## 3 Experimental Measurement Procedure and Results
### Theoretical Procedure
* RF Power Gain Theory The theoretical RF gain for an optical fiber link using an intensity modulator and direct detection (IM/DD), which takes into account the optical amplification of the signal through the stimulated Raman scattering, is defined in dB as [2]: \[\mathrm{G_{RF}^{T}}=20\mathrm{log}\left(\frac{\mathrm{\Re_{op}}\mathrm{P_{L}} \mathrm{I_{op}}\mathrm{\pi Z}}{2\mathrm{V_{\pi}}}\right),\] (4) where \(\mathrm{\Re}\) is the photodetector's responsivity, \(\mathrm{g_{op}}\) is the link optical gain, \(\mathrm{P_{L}}\) is the TLS optical power, \(\mathrm{I_{op}}\) is the link to optical loss, \(\mathrm{V_{\pi}}\) is the half-wave voltage, and \(\mathrm{Z}\) is the common impedance of the link.
* Noise Figure Theory Typically, four noise components are considered in back-to-back RoF links. These are PSD thermal noises from the MZM (\(\mathrm{n_{th}^{MZM}}\)) and PD (\(\mathrm{n_{th}^{PD}}\)) impedances, the PSD relative intensity noise (RIN) of the TLS (\(\mathrm{n_{min}^{TLS}}\)) and the PSD shot noise (\(\mathrm{n_{shot}^{TLS}}\)) [2]. However, Raman optical amplification introduces new noise components into the system. During the optical amplification process, the relative intensity noise (RIN) from the HPLS can be transferred to the optical signal of the TLS. This crosstalk arises from the nonlinear interaction between the signals of the HPLS and the TLS. This phenomenon is commonly referred to as RIN transfer and occurs during forward transmission (\(\mathrm{n_{Tf}^{rim}}\)) and backward transmission (\(\mathrm{n_{fp}^{rim}}\)) [5; 20].  
The use of square-law photodetectors requires careful consideration, as their output is proportional to the square of the amplitude of the incident-modulated optical field. This nonlinearity leads to beat noise, which arises from the interference of optical waves with slightly different frequencies or phases. When converted to the electrical domain, this interference generates noise that can degrade the quality of the received signal. In the case of the proposed link, these beats are the beats between the ASE-TLS (n\({}_{\text{TLS}}^{\text{ASE}}\)) and the ASE-ASE (n\({}_{\text{ASE}}^{\text{ASE}}\)) in the PD [5].  
Finally, one last noise to consider is the PSD ASE shot noise (\(n_{slot}^{ASE}\)). Equation (5) shows the theoretical NF (\(NF^{T}\)) for a Raman amplified link [2; 5].  
\[\text{NF}^{\text{T}}=10\text{log}\left(1+\frac{\text{n}_{\text{th}}^{\text{ MZM}}+\text{r}_{\text{th}}^{\text{PD}}+\text{n}_{\text{shot}}^{\text{TLS}}+ \text{n}_{\text{shot}}^{\text{ASE}}+\text{n}_{\text{rin}}^{\text{TLS}}+\text{ n}_{\text{TLS}}^{\text{ASE}}+\text{n}_{\text{ASE}}^{\text{TE}}+\text{n}_{\text{ Tf}}^{\text{rin}}+\text{n}_{\text{Tb}}^{\text{rin}}}}{\text{g}_{\text{RF}}^{\text{T}}\text{k} \text{g}_{\text{T}}\text{s}}\right), \tag{5}\]  
where \(\text{k}_{\text{B}}\) is the Boltzmann constant and where \(\text{T}_{\text{s}}\) is the standard room temperature in Kelvin.  
* Spurious-free dynamic range theory The theoretical SFDR (SFDR\({}^{\text{T}}\)) is defined by Equation (6) [2]: \[\text{SFDR}^{\text{T}}=10\text{log}\Bigg{[}\frac{4\text{V}_{\pi}^{2}}{\pi^{2} \text{Zk}_{\text{B}}\text{T}_{\text{s}}\text{NF}^{\text{T}}}\Bigg{]}^{2/3}\] (6)  
In this case, there are no changes to the definition of the SFDR\({}^{\text{T}}\) for a system with Raman amplification, but the new definition of the NF\({}^{\text{T}}\) to the system is also taken into account in Equation (6).