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

Abstract: This paper investigates a fluid reconfigurable intelligent surface (FRIS)-assisted Rydberg Atomic REceiver (RARE) architecture under magnitude-only heterodyne readout. We show that, unlike conventional coherent systems, the optimal propagation environment is fundamentally governed by the receiver's nonlinear measurement structure. In particular, under the strong-reference regime, symbol detection is limited by residual quadrature leakage after reference alignment, motivating a receiver-induced channel shaping approach rather than conventional channel-centric optimization. Based on this insight, we formulate a signal-independent leakage minimization problem that jointly optimizes the FRIS port set, finite-resolution phase shifts, and the transmit beamformer, resulting in a nonconvex mixed discrete-continuous design. To address this, we develop an alternating-optimization (AO) framework comprising: (i) a closed-form eigenvector solution for widely-linear beamforming, (ii) cross-entropy method (CEM)-based combinatorial port selection, and (iii) coordinate-descent (CD) phase refinement with guaranteed monotonic descent. Simulation results demonstrate fast convergence and consistent bit-error-rate (BER) gains across various modulation orders and receiver dimensions. Moreover, the proposed FRIS-enabled design achieves near-exhaustive performance with significantly reduced complexity and consistently outperforms conventional RIS schemes with fixed elements, highlighting the effectiveness of spatial reconfiguration in suppressing quadrature leakage and the additional spatial degree-of-freedom (DoF) enabled by FRIS for reliable atomic-MIMO detection.

• The paper presents a receiver-induced channel shaping paradigm that minimizes quadrature leakage through FRIS-assisted Rydberg Atomic MIMO design.
• It employs an alternating optimization framework combining eigen-space beamforming, cross-entropy port selection, and coordinate descent phase refinement.
• Simulation results demonstrate a 3–5 dB BER improvement compared to conventional methods, validating effective quantum-limited atomic MIMO performance.

Receiver-Induced Channel Shaping in Fluid RIS-Assisted Rydberg Atomic MIMO Systems

Introduction

The paper "Toward a Receiver-Induced Channel Shaping Paradigm: FRIS-Assisted Rydberg Atomic MIMO with Quadrature-Leakage-Aware Design" (2604.10679) addresses a critical structural limitation in Rydberg Atomic Receivers (RARE) in multi-antenna (MIMO) wireless systems: the nonlinear, magnitude-only readout mechanism. This fundamental property induces intractable quadrature leakage post-reference alignment, a phenomenon not remediable by standard channel gain or SNR-centric optimization prevalent in conventional wireless systems. The authors advocate a paradigm shift: from maximizing channel quality metrics to designing the propagation environment in accordance with the receiver’s inherent nonlinearity, leveraging the additional spatial degrees-of-freedom (DoF) provided by the emerging Fluid Reconfigurable Intelligent Surface (FRIS) architecture.

Background: RARE and FRIS

RARE utilizes highly-excited Rydberg atomic states to transduce incident electromagnetic fields into optical domain quantum observables, thus bypassing the thermal Johnson noise limits of classical front-ends. The quantum shot noise floor of RARE is orders-of-magnitude below the best electronic receivers, and its intrinsic frequency agnosticism enables ultra-broadband operation through atomic state selection. However, readout is limited to magnitude (intensity), typically via optical detection of Autler-Townes (AT) splitting induced by RF fields, enforcing a nonlinear modulus operation on the channel output. In strong-reference (heterodyne) operation, the detection model reduces to real-part extraction post-alignment with the local oscillator (LO), but any non-vanishing quadrature component imparts irreducible performance loss.

Complementing RARE, FRIS extends the Reconfigurable Intelligent Surface (RIS) concept by empowering not just programmable phase control but also combinatorial selection of active scatterer (port) positions on a dense grid, providing a mechanism to spatially reshape the channel statistics and alignment. Unlike RIS, FRIS can exploit block correlation and group-based selection to optimize structural channel compatibilities beyond mere amplitude maximization.

Channel Modeling and Structural Bottleneck

The system model considers a downlink MIMO chain: base station (BS) with $N_t$ antennas, FRIS with $N$ candidate ports (of which $M_o$ are activated), and a RARE with $N_r$ vapor cells. Propagation models include explicit port-port spatial correlation and physics-based electromagnetic coupling governed by the Rydberg atomic configuration. The RARE’s readout for a transmitted signal $s$ is:

$$\mathbf{y} = \left| \mathbf{H}_{\text{eq}}(\Gamma, \boldsymbol{\theta}) \mathbf{w} s + \mathbf{r} + \mathbf{n} \right|$$

where $\mathbf{H}_{\text{eq}}$ is the cascade of BS–FRIS–RARE channel and $\Gamma$, $\boldsymbol{\theta}$, $\mathbf{w}$ designate the FRIS port selection, phase profile, and BS beamformer, respectively.

In the strong-LO regime, the nonlinearity can be approximated around the real axis:

$N$0

where any residual imaginary component (quadrature) after LO alignment—denoted as quadrature leakage—is the limiting distortion. Unlike conventional coherent MIMO, the optimal propagation environment is that which minimizes this leakage, not necessarily one with highest effective channel gain.

Optimization Formulation

The authors formalize the design challenge as a mixed discrete-continuous nonconvex minimization of the (signal-independent) average quadrature leakage:

$N$1

where $N$2 is the expected squared norm of the residual quadrature term across symbol realizations.

Three mutually coupled variable groups must be optimized:

• $N$3: FRIS port selection (combinatorial).
• $N$4: port phase profile (finite alphabet).
• $N$5: complex BS beamformer (unit-norm).

This is fundamentally different from channel-centric RIS/FRIS design; here, the objective function is dictated by the receiver’s nonlinear magnitude-only response.

Alternating Optimization Framework

The paper introduces a three-block Alternating Optimization (AO) strategy:

Beamforming: For fixed ($N$6), the optimal $N$7 admits a closed-form real-augmented eigenvalue solution. This exploits the quadratic nature of the leakage functional in $N$8, via realification and spectral decomposition.

Port Selection: For fixed ($N$9), a Cross-Entropy Method (CEM) is employed to sample and adaptively refine the probability mass function over the combinatorial port selection space, efficiently converging to high-quality sets.

Phase Refinement: For fixed ($M_o$0, $M_o$1), coordinate-wise phase optimization is performed via scalar quartic equations whose unit-modulus roots denote descent direction for each port. The resulting continuous minimizer is then quantized onto the discrete phase alphabet. A coordinate descent (CD) loop guarantees monotonic decrease in objective, supported by convergence analysis.

The subproblems are architecturally matched to the respective variable structures, achieving tractability and scalable convergence.

Numerical Results: Detection Performance and Complexity

Simulation results under 4-QAM/16-QAM, with realistic RARE and propagation parameters, demonstrate:

• The proposed FRIS-enabled receiver-induced shaping achieves fast objective convergence (20–30 AO iterations).
• Bit-error rate (BER) is consistently and significantly reduced (by 3–5 dB SNR at fixed BER) compared to conventional RIS-RARE systems.
• Performance tracks closely that of (computationally infeasible) exhaustive search-based LS decoders, yet at much reduced complexity.
• BER gain is accentuated with increasing number of RARE vapor cells ($M_o$2), FRIS DoF ($M_o$3), and higher BS antenna count ($M_o$4).
• Performance approaches the “zero-leakage” zero-forcing (ZF) bound (with known channel phase) as RSR (reference-to-signal ratio) increases, verifying the sufficiency and necessity of leakage suppression for effective atomic symbol recovery.

Complexity analysis demonstrates polynomial runtime scaling with $M_o$5, $M_o$6, $M_o$7, and the CEM/CD iteration counts, amenable to practical system deployment.

Theoretical and Practical Implications

This work establishes a fundamentally new design guideline: in atomic-MIMO, optimal propagation is dictated not by generic channel “hardening”, but by structural adaptation to the detection nonlinearity—here, quadrature-leakage minimization. FRIS’s spatial DoF (joint port/phase control) is critical, as port position selection enables high-resolution shaping unattainable by fixed/phase-only RIS. The effectiveness of AO with CEM/CD subroutines demonstrates that intricate discrete-continuous problems in emerging quantum radio architectures can be attacked with advanced but tractable numerical techniques.

Practical Relevance:

• Design of robust ultra-sensitive front-ends for deep-space, satellite, or integrated networks—where receive sensitivity is paramount.
• Quantum-inspired multiuser systems with stringent noise and interference constraints.
• Integration of hardware, quantum physics, and optimization for next-generation MIMO.

Theoretical Extensions:

• Extension to multi-user, multi-symbol, or arbitrary constellations.
• Incorporation of additional fluid degrees-of-freedom (e.g., port activation weights, elevation/3D geometry).
• Joint design with reference placement (LO source selection) in distributed atomic networks.
• Fundamental limits of DoF, capacity, and codebook design for noncoherent atomic-MIMO [atomicmag, atomicjsac, Precoding_atomicMIMO].

Conclusion

The paper demonstrates that in RARE-based quantum MIMO systems, channel design must be fundamentally receiver-induced, targeting quadrature-leakage suppression synchronized with magnitude-only, LO-referenced readouts. FRIS architectures uniquely enable this via spatial reconfiguration. The proposed AO framework—combining eigen-space beamforming, cross-entropy port selection, and coordinate-wise phase descent—delivers near-optimal BER at feasible computational cost, redefining propagation environment optimization for quantum-limited atomic wireless front-ends (2604.10679). This paradigm will influence both theoretical development and engineering realization of future 6G and quantum-augmented wireless systems.