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Mutual-Coupling-Aware Electromagnetic and Signal Processing Co-Design for Pixel Antenna Arrays

Ping Ma, Mengzhen Liu, Rang Liu, Ming Li, A. Lee Swindlehurst

arXiv:2610.08550v1eess.SP

TL;DR

In practical pixel antenna arrays, mutual coupling changes switch-state-dependent responses, making MC-unaware designs mismatch the realized channels. The paper combines a full-array multi-port model with EM and signal-processing co-design, and its simulations report higher sum rates than MC-unaware, MC-free, and patch-array baselines. The results indicate that accurately modeled coupling can also be exploited as embedded-response diversity.

  • Problem

    Inter-element mutual coupling changes pixel-array radiation responses, making MC-unaware designs mismatch the realized coupled-array channels.

    Source: §I · p. 1, §II · p. 2

  • Method

    A full-array multi-port circuit model and CST-extracted impedance and radiation responses form a switch-dependent channel used to jointly optimize switch states and the transmit precoder.

    Source: §II · pp. 2–3, §I · p. 2

  • Results

    The MC-aware design achieves higher sum rates than the MC-unaware, MC-free, and patch-array baselines in CST-based simulations.

    Source: §VI · p. 6, §V · p. 6

  • Takeaways & Limitations

    The simulations indicate that accurately modeled inter-element coupling can be exploited as embedded-response diversity for channel shaping.

    Source: §V · p. 6

Abstract

from arXiv · show

Reconfigurable pixel antenna arrays provide additional electromagnetic (EM) degrees of freedom for wireless transmission by enabling hardware-level adaptation of radiation responses. In practical arrays, inter-element mutual coupling (MC) alters the switch-state-dependent responses, causing MC-unaware designs to be mismatched with the realized coupled-array channels. To address this issue, we propose an MC-aware EM and signal-processing co-design framework for downlink multi-user multiple-input single-output (MU-MISO) systems. The full pixel antenna array is modeled as a unified multi-port circuit network that jointly characterizes the feed ports and switch-controlled pixel ports. By combining the impedance matrix extracted from Computer Simulation Technology (CST) Studio Suite simulations with the full-array open-circuit far-field responses, we construct a switch-state-dependent EM-domain channel that explicitly captures both intra-antenna pixel coupling and inter-element MC. Based on this model, we formulate a sum-rate maximization problem over the binary switch-state vector and the transmit precoder. To address the resulting mixed-integer non-convex problem, we develop an alternating optimization algorithm in which the binary switch-state vector is updated via sequential exhaustive block optimization (SEBO), while the transmit precoder is optimized using fractional programming (FP). CST-based simulations show that the proposed MC-aware design outperforms MC-unaware, MC-free, and conventional patch-array baselines. These results demonstrate that accurate MC modeling is essential not only for reducing model mismatch, but also for exploiting the coupled embedded responses of practical pixel antenna arrays.

I. Introduction

Pixel antennas add hardware-level control of radiation responses, but mutual coupling can make designs based on idealized models mismatch practical coupled-array channels. The paper proposes a full-array, MC-aware co-design framework for downlink MU-MISO systems and reports that it outperforms the stated baselines.

I. Introduction

  • Inter-element mutual coupling can distort radiation responses and effective channels, so MC-unaware configurations may suffer beam mismatch and rate loss.In pixel arrays, switch states affect both intra-element currents and the array's mutual-coupling behavior.Source: §I · p. 1
  • Existing approaches often use idealized models, isolated elements, or only intra-antenna interactions, leaving inter-element coupling insufficiently represented in practical MU-MISO arrays.The paper addresses this gap by extracting impedance and open-circuit radiation responses from a full-array CST simulation.Source: §I · p. 1
  • The proposed framework jointly optimizes pixel switch states and the transmit precoder using an MC-aware channel built from full-array EM parameters.SEBO updates the binary switch-state vector, while FP optimizes the precoder; simulations report higher sum rates than MC-unaware, MC-free, and patch-array baselines.Source: §I · pp. 1–2

II. Pixel Antenna Array

Pixel switch states reshape antenna currents and radiation, while the resulting interactions among antennas affect the realized array response. The section models the array as a multi-port network and uses its currents and open-circuit radiation responses to represent switch-dependent, coupled behavior.

II. Pixel Antenna Array

  • Switch-controlled pixel interconnections reshape surface currents and radiation, while their interactions with neighboring antennas alter embedded responses and can cause channel mismatch and rate loss.Pixel antennas offer reconfigurable radiation and polarization but require more complex switching and EM modeling than fixed-pattern patches.Source: §II · p. 2
  • The unified circuit model represents the array as an (N + NQ)-port network, jointly characterizing N feed ports and Q pixel ports per antenna through an impedance matrix.Its impedance entries capture self and transfer impedances among antenna and pixel ports.Source: §II · p. 2
  • Switch states determine pixel-port load impedances, and the pixel-port currents depend on feed currents through the array network.The current relation reflects mutual coupling among antennas, not only currents within an individual antenna.Source: §II · pp. 2–3
  • The array radiation response is constructed as a superposition of open-circuit port-response bases weighted by the corresponding port currents.The bases cover antenna and pixel ports, and the full-array CST simulation inherently incorporates mutual coupling.Source: §II · p. 3
  • Each antenna's response depends on the switch-state vector, allowing configuration design to reshape the overall array response while accounting for mutual coupling.The resulting response matrix has one column per antenna element under the chosen switch state.Source: §II · p. 3

III. System Model and Problem Formulation

The system models downlink transmission from a pixel-array base station to single-antenna users through EM-domain channels. It jointly optimizes the binary antenna switch state and baseband precoder to maximize sum rate under a transmit-power constraint.

III. System Model and Problem Formulation

  • The EM-domain channel uses an angle-polarization virtual channel matrix whose entries represent gains between discretized AoD and AoA polarization components.Source: §III · p. 3
  • Transmission is precoded in baseband before radiation through the pixel array; the model specifies a baseband precoder, unit-covariance transmitted symbols, and additive Gaussian noise.Source: §III · p. 3
  • The design jointly chooses the binary switch-state vector and transmit precoder to maximize sum rate subject to total transmit power.Source: §III · p. 3

IV. Joint Switch-State and Precoder Optimization

The proposed method alternates between switch-state and precoder optimization to address the joint problem's non-convexity. It uses SEBO for switch states and FP for the precoder until convergence.

IV. Joint Switch-State and Precoder Optimization

  • The method jointly optimizes the binary switch state and transmit precoder to address the non-convex design problem.Source: §IV · p. 4
  • For a fixed precoder, SEBO updates the binary switch state; for a fixed switch state, FP optimizes the transmit precoder.Source: §IV · p. 4
  • The switch-state and precoder updates alternate until convergence.Source: §IV · p. 4

A. Antenna Switch-State Design

SEBO updates the binary switch-state vector block by block while holding the other blocks fixed. This replaces a global search with smaller exhaustive searches and preserves the discrete design variables.

A. Antenna Switch-State Design

B. Precoder Design

For a fixed antenna configuration, the method uses fractional programming to optimize the transmit precoder. Auxiliary-variable updates and a power-constraint multiplier are iterated until convergence.

B. Precoder Design

  • With the antenna configuration fixed, FP iteratively updates auxiliary variables µ and ξ together with the precoder.Source: B. Precoder Design · p. 4
  • The precoder update uses λ as the Lagrange multiplier for the transmit-power constraint; bisection selects λ when the unconstrained solution exceeds the power limit.Source: B. Precoder Design · p. 5
  • The auxiliary-variable and precoder updates repeat until convergence.Source: B. Precoder Design · p. 5

V. Simulation Results

In the simulated three-user LoS setting, the MC-aware pixel design has the strongest reported sum-rate performance across transmit powers and the swept-user angular range. The embedded-pattern comparisons show that mutual coupling changes switch-state-dependent radiation responses and that MC-aware responses align more consistently with desired directions.

V. Simulation Results

  • The evaluation considers three users in a LoS environment, with noise power set to −70 dBm and an array of 50 metallic pixels interconnected by 80 PIN diodes per antenna.User angles are randomized over [−90◦, 90◦] for the transmit-power comparison; the angular sweep fixes the other two users at ±45◦ with PT = 20 dBm.Source: §V · p. 5, Figure 4 · p. 5
  • The MC-aware pixel design achieves the highest sum rate over the transmit-power range, outperforming MC-unaware, MC-free, and patch-array baselines.The MC-unaware pixel scheme's loss becomes more evident at medium and high SNRs; the text attributes its dominant loss to mismatch with the actual coupled-array response rather than thermal noise.Source: Figure 3 · p. 5, §V · pp. 5–6
  • Across the swept-user AoD range, the MC-aware pixel design has the best overall performance and outperforms the MC-unaware design, including near the rate dips around ±45◦.The dips occur when the swept user is angularly close to a fixed user, increasing effective channel correlation and making spatial interference suppression more difficult.Source: Figure 4 · p. 5, §V · p. 6
  • The comparison includes MC-aware, MC-unaware, and MC-free pixel designs, plus fixed-aperture patch-array baselines.MC-unaware designs use a decoupled model for design but are evaluated with the actual coupled-array response; MC-free references remove inter-element MC in both design and evaluation.Source: §V · p. 5
  • For a representative user direction of −30◦, the pixel designs produce different embedded radiation patterns, while the MC-aware responses are more consistently oriented toward the desired direction.The pattern differences show that inter-element MC changes the mapping from switch states to realized radiation responses.Source: Figure 5 · p. 6, §V · p. 6

VI. Conclusions

The paper presents an MC-aware EM and signal-processing co-design for downlink MU-MISO pixel arrays, using a full-array multi-port model and alternating switch-state and precoder optimization. Simulations report higher sum rates than MC-unaware, MC-free, and patch-array baselines, and indicate that modeled mutual coupling can be used for channel shaping.

VI. Conclusions

  • The proposed MC-aware design achieves higher sum rates than MC-unaware, MC-free, and patch-array baselines in simulation.The reported results indicate that inter-element MC can be leveraged as part of the EM-domain channel-shaping capability of practical pixel arrays.Source: §VI · p. 6
  • A full-array multi-port circuit model combines CST-extracted impedance and embedded far-field responses to construct a switch-state-dependent channel capturing intra-antenna pixel coupling and inter-element MC.The binary switch-state vector is optimized using SEBO, while the transmit precoder is optimized using FP.Source: §VI · p. 6
  • The framework jointly designs antenna switch states and the transmit precoder for downlink MU-MISO systems with pixel antenna arrays.Source: §VI · p. 6
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