## 2 Performance Assessment
### Signal-to-Noise Ratio Simulations
#### 2.2.3 Signal-to-Noise Ratio Simulations at 905 nm  
In the SNR simulations which are presented below, various photodetector types were considered and the value of the optics transmission factor \(\xi_{0}\) was tuned as shown in the variants of Table 2.  
At wavelengths of 905 and 1064 nm there are three photodetector options: silicon PIN photodiodes, silicon avalanche photodiodes (APD) and photomultiplier tubes (PMT). In this design it was decided to use photodiodes given their superior quantum efficiency in comparison with PMTs. A PIN photodetector module and an APD module were considered in the simulations that were performed. Both modules are comprised of a photodiode and transimpedance amplifier (TIA), with the latter being the element which limits the noise-equivalent bandwidth \(B_{N}\) of the receiver. Noise-equivalent bandwidth. In order to determine \(B_{N}\), a range resolution of \(\Delta R=1\) m is considered in these simulations. When applying \(\Delta R=c(\tau_{t}+\tau_{d})/2\)[18], a bandwidth greater than 107 MHz is required. In this calculation, a pulse duration \(\tau_{t}\leq 2\) ns and a detection time given by \(\tau_{d}=1/2B_{N}\)[22] are assumed. In a photodiode-based (APD/PIN) optoelectronic receiving chain, \(B_{N}\) is the transimpedance amplifier (TIA) bandwidth because its bandwidth is much smaller than that of the photodiode (typically, a few GHz). At the receiver output, the signal must be sampled at a frequency \(f_{s}\geq 2B_{N}\) according to [PERSON]'s criterion (that is, \(f_{s}\geq 215\) MHz considering the example figures given). It is assumed that both receiver modules are comprised of a TIA with a bandwidth of 200 MHz and a typical input noise current \(I_{s}=6.5\) pA/\(\sqrt{\mathrm{Hz}}\). APD module noise-equivalent power. A noise equivalent power \(NEP_{m}\) of 0.105 pW/\(\sqrt{\mathrm{Hz}}\) is assumed for the APD module. This value is obtained from the equation [23]:  
\[NEP_{m}=\frac{I_{noise(total)}}{M\cdot R_{o}} \tag{10}\]  
where \(I_{noise(total)}\) [ pA/\(\sqrt{\mathrm{Hz}}\) ] is the total input noise-current spectral density. The transimpedance amplifier nearly always generates much more noise than the photosensitive diode and, therefore, the approximation \(I_{noise(total)}\approx I_{a}\) has been used. For the APD receiver module, intrinsic responsivity \(R_{io}=0.62\) A/W at 905 nm and a gain \(M=100\) are considered. An excess noise factor \(F=4\) is \begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline \begin{tabular}{c} **Variant** \\ **Number** \\ \end{tabular} & \begin{tabular}{c} **Photodetector** \\ **[A/W]** \\ \end{tabular} & \begin{tabular}{c} **R\({}_{\mathrm{io}}\)** \\ **[A/W]** \\ \end{tabular} & \begin{tabular}{c} **M** \\ \end{tabular} & \begin{tabular}{c} **F** \\ \end{tabular} & \begin{tabular}{c} **NEP\({}_{m}\) [ pW/\(\sqrt{\mathrm{Hz}}\) ]** \\ \end{tabular} & \begin{tabular}{c} **\(\xi_{0}\)** \\ \end{tabular} & \
\begin{tabular}{c} **\(K_{b}\) [m\({}^{2}\cdot\)nm\(\cdot\)sr]** \\ \end{tabular} &
\begin{tabular}{c} **Required \(K_{s}\)** \\ **[W\(\cdot\)m\({}^{3}\)]** \\ \end{tabular} \\ \hline
**1** & Silicon APD & 0.62 & 100 & 4 & 0.11 & 0.5 & \(6.17\times 10^{-9}\) & 16.33 \\
**2** & Silicon APD & 0.62 & 100 & 4 & 0.11 & 0.25 & \(6.17\times 10^{-9}\) & 32.65 \\
**3** & Silicon APD & 0.62 & 100 & 4 & 0.11 & 0.1 & \(6.17\times 10^{-9}\) & 81.58 \\
**4** & Silicon PIN & 0.62 & 1 & 1 & 10.49 & 0.5 & \(6.17\times 10^{-9}\) & 852.3 \\
**5** & Silicon PIN & 0.62 & 1 & 1 & 10.49 & 0.25 & \(6.17\times 10^{-9}\) & 1705 \\
**6** & Silicon PIN & 0.62 & 1 & 1 & 10.49 & 0.1 & \(6.17\times 10^{-9}\) & 4261 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Required system constant, \(K_{s}\), for various combinations of design parameters at 905 nm. estimated, with application of the empirical formula \(F=M^{c}\)[24], where \(x=0.3\) is the excess noise index for a Si-APD. PIN module noise-equivalent power. Intrinsic responsivity \(R_{io}=0.62\) A/W at 905 nm is also considered for the PIN module.