples that do not satisfy the required count.Source: 2) Sampling distribution model for… · p. 3

3) Joint sampling distribution model:

The method represents feasible solutions with a joint sampling distribution whose tilting parameters are updated during optimization.

3) Joint sampling distribution model:

4) Updating formulas for tilting parameters:

The update procedure samples feasible solutions, favors high-performing samples, and adjusts the distribution parameters through cross-entropy minimization and smoothing.

4) Updating formulas for tilting parameters:

  • The procedure samples feasible solutions from the joint distribution and evaluates their objective values.The samples are ordered by objective value, with the best-ranked solutions forming the elite set.Source: 4) Updating formulas for tilting… · p. 4
  • The elite set defines a reference distribution, and the tilting parameters are tuned by minimizing cross-entropy.The cross-entropy problem is transformed into a convex optimization problem addressed with the Lagrange multiplier method.Source: 4) Updating formulas for tilting… · p. 4
  • The Lagrange multiplier is obtained using the equality constraint in (13a).The passage relates this multiplier to the result for P.Source: 4) Updating formulas for tilting… · p. 4
  • A smoothing technique modifies the tilting parameters, which are updated iteratively until adjacent objective values meet a predetermined threshold.The smoothing parameter ω lies in (0, 1).Source: 4) Updating formulas for tilting… · p. 4

IV. SIMULATION RESULTS

Simulations compare FRIS with conventional RIS and report higher achievable rates from position selection, with gains depending on the number of available positions and phase resolution.

IV. SIMULATION RESULTS

  • Rate growth diminishes as potentially valuable positions become less available, and the rate–location relationship depends on instantaneous channel conditions.The simulations use P_t^max = 30 dBm and a uniformly distributed conventional-RIS benchmark.Source: §IV · pp. 4–5
  • Achievable rate rises with c_M, while the FRIS–RIS performance gap narrows as c_M increases.The authors attribute the narrowing gap to FRIS progressively converging toward conventional RIS.Source: Figure 3 · p. 5, §IV · p. 5
  • 40% performance gain is reported for FRIS over conventional RIS at M = 14 × 14.The comparison uses identical conditions and the conventional RIS's best condition, c_M = 25 and b = 2.Source: §IV · pp. 4–5
  • FRIS surpasses conventional RIS at M = 16 × 16 even with c_M = 16 and b = 1.The reported performance advantage becomes more pronounced as the number of available positions increases.Source: §IV · pp. 4–5

V. CONCLUSION

The conclusion presents a dense on-off FRIS framework for increasing spatial degrees of freedom and jointly optimizing element positions and discrete phases.

V. CONCLUSION

  • The proposed FRIS uses a dense matrix of on-off elements to enhance degrees of freedom.For an SU-SISO system, the paper formulates rate maximization through joint position selection and discrete phase-shift design, then applies an iterative CEO algorithm.Source: §V · p. 5
  • Simulations show that the proposed FRIS significantly outperforms conventional RIS.Source: §V · p. 5
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