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Stochastic Design of Active RIS-Assisted Satellite Downlinks under Interference, Folded Noise, and EIRP Constraints

Muhammad Khalil, Ke Wang, Jinho Choi

TL;DR

The paper develops a stochastic reliability framework for active RIS–assisted satellite downlinks, modeling fading, interference, and gain-dependent amplifier noise to derive a realizable SINR expression. It jointly optimizes a binary RIS configuration and a common amplification gain under a chance constraint via an SAA–MISOCP approach, while enforcing small-signal stability and EIRP limits. Realization-wide SINR envelopes and an interference-aware high-gain ceiling explain why amplification saturates and guide reliable, hardware-compliant designs. Monte Carlo validation confirms the envelopes, ceiling behavior, and reliability targets, demonstrating a practical methodology for reliability-guaranteed RIS-enabled SatCom links.

Abstract

Active reconfigurable intelligent surfaces (RISs) can mitigate the double-fading loss of passive reflection in satellite downlinks. However, their gains are limited by random co-channel interference, gain-dependent amplifier noise, and regulatory emission constraints. This paper develops a stochastic reliability framework for active RIS-assisted satellite downlinks by modeling the desired and interfering channels, receiver noise, and RIS amplifier noise as random variables. The resulting instantaneous signal-to-interference-plus-noise ratio (SINR) model explicitly captures folded cascaded amplifier noise and reveals a finite high-gain SINR ceiling. To guarantee a target outage level, we formulate a chance-constrained max-SINR design that jointly optimizes the binary RIS configuration and a common amplification gain. The chance constraint is handled using a sample-average approximation (SAA) with a violation budget. The resulting feasibility problem is solved as a mixed-integer second-order cone program (MISOCP) within a bisection search over the SINR threshold. Practical implementation is enforced by restricting the gain to an admissible range determined by small-signal stability and effective isotropic radiated power (EIRP) limits. We also derive realization-wise SINR envelopes based on eigenvalue and l1-norm bounds, which provide interpretable performance limits and fast diagnostics. Monte Carlo results show that these envelopes tightly bound the simulated SINR, reproduce the predicted saturation behavior, and quantify performance degradation as interference increases. Overall, the paper provides a solver-ready, reliability-targeting design methodology whose achieved reliability is validated through out-of-sample Monte Carlo testing under realistic randomness and hardware constraints.

Stochastic Design of Active RIS-Assisted Satellite Downlinks under Interference, Folded Noise, and EIRP Constraints

TL;DR

The paper develops a stochastic reliability framework for active RIS–assisted satellite downlinks, modeling fading, interference, and gain-dependent amplifier noise to derive a realizable SINR expression. It jointly optimizes a binary RIS configuration and a common amplification gain under a chance constraint via an SAA–MISOCP approach, while enforcing small-signal stability and EIRP limits. Realization-wide SINR envelopes and an interference-aware high-gain ceiling explain why amplification saturates and guide reliable, hardware-compliant designs. Monte Carlo validation confirms the envelopes, ceiling behavior, and reliability targets, demonstrating a practical methodology for reliability-guaranteed RIS-enabled SatCom links.

Abstract

Active reconfigurable intelligent surfaces (RISs) can mitigate the double-fading loss of passive reflection in satellite downlinks. However, their gains are limited by random co-channel interference, gain-dependent amplifier noise, and regulatory emission constraints. This paper develops a stochastic reliability framework for active RIS-assisted satellite downlinks by modeling the desired and interfering channels, receiver noise, and RIS amplifier noise as random variables. The resulting instantaneous signal-to-interference-plus-noise ratio (SINR) model explicitly captures folded cascaded amplifier noise and reveals a finite high-gain SINR ceiling. To guarantee a target outage level, we formulate a chance-constrained max-SINR design that jointly optimizes the binary RIS configuration and a common amplification gain. The chance constraint is handled using a sample-average approximation (SAA) with a violation budget. The resulting feasibility problem is solved as a mixed-integer second-order cone program (MISOCP) within a bisection search over the SINR threshold. Practical implementation is enforced by restricting the gain to an admissible range determined by small-signal stability and effective isotropic radiated power (EIRP) limits. We also derive realization-wise SINR envelopes based on eigenvalue and l1-norm bounds, which provide interpretable performance limits and fast diagnostics. Monte Carlo results show that these envelopes tightly bound the simulated SINR, reproduce the predicted saturation behavior, and quantify performance degradation as interference increases. Overall, the paper provides a solver-ready, reliability-targeting design methodology whose achieved reliability is validated through out-of-sample Monte Carlo testing under realistic randomness and hardware constraints.
Paper Structure (7 sections, 57 equations, 5 figures, 3 tables, 1 algorithm)

This paper contains 7 sections, 57 equations, 5 figures, 3 tables, 1 algorithm.

Table of Contents

  1. Introduction
  2. System Model (Stochastic)
  3. Stochastic Problem Formulation and SAA--MISOCP
  4. Mixed-Integer Conic Feasibility (at fixed $\tau$)
  5. Performance Bounds and Interference-Aware Analysis
  6. Numerical Results and Discussions
  7. Conclusion

Figures (5)

  • Figure 1: Active RIS--assisted satellite downlink with one desired satellite and $M$ cochannel interferers. Desired and interfering signals reach the ground receiver via direct links $\mathbf H_d(\omega)$ and $\{\mathbf H_{d,m}(\omega)\}$ and via the RIS-assisted paths through $\mathbf G_t(\omega)$, $\{\mathbf G_{t,m}(\omega)\}$, and $\mathbf H_r(\omega)$. Blue links denote desired propagation; red links denote interference.
  • Figure 2: $(1-\varepsilon)$-quantile SINR versus number of interferers $M$ at fixed gains $g$ (panels) and RIS sizes $N$ (curves), computed from \ref{['eq:sinr-compact-stoch']} under the SAA sampling settings in Table \ref{['tab:params-results']}. The passive baseline ($g=0$) follows directly from \ref{['eq:sinr-compact-stoch']}, while saturation at larger $g$ is consistent with the high-gain ceiling in \ref{['eq:ceiling-stoch']}.
  • Figure 3: Reliability-guaranteed SINR threshold $\tau^\star(g)$ obtained by the SAA-MISOCP bisection oracle (Algorithm \ref{['alg:saa_misocp']}) for \ref{['eq:chance-prob']}, with sample-wise constraints \ref{['eq:feas-int-stoch']} enforced via \ref{['eq:bigM']}. The saturation/decline trend at large $g$ is explained by the folded-noise term $g^2D_1(\omega)$ in \ref{['eq:D0D1-stoch']} and the ceiling behavior in \ref{['eq:ceiling-stoch']}.
  • Figure 4: Reliability-guaranteed SINR surface $\tau^\star(N,M;g)$ at fixed gains $g\in\{0,0.5,1,2\}$ obtained for \ref{['eq:chance-prob']} using the SAA--MISOCP model with sample-wise constraints \ref{['eq:feas-int-stoch']} enforced through \ref{['eq:bigM']}. The scaling with $N$ follows the quadratic-reflection term $C(\mathbf b,\omega)$ bounded in \ref{['eq:BC-bounds']}, while degradation with $M$ follows the additive interference structure in \ref{['eq:sinr-compact-stoch']}.
  • Figure 5: Envelope consistency across gains: for each realization $\omega$, the path-wise bounds \ref{['eq:LB-stoch']}--\ref{['eq:UB-stoch']} provably sandwich $\mathrm{SINR}(\mathbf b,g;\omega)$ for all $\mathbf b$ and $g\in[0,g_{\max}]$. The plotted empirical “best over $\mathbf b$” curve therefore lies between the two envelopes, validating the bound tightness and the ceiling trend \ref{['eq:ceiling-stoch']}.