Toward a Receiver-Induced Channel Shaping Paradigm: FRIS-Assisted Rydberg Atomic MIMO with Quadrature-Leakage-Aware Design

1. Problem Statement

The paper addresses the fundamental limitations of Rydberg Atomic Receivers (RARE) in next-generation wireless systems (6G). While RAREs offer ultra-high sensitivity and wideband operation by exploiting quantum-mechanical interactions, they suffer from a unique structural constraint:

• Magnitude-Only Heterodyne Readout: Unlike conventional coherent RF receivers that measure complex baseband signals (In-phase and Quadrature, or I/Q), RAREs typically output magnitude-only measurements due to the physics of atomic sensing (Autler-Townes splitting).
• Residual Quadrature Leakage: Even with a strong reference signal (Local Oscillator) to align phases, the magnitude-only detection inherently leaves a residual "quadrature leakage" component. This leakage acts as a structural distortion that limits symbol detection performance.
• Limitations of Conventional Optimization: Traditional Reconfigurable Intelligent Surface (RIS) designs focus on maximizing channel gain or Signal-to-Noise Ratio (SNR). However, for RARE, simply boosting the channel is insufficient. The propagation environment must be specifically shaped to align with the receiver's nonlinear measurement structure to minimize this quadrature leakage.
• RIS vs. FRIS: Conventional RIS has fixed element locations, limiting its ability to reshape the spatial structure of the channel. The paper proposes using Fluid Reconfigurable Intelligent Surfaces (FRIS), which allow dynamic selection of active ports from a dense grid, providing an additional spatial Degree-of-Freedom (DoF) beyond phase control.

2. Methodology

The authors propose a Receiver-Induced Channel Shaping framework that jointly optimizes the transmit beamformer, FRIS port selection, and phase shifts to minimize quadrature leakage.

A. System Model

• Architecture: A Base Station (BS) with $N_t$ antennas communicates with a RARE equipped with $N_r$ vapor cells via an FRIS with $N$ candidate ports (selecting $M_o$ active ports).
• Channel Specification: The model incorporates port correlation (using spherical Bessel functions) and physics-driven atomic channel models (dipole interactions).
• Signal Model: Under the strong-reference regime, the received signal is linearized. The measurement is dominated by the real part of the aligned channel, while the imaginary part represents the quadrature leakage.

B. Optimization Objective

The core innovation is the formulation of a signal-independent quadrature-leakage minimization problem. Instead of maximizing SNR, the objective is to minimize the expected energy of the residual quadrature component:
$$\min_{\Gamma, \theta, w} \mathbb{E}_x \left[ \| \Im \{ D_r H_{eq}(\Gamma, \theta) x \} \|^2 \right]$$
Where:

• $\Gamma$: Selected port set.
• $\theta$: Discrete phase shifts.
• $w$: Transmit beamformer.
• $H_{eq}$: Effective equivalent channel.
• $D_r$: Reference alignment matrix.

This results in a nonconvex mixed discrete-continuous optimization problem due to the coupling of combinatorial port selection, finite-resolution phases, and continuous beamforming.

C. Proposed Algorithm: Alternating Optimization (AO)

To solve the complex problem, the authors develop an efficient AO framework with three sub-steps:

1. Beamformer Update ($w$): For fixed FRIS configuration, the problem reduces to a widely-linear quadratic form. A closed-form eigenvector solution is derived using real-augmented representation.
2. Port Selection ($\Gamma$): A Cross-Entropy Method (CEM) is employed to efficiently explore the combinatorial space of port selections. It adaptively updates a probability distribution to concentrate on high-quality port sets.
3. Phase Refinement ($\theta$): A Coordinate Descent (CD) approach is used. For each port, the optimal phase is found by solving a scalar quartic equation derived from the first-order optimality condition. The continuous solution is then projected onto the finite-resolution phase codebook.
   • Theoretical Guarantee: The authors prove that the CD update guarantees monotonic descent of the objective function, ensuring convergence.

3. Key Contributions

1. Receiver-Induced Channel Shaping Principle: The paper establishes that for RARE systems, the optimal environment is not defined by channel strength but by alignment with the receiver's nonlinear structure. It identifies residual quadrature leakage as the primary bottleneck.
2. FRIS-Enabled Leakage Suppression: It demonstrates that FRIS, through dynamic port selection, provides the necessary spatial DoF to actively sculpt the effective channel to suppress leakage, a capability conventional RIS lacks.
3. Novel Optimization Framework: The development of a structured AO algorithm that combines:
   • Closed-form widely-linear beamforming.
   • CEM-based combinatorial port selection.
   • CD-based phase refinement with provable monotonic convergence.
4. Signal-Independent Metric: Derivation of a closed-form, signal-independent leakage metric that serves as a robust objective for joint optimization.

4. Simulation Results

The proposed framework was validated through extensive Monte Carlo simulations:

• Convergence: The AO algorithm converges rapidly (within 20–30 outer iterations) and the inner CD phase refinement shows monotonic decrease in the objective function.
• BER Performance:
  • The proposed FRIS-assisted design consistently outperforms conventional RIS-assisted RARE schemes, achieving 3–5 dB SNR gain at the same Bit-Error-Rate (BER).
  • It achieves performance near-exhaustive search levels but with significantly reduced computational complexity.
  • It approaches the performance of an ideal Zero-Forcing (ZF) detector (which assumes perfect phase knowledge), despite operating without explicit phase information.
• Impact of Parameters:
  • Increasing the number of RARE elements ($N_r$) or transmit antennas ($N_t$) significantly improves BER.
  • Increasing the number of selected FRIS ports ($M_o$) yields substantial gains (4–5 dB), highlighting the value of the additional spatial DoF.
  • Higher Reference-to-Signal Ratios (RSR) improve detection reliability by mitigating phase ambiguity.

5. Significance and Impact

• Paradigm Shift: The paper shifts the design philosophy for atomic-MIMO systems from "channel-centric" (maximizing gain) to "receiver-centric" (shaping the channel to match nonlinear constraints).
• Enabling 6G Atomic Communications: It provides a practical solution to the detection limitations of RARE, making high-reliability atomic-MIMO feasible for 6G applications like satellite and space-air-ground networks.
• FRIS Superiority: It validates FRIS as a critical enabler for future wireless systems, demonstrating that spatial reconfigurability (port selection) is essential for overcoming fundamental physical limitations that phase-only control cannot address.
• Practical Implementation: The proposed algorithm offers a computationally tractable solution for real-world deployment, balancing performance and complexity.