## 2 Theory
### Performance Model  
The LAnTeRN performance model was developed by leveraging extensive prior Exelis modeling efforts for point-to-point optical communications systems. A graphical representation of the model is shown in Figure 3. The model simulates the system performance over a wide range of configurations and environmental conditions and is capable of simulating space-to-ground, airborne-to-ground, and ground-to-ground links. The block diagram shows how the simulation controller interfaces with five separate models to characterize system performance. Transfer Model (LBLRTM) [26] to simulate high-resolution atmospheric transmission spectra and Betaspec/LOWTRAN to calculate aerosol extinction. The background solar radiance is calculated from MODTRAN [27,28] and allows for day and night performance estimates. In addition, the effects of atmospheric scintillation on beam propagation are calculated using the Andrews and Phillipsformulations [29,30]. Presently, the model is limited to operating between 1.25 \(\upmu\)m and 1.68 \(\upmu\)m. Transmitter and receiver locations are specified in three-dimensional space on a WGS-84 ellipsoid [31], thus, model predictions can be made for specific test sites. The receiver model calculates the resulting signal and background spectra at the aft end of the receiver optics and then passes them to the sensor module, which contains high-fidelity models of the photodiode detector, transimpedance amplifier (TIA) noise, and lock-in amplifier. All outputs are then fed into the link analysis model that calculates the final system SNR, a link budget, and other signal quality parameters, including individual noise source contributions. The detector and TIA noise is composed of several noise components. The total electronic current noise in units of \(A/\sqrt{Hz}\) is given by,  
\[I_{total}=\sqrt{I_{dark}^{2}+I_{shot}^{2}+I_{input\_V}^{2}+I_{fb}^{2}} \tag{10}\]  
\(I_{dark}\) is the dark noise associated with a photodetector that has a dynamic impedance of \(R_{0}\) (\(\Omega\)) and a temperature of \(T_{det}\) (K). [PERSON]'s constant \(k\) is 1.3807e-23 (J/K). \[I_{dark}=\sqrt{\frac{4\ k\ T_{det}}{R_{0}}} \tag{11}\]  
\(I_{shot}\) is the shot noise associated with a photodetector given a DC photocurrent (\(I_{DC}\)), optical gain (\(M\)), and excess noise factor (\(F_{noise}\)). The elementary charge (\(q\)) is 1.6022e-19 (C). \[I_{shot}=\sqrt{2\ q\ I_{DC}\ M^{2}\ F_{noise}} \tag{12}\]  
Figure 3: Functional block diagram of the high-fidelity performance model developed to predict instrument performance of the LAnTeRN system. The DC photocurrent is a sum of all the photocurrent (A) reaching the device, given by,  
\[I_{DC}=I_{signal}+I_{solar}+I_{leakage} \tag{13}\]  
\(I_{signal}\) is the photocurrent generated by the source laser, \(I_{solar}\) is the photocurrent generated from the solar radiance that passes through the optical bandpass filter, and \(I_{leakage}\) is the leakage current of the detector as measured by I-V traces of the device. \(I_{input\_{\_}{V}}\) is the current noise associated with the TIA voltage input noise. \[I_{input\_{\_}{V}}=\sqrt{\frac{e_{n}^{2}}{Z_{D}^{2}}} \tag{14}\]  
\(e_{n}\) is the TIA voltage input noise, and \(Z_{D}\) is the detector reactance, defined as,  
\[Z_{D}=\frac{R_{0}}{\sqrt{1+(2\pi f)^{2}\ C_{det}^{2}\ R_{0}^{2}}} \tag{15}\]  
\(f\) is the frequency of interest (Hz), and \(C_{det}\) is the detector and cable capacitance (F) to the input of the TIA. \(I_{fb}\) is the current noise associated with the feedback resistor of the TIA. \[I_{fb}=\sqrt{\frac{4\ k\ T_{fb}}{R_{fb}}} \tag{16}\]  
\(T_{fb}\) is the temperature of the TIA feedback resistor (K), and \(R_{fb}\) is the value of the feedback resistor (\(\Omega\)). To get total voltage noise at the output of the TIA, the total current noise is multiplied by the transimpedance gain.