## 3 Simulation Results and Discussion
\begin{table}
\begin{tabular}{c c c} \hline \hline \multicolumn{2}{c}{**Parameter**} & \multicolumn{1}{c}{**Value**} \\ \hline \multirow{3}{*}{Room:} & width (\(x\)), m & 6 \\  & length (\(y\)), m & 7.8 \\  & height (\(z\)), m & 2.75 \\ \hline \multirow{3}{*}{Emitter:} & mode (\(n\)) & 1 \\  & Power (\(P_{E}\)), mW & 15 \\  & position (\(x\), \(y\), \(z\)), m & (-, -, 1) \\ \hline \multirow{3}{*}{Receivers:} & photodetectors: responsivity (\(R\)), A/W & 0.6 \\  & photodetectors: minimum power detected, W & \(10^{-12}\) \\  & position (\(x\), \(y\), \(z\)), m & (3, 3.9, 1) \\ \hline \multirow{3}{*}{CPC:} & FOV & \(50^{\circ}\) \\  & refractive index & 1.8 \\  & exit aperture, mm & 5.64 \\ \hline \multirow{3}{*}{Bandpass filter:} & number of layers & 20 \\  & peak transmission (\(T_{0}\)) & 0.92 \\  & effective index (\(n_{s}\)) & 2.293 \\  & filter order (\(m\)) & 3 \\  & angular bandwidth (\(\Delta\psi\)), degrees & 50 \\  & spectral bandwidth (\(\Delta\lambda\)), nm & 50 \\  & \(\lambda_{0}\), nm & 810 \\ \hline \multirow{3}{*}{Longpass filter:} & filter transmission (\(T_{0}\)) & 0.99 \\  & cutoff wavelength, nm & 780 \\  & filter-photodetector combination (\(\Delta\lambda\)), nm & 320 \\ \hline \multirow{3}{*}{Tungsten lamps:} & mode (\(n\)) & 2 \\  & lamp power-spectral density, W/nm & 0.037 \\  & position (x\({}_{1}\),\(\gamma_{1}\),\(\
u_{1}\)), m & (1.5, 1.4, 2.75) \\  & position (x\({}_{2}\),\(\gamma_{2}\),\(\
u_{2}\)), m & (4.5, 1.4, 2.75) \\  & position (x\({}_{3}  
In order to obtain the SNR given by Equation (21), it is necessary to determine the total noise variance as the sum of the contributions from the background light-induced shot noise and thermal noise due to the amplifier. To this end, a bit rate of \(R_{b}\) = 115 kbps was considered since the study involves the application of non-imaging angle-diversity receivers to indoor IR wireless sensor networks. The shot noise can be computed using Equation (23), where the incident optical power from ambient light \(P_{bg}\) originates at the windows and six tungsten bulbs located in the ceiling of the room (see Figure 4). To compute the incident optical power from the windows, each window surface is divided into small square elements of equal area (25 cm\({}^{2}\)), and each element is modelled as a first-order Lambertian emitter with a spectral radiant emittance of 0.20 W/nm/m\({}^{2}\)[8], i.e., the noise PSD of each element is 0.5 mW/nm. The noise optical power emitted by each element can be obtained by multiplying the noise PSD by \(\Delta\lambda\), which represents the spectral bandwidth of the optical filter used to limit the ambient radiation reaching the photodetector, which was set at 50 nm for the CDR and SOR structures and 320 nm for SDR. Therefore, applying the Monte Carlo ray-tracing algorithm to each element \(E\), and using Equation (8), the incident optical power from the windows act as an ambient light (noise) source that can be expressed as a sum of the form:  
\[P_{bg}=\sum_{j=1}^{N_{e}}\left(\sum_{j=0}^{M}h(t;E,R)\right)=\sum_{j=1}^{N_{e} }\left(\frac{1}{d^{2}}R_{E}(\theta,\,1)A_{eff}(\psi)+\sum_{j=1}^{M-1}p_{k}\right) \tag{33}\]  
where \(M\) = \(t_{max}/\Delta t\) is the number of time intervals of width \(\Delta t\), and \(N_{e}\) is the number of elements used to divide the window surface. Moreover, the radiant intensity from the bulbs can be modelled as Lambertian sources of second order with an optical spectral density of 0.037 W/nm. Analogously to the calculation of the noise power from ambient light, the incident optical power from the bulb can be obtained by multiplying the power spectral density by \(\Delta\lambda\).