FARIS: Fluid-Active-RIS

1. Problem Statement

The paper addresses two fundamental limitations in current Reconfigurable Intelligent Surface (RIS) technology for 6G networks:

• Multiplicative Fading: Conventional passive RIS (PRIS) suffers from severe double-reflection path loss (Tx-RIS $\times$ RIS-Rx), which significantly degrades signal quality. While Active RIS (ARIS) introduces amplification to counteract this, it operates on a fixed geometry, limiting its ability to concentrate energy on spatially favorable locations.
• Rigid Spatial Degrees of Freedom (DoF): Conventional RIS and even Fluid RIS (FRIS) have structural constraints. FRIS allows element movement to gain spatial DoF but relies on passive reflection, failing to fully overcome multiplicative fading. Conversely, ARIS amplifies signals but lacks the spatial adaptability to optimize where the amplification occurs.

The Core Challenge: How to design a system that simultaneously exploits spatial mobility (to select optimal reflection points) and active amplification (to overcome path loss) within a unified, power-efficient architecture, while solving the resulting complex mixed-integer non-convex optimization problem.

2. Methodology

A. System Model: Fluid-Active RIS (FARIS)

The authors propose FARIS, a novel architecture where each RIS element acts as a "fluidic active unit."

• Architecture: The RIS consists of $M$ candidate ports. Only $M_o$ ports are selected to be active at any time.
• Dual Capability: Selected elements can:
  1. Reposition: Move within a designated sub-region (Fluid Antenna System concept) to optimize spatial correlation and channel gain.
  2. Amplify: Apply active reflection with controllable gain ($g_i$) and phase ($\phi_i$) to compensate for path loss.
• Power Model: A realistic circuit-level power consumption model is established, accounting for:
  • $P_c$: Control/switching power for all $M$ candidates (logical control).
  • $P_{DC}$: DC bias power for the $M_o$ active reflection modules.
  • $\xi P_{RIS}$: Power consumed by the amplified signal.
  • Constraint: The total power must satisfy $P_{tot} \leq P_{max,t}$, leading to a constraint on the radiated power $P_{RIS}$.

B. Optimization Problem

The goal is to maximize the ergodic rate of the downlink system by jointly optimizing:

1. Continuous Variables: The active amplification-reflection vector $\mathbf{v}$ (containing magnitudes and phases).
2. Discrete Variables: The selection matrix $\mathbf{S}_{M_o}$ (which determines which $M_o$ ports out of $M$ are active).

This results in a mixed-integer non-convex optimization problem due to the coupling between discrete port selection and continuous beamforming, along with non-convity in the objective function (logarithm of a ratio).

C. Proposed Algorithm: Alternating Optimization (AO) Framework

To solve the problem, the authors develop an AO framework that iterates between two sub-problems:

1. Active Reflection Design (Fixed Port Selection):

   • Technique: Uses Sample Average Approximation (SAA) to handle the ergodic rate expectation.
   • Transformation: Applies a quadratic transform (fractional programming) to convert the fractional objective into a concave form.
   • Relaxation: Lifts the problem to a matrix variable $\mathbf{V} = \mathbf{v}\mathbf{v}^H$ and relaxes the rank-1 constraint.
   • Solution: Solves a convex conic subproblem (using Second-Order Cone constraints). If the solution is not rank-1, Gaussian randomization and magnitude projection are used to recover a feasible vector.
   • Guarantee: Proven to monotonically increase the objective function.

2. Discrete Port Selection (Fixed Reflection Vector):

   • Technique: Proposes a Cardinality-Constrained Cross-Entropy Method (CEM).
   • Mechanism: Samples port selection vectors from a Bernoulli distribution. It identifies an "elite" set of high-performing selections and updates the selection probabilities to fit this elite set.
   • Constraint Handling: Derives a closed-form update rule using a Lagrange multiplier to strictly enforce the cardinality constraint (exactly $M_o$ ports selected).
   • Guarantee: Proven to monotonically increase the empirical log-likelihood and ergodic rate.

3. Key Contributions

1. New Paradigm (FARIS): First work to formally integrate fluid port reconfigurability with active reflection in a single architecture, creating a coupled "spatial-amplitude" design space.
2. Practical Modeling: Developed a comprehensive power consumption model that distinguishes between the control power of all candidates and the amplification power of active elements, enabling realistic trade-off analysis.
3. Algorithmic Innovation:
   • An AO framework that decouples continuous and discrete optimization.
   • A novel Cardinality-Constrained CEM with a closed-form update for discrete port selection, ensuring strict adherence to hardware constraints.
   • Rigorous proofs of monotonic convergence and complexity analysis showing polynomial-time implementability.
4. Performance Validation: Demonstrated that FARIS outperforms existing baselines (Passive RIS, Active RIS, and Amplify-and-Forward relays) in terms of rate and power efficiency.

4. Simulation Results

Extensive Monte Carlo simulations were conducted to validate the framework:

• Near-Optimal Performance: The proposed AO framework achieves ergodic rates very close to a brute-force search (BFS) baseline but with drastically lower computational complexity.
• Superiority over Baselines:
  • vs. FRIS/ARIS: FARIS consistently achieves higher rates even with fewer active elements ($M_o$) or smaller physical apertures. For example, with $M_o=16$, FARIS outperformed a passive FRIS with $M_o=81$ by ~4 bps/Hz.
  • vs. AF Relay: FARIS offers a better rate-power trade-off than Amplify-and-Forward relays, avoiding the excessive hardware power consumption associated with independent transceivers.
• Convergence: The algorithm converges rapidly (within 15–20 iterations) despite the high dimensionality of the problem.
• Port Selection Behavior: The CEM algorithm naturally selects ports near the array boundaries, exploiting larger angular separation and lower spatial correlation to maximize diversity.

5. Significance

This paper establishes FARIS as a promising candidate for 6G wireless networks. By synergizing spatial mobility (fluidity) and signal amplification (activity), it overcomes the "multiplicative fading" bottleneck of passive RIS and the "fixed geometry" limitation of active RIS. The proposed framework provides a practical, computationally efficient path to realizing smart radio environments that can dynamically shape both the spatial distribution and the strength of reflected signals, offering a significant leap in spectral efficiency and coverage reliability.