## 3 Results
### Mission Analysis
#### 3.1.1 Payload Analysis
\[Signal\ Power=\frac{\mathrm{E}_{\lambda_{0}}\tau_{\mathrm{atm}}^{2}\cdot\rho_{ \lambda}\cdot\mathrm{Area}_{\mathrm{det}}\cdot\Delta_{\lambda}}{\pi\cdot\mathrm{ G}_{\#}}, \tag{5}\]  
where \(\mathrm{E}_{\lambda_{0}}\) is the Exo-Atmospheric Irradiance (EAI) in (W\({}^{2}\)/m\({}^{2}\).nm), \(\tau_{\mathrm{atm}}\) is the atmospheric transmission coefficient, \(\rho_{\lambda}\) is the reflectance over the Earth's surface, which depends on the albedo value, \(\mathrm{Area}_{\mathrm{det}}\) is the area of the pixel in the detector provided by the manufacturer, \(\Delta_{\lambda}\) is the receiver optical spectral width, and the G-number (\(G_{\#}\)), which includes the f-number (\(f_{\#}\)), characterizes the optical system:  
\[G_{\#}=\frac{1+4\times f_{\#}^{2}}{\tau_{\mathrm{opt}}\times\pi}, \tag{6}\]  
where \(f_{\#}\) is defined as the ratio between the focal length and the aperture: \(f_{\#}=f/\mathrm{AP}\), and \(\tau_{\mathrm{opt}}\) is the optical transmissivity for all of the optical train (optical sensor plus lens). The other factor needed to compute the SNR is the Noise Equivalent Power (\(NEP\)), which is a measure of the goodness of the photodetector in terms of noise:  
\[NEP=\frac{\sqrt{2\cdot q(I_{ds}+F\cdot M^{2}\cdot I_{db})\cdot B}}{\eta\cdot \left(\frac{q\cdot\lambda}{\mathrm{c}\cdot\mathrm{h}}\right)\cdot M}. \tag{7}\]  
In Equation (7), \(q\) is the electric charge of the electron (C), h = 6.63\(\cdot\)10\({}^{-34}\) J\(\cdot\)S is the Planck constant, \(\eta\) is the quantum efficiency, which changes for each band and it is particular for the optical sensor, \(I_{ds}\) and \(I_{db}\) are the surface and bulk dark currents, respectively (A), \(F\) is the excess noise factor (\(-\)), \(M\) is the multiplication factor of the avalanche diode, which in this case is \(F=M=1\), because there is no photo multiplication involved, and \(B\) (Hz) is the inverse of the integration time,  
\[B\geq\frac{1}{T_{integration}}=\frac{1}{\frac{\mathrm{GSD}}{2\cdot V_{gd}}}= \frac{2\cdot V_{grd}}{GSD}, \tag{8}\]  
which is related to the \(V_{grd}\) satellite's ground speed and the \(GSD\) (Equation (1)). Results are presented in Table 4 and fulfill the mission statement requirements. The following sections specify the design and simulated performance of all of the required subsystems needed to enable the payloads and the transmission of the data acquired to the ground stations. \begin{table}
\begin{tabular}{l c c c c c} \hline \hline
**Optical parameters** & \multicolumn{5}{c}{**Bands performance**} \\ \hline Swath in (km): & & & & 34.7 & & \\ Max. aperture of the lens in (mm): & & & & 33.6 & & \\ Studied Bands: & 475 (nm) & 555 (nm) & 650 (nm) & 710 (nm) & 870 (nm) \\ Aperture required for each band to & 8.9 & 10.4 & 12.2 & 13.3 & 16.3 \\ satisfy Rayleigh criterion in (mm): & & & & & \\ GSD for each band after Rayleigh criterion in (m): & 26.8 & 26.78 & 26.78 & 26.78 \\ SNR for each band in (dB): & 37.3 & 40.4 & 41.2 & 41.6 & 36.9 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Results of the mission analysis for the optical payload performance considering the Commercial off the Shelf (COTS) camera and lens specified in Table 3 and the orbital configuration described in Section 2.1. * GNSS-Reflectometer  
The GNSS payload of the \({}^{3}\)CAT-3 is being developed in parallel with the \({}^{3}\)Cat-4 ESA Fly Your Satellite project, in which the UPC NanoSat Lab [12] is also participating. This 1U CubeSat will carry a flexible microwave payload: an Automatic Identification System (AIS), a GNSS Reflectometer, and a microwave Radiometer [30]. The use of a software-defined radio (SDR) as a data logger is essential to reduce power consumption, the size of the payload, and cost. The scope of the \({}^{3}\)Cat-3 is to perform data fusion between the optical payload and the GNSS-R data.