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.

💡 Research Summary

This paper presents a comprehensive stochastic design methodology for active reconfigurable intelligent surface (RIS)‑assisted satellite downlinks, explicitly accounting for random co‑channel interference, gain‑dependent amplifier (folded) noise, and regulatory emission constraints. The authors first construct a detailed system model: a single desired satellite transmits to a ground receiver while M neighboring satellites reuse the same carrier, creating interference. The satellite‑to‑RIS, RIS‑to‑receiver, and direct satellite‑to‑receiver links follow block‑fading Rician distributions, and all channel coefficients are treated as random variables. The active RIS consists of N elements, each capable of a binary phase shift (±1) and a common small‑signal gain g (scaled by a passive retention factor ρ).

A key contribution is the folded‑noise model. Each RIS element’s low‑power amplifier introduces zero‑mean complex Gaussian noise with variance σ²_min + η g², i.e., the noise power grows quadratically with the amplification gain. After propagation through the RIS‑receiver channel H_r and linear combining by the receiver weight vector w, this noise is “folded” into an effective noise term wᴴ H_r Σ_a(g) H_rᴴ w, where Σ_a(g)= (σ²_min + η g²) I for the i.i.d. case. Consequently, the instantaneous signal‑to‑interference‑plus‑noise ratio (SINR) for a given binary RIS configuration b∈{±1}ⁿ and gain g can be expressed as a quadratic function of g:

S(b,g;ω)=A(ω)+g B(b,ω)+g² C(b,ω)

I(b,g;ω)=∑_{m=1}^M P_m