Performance Analysis of RIS-Assisted Hybrid RF/FSO Communication Systems over Nakagami-m and Gamma–Gamma Channels with Decode-and-Forward Relaying

<title>Abstract</title> <p>Reconfigurable intelligent surfaces (RIS) and hybrid radio-frequency/free-space-optical (RF/FSO) links promise low-cost backhaul, yet no end-to-end analysis combines them. A source–RIS–relay–destination topology was analysed: an N-element RIS assists the first hop over Nakagami-m fading, a decode-and-forward relay retransmits over parallel RF (Nakagami-m) and FSO (Gamma–Gamma) links, and the destination applies selection combining. A central-limit-theorem (CLT) approximation characterises the cascaded RIS channel. A skewness criterion fixes its validity: the Gaussian model holds for N ≥ 20 (skewness 0.168 at N = 50), and in the cost-effective N = 10–20 range the residual error, quantified end-to-end, is conservative and below 0.5% in outage at practical SNR. Closed-form outage probability is derived; ergodic capacity and average bit-error rate follow by adaptive quadrature. Monte Carlo simulation confirms all expressions within 4% from −10 to +12 dB. The RIS-assisted system reaches any reliability target at 7–8 dB lower SNR than RF-only and non-RIS hybrid baselines, a fivefold transmit-power saving. Capacity saturates beyond roughly N = 10, so N = 10–20 is the economical array size. Without the RIS, the hybrid underperforms a single RF link: the surface is a precondition for hybrid diversity, not an add-on.</p>