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Robust Joint Beamforming and Configuration Design in FARIS-Aided Systems
Hong-Bae Jeon, Yonghwi Kim, Hyung-Joo Moon, Kai-Kit Wong
TL;DR
The paper addresses robust multi-user downlink design for FARIS-assisted systems with imperfect CSI, where active amplification and port selection create coupled optimization challenges. It jointly designs the beamformer, FARIS coefficients, and active ports using a WMMSE reformulation and AO framework. Simulations report consistent gains over conventional designs under CSI uncertainty.
Problem
Robustly maximizing multi-user sum rate under CSI uncertainty requires jointly handling beamforming, FARIS configuration, active port selection, and practical power constraints.
Method
The paper uses a WMMSE reformulation followed by alternating optimization to solve the coupled nonconvex design through efficiently solvable subproblems.
Results
The proposed robust FARIS consistently outperforms conventional ARIS, FRIS, and RIS schemes under increasing CSI uncertainty and varying utilized-port counts.
Takeaways & Limitations
FARIS can jointly exploit active amplification and fluid spatial DoF to enlarge the robustness and performance design space under statistical CSI uncertainty.
Abstract
from arXiv · showhide
In this paper, we propose a robust transmission design for multi-user systems assisted by a fluid active reconfigurable intelligent surface (FARIS), which enables both active reflection and dynamic port selection and thereby offers enhanced flexibility, under imperfect channel state information (CSI). We formulate a robust minimum sum-rate maximization problem by jointly optimizing the base station beamformer, the utilized FARIS coefficients, and the active element selection, while explicitly accounting for CSI errors and practical power constraints. The resulting problem is inherently nonconvex due to the coupled optimization variables and discrete port-selection structure. To tackle this challenge, we first reformulate the original problem via a weighted minimum mean square error (WMMSE) approach and then devise an alternating optimization (AO) framework, where each resulting subproblem admits efficient solutions and the overall algorithm converges to a stationary point. Simulation results demonstrate that the proposed robust FARIS scheme consistently outperforms conventional designs, highlighting the effectiveness of jointly leveraging degree-of-freedom (DoF) enhancement and active signal amplification under CSI uncertainty.
I. INTRODUCTION
FARIS combines active signal amplification with dynamic port selection, expanding the design space beyond passive and fixed-location RIS architectures. This paper targets robust multi-user transmission under imperfect CSI by jointly optimizing beamforming, FARIS configuration, and port activation under practical constraints.
- I. INTRODUCTION: Active-RIS amplifies signals and mitigates double-fading, but introduces thermal noise and stringent surface power constraints.These complications become especially important under imperfect CSI.
- I. INTRODUCTION: Fluid-RIS activates a subset of ports from dense candidate locations, adding location diversity and spatial DoF to phase control.Its passive architecture limits the benefits available from amplification.
- I. INTRODUCTION: FARIS unifies active amplification and dynamic port activation, enabling selective use of favorable signal paths and spatial locations.This hybrid structure provides a richer design space than conventional RIS, active-RIS, or fluid-RIS architectures.
- I. INTRODUCTION: The paper formulates robust minimum sum-rate maximization under CSI uncertainty by jointly optimizing the beamformer, FARIS coefficients, and active port selection.The formulation accounts for CSI errors and practical power constraints at both the base station and FARIS.
- I. INTRODUCTION: A WMMSE reformulation and alternating optimization framework decompose the coupled nonconvex design into convex or efficiently solvable subproblems.The nonconvexity arises from coupling among beamforming, active-surface coefficients, and port selection.
- I. INTRODUCTION: Numerical results show that the proposed robust FARIS design outperforms the benchmarks by jointly exploiting active amplification and additional spatial DoF under CSI uncertainty.The reported comparison concerns conventional benchmark designs.
II. SYSTEM MODEL
The system jointly models FARIS port selection, active reflection, imperfect CSI, and BS beamforming under practical power constraints. The resulting robust design problem is nonconvex because these variables are coupled.
- II. SYSTEM MODEL: Each FARIS port operates either on, applying controllable amplitude and phase changes, or off, isolating itself with a matched load.The port model is inherited from the fluid-antenna architecture, with FARIS adding an amplification module.
- II. SYSTEM MODEL: The downlink system has an N-antenna BS, K single-antenna users, and M candidate FARIS ports, of which only M_o are active.The candidate ports are arranged as M = M_x × M_x reflective elements on a square aperture.
- II. SYSTEM MODEL: The FARIS operator combines port selection with per-port coefficients that encode phase shifts and amplification gains.The selected-port representation uses v, while the equivalent vector w provides a compact selection-free formulation.
- II. SYSTEM MODEL: A continuous activation vector p relaxes binary port selection while enforcing a fixed activation budget and coupling each coefficient w_m to its activation level.For binary p, the perspective constraint sets inactive coefficients to zero and bounds active coefficients by g_max.
- II. SYSTEM MODEL: The robust formulation accounts for statistical CSI errors, BS beamformer power, FARIS output power, and hardware consumption from control, switching, and DC bias circuits.The optimization jointly designs F and w under the resulting power constraints.
- II. SYSTEM MODEL: The joint beamforming and FARIS-coefficient problem remains nonconvex, motivating an alternating optimization framework.The nonconvexity arises from coupling the beamformer with the utilized FARIS coefficients and selection structure.
A. WMMSE reformulation with auxiliary variables
The paper reformulates the robust rate objective using auxiliary receiver and weight variables in a WMMSE framework. This reformulation preserves the robust rate relationship while enabling an alternating optimization procedure.
- A. WMMSE reformulation with auxiliary variables: The user MSE is defined under a linear receiver, and channel-error statistics provide its closed-form expression.The formulation uses the receiver u_k together with the BS beamformer and FARIS coefficients.
- A. WMMSE reformulation with auxiliary variables: For any positive weight variable and receiver, concavity yields a lower bound relating the robust minimum rate to a weighted-MSE expression.The bound is established through the concavity of the right-hand side in the auxiliary variables.
- A. WMMSE reformulation with auxiliary variables: Unlike conventional WMMSE, the reformulation explicitly accounts for FARIS-related CSI errors and connects each user’s robust rate to its weighted MSE.This provides the key robust WMMSE relationship used in the subsequent optimization.
- A. WMMSE reformulation with auxiliary variables: For fixed beamforming and FARIS coefficients, optimizing the auxiliary receiver and weight variables recovers the robust minimum achievable rate.The auxiliary variables are obtained by setting the corresponding derivatives to zero.
- A. WMMSE reformulation with auxiliary variables: The resulting reformulation leads to an alternating optimization framework.The paper introduces the AO procedure after deriving the auxiliary-variable reformulation.
B. AO updates
The AO framework updates receiver weights and equalizers, FARIS coefficients, and the beamformer with port-selection variables in alternating subproblems. The beamformer and selection update is relaxed to an SDP and followed by Gaussian randomization to recover an M_o-sparse solution.
- Fixing the other variables reduces the FARIS-coefficient update to a convex QCQP.
- The (w, p) update lifts W = ww* and augments it with a rank-one matrix variable to express the MSE constraints.
- The AO procedure is summarized as Algorithm 1, beginning from initialized feasible variables and iteratively updating the design blocks.
- After solving the relaxed problem, Gaussian randomization reconstructs the beamformer and the algorithm updates p until convergence.
- The relaxed (w, p) subproblem is an SDP whose p solution indicates FARIS-port activation likelihood and guides recovery of an M_o-sparse beamformer.
4) Complete AO Framework:
The complete AO framework cycles through receiver-variable, FARIS-coefficient, and beamformer/port-selection updates. Each block optimization makes the surrogate objective non-decreasing, while power constraints provide an upper bound.
- Complete AO Framework: AO iteratively updates (ν, u), F, and (w, p), with the last block solved through the rank-relaxed SDP and Gaussian randomization.
- Complete AO Framework: The objective is non-decreasing across AO iterations because each subproblem is solved for its corresponding variable block.
- Complete AO Framework: BS and FARIS power constraints upper-bound the surrogate objective, supporting convergence of the iterative procedure.
C. Computational Complexity
The complexity analysis decomposes the AO cost into receiver-variable, FARIS-coefficient, and beamformer/port-selection updates. The SDP component contributes a term scaling with M^4.5.
- The (u, ν)-update has complexity O(MNK^2) when evaluated for all users and selected-port indices.
- The F-update solves a convex QCQP with variable dimension NK and generic interior-point complexity O(I_qc(NK)^3).
- Forming the (w, p)-update matrices costs O(KMN + K^2M^2), while solving the SDP contributes I_sdpM^4.5.
- The stated overall complexity combines QCQP, matrix-construction, SDP, and related iteration terms.
IV. SIMULATION RESULTS
Simulations evaluate robust FARIS in a multi-user setting against robust ARIS, FRIS/RIS, and No-RIS benchmarks. The proposed design consistently performs best as transmit power, activated ports, amplification limit, or CSI-error variance changes.
- Simulation setup: N = 16 BS antennas serve K = 4 users using M = 64 candidate FARIS elements, with M_o = 16 activated elements and g_max = 40 dB.
- Simulation setup: The evaluation uses sum-rate as the primary metric and compares robust FARIS with robust ARIS, FRIS/RIS, and No-RIS designs.
- Power and CSI uncertainty: As P_B increases, robust FARIS improves more steeply and consistently outperforms ARIS, FRIS, RIS, and No-RIS, including under FARIS radiated-power limits.
- Power and CSI uncertainty: As δ increases, all schemes degrade monotonically, but robust FARIS remains ahead of conventional ARIS, FRIS, and RIS schemes.
- FARIS configuration: Increasing M_o produces significant FARIS sum-rate gains through enhanced spatial DoF and array and amplification gain.
- FARIS configuration: Increasing g_max rapidly raises robust FARIS sum-rate and widens its performance gap over robust ARIS.
V. CONCLUSION
FARIS enlarges robust multi-user downlink design by jointly exploiting active amplification and fluid port utilization under statistical CSI uncertainty. Robust co-design with WMMSE and AO incorporates noise, power coupling, port sparsity, and CSI-error effects.
- FARIS jointly exploits active amplification and fluid port utilization, enlarging the robustness and performance design space of multi-user downlink systems.
- Robust FARIS design co-designs amplification-induced noise, radiated-power coupling, sparse port utilization, and BS beamforming to preserve interference control.
- The WMMSE-based reformulation and AO decomposition provide a pathway for stable updates of beamformer and surface variables under CSI uncertainty.
- The design explicitly incorporates CSI-error contributions from both direct and FARIS-assisted links.