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

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.