# Polarization Differential Visible Light Communication: Theory and Experimental Evaluation +
## 4 Measurement Results
### Setup A  
The data transmission and \(SNR\) are evaluated with receiver polarizers equipped for setup A by applying matched filtering. The output of the matched filter for \(T_{b}=250\,\upmu\)s and \(\theta=0\,^{\circ}\) is shown in Figure 9.  
Figure 8: Measured photodiode voltages without receiver polarizers for bit period \(T_{b}=250\,\upmu\)s using setup A [17].  
The histogram of the matched filter output distribution \(R\) is shown in Figure 10 for \(\theta=0\,^{\circ}\) for both transmitted '1'-bits and '0'-bits. A Gaussian is fitted to this data using a non-linear least squares error (LSE) fit. This results in \(\mu_{R}=3.191\,\mathrm{\upmu V^{2}s}\) and \(\sigma_{R}=0.013\,\mathrm{\upmu V^{2}s}\) for transmitted '1'-bits and \(\mu_{R}=-3.178\,\mathrm{\upmu V^{2}s}\) and \(\sigma_{R}=0.013\,\mathrm{\upmu V^{2}s}\) for transmitted '1'-bits. The small deviation between the mean values is most likely attributable to slight variations among the LED drivers.  
Finally, the \(SNR\) can be calculated according to Equation (10) using the LSE fitted values for \(\mu_{R}\) and \(\sigma_{R}\). The measured \(SNR\) for setup A as a function of the receiver orientation \(\theta\) is plotted in Figure 11 for transmitted '1'- and '0'-bits along with \(\pm 2^{\circ}\) error bars representing a possible systematic error due to the polarization axis tolerance. The derived model is fitted to this data, resulting in \(SNR_{0}=48.14\) dB and \(SNR_{0}=47.41\) dB for transmitted '1'- and '0'-bits respectively. Please note that the logarithmic function plot progresses steeply at \(\theta=45\,^{\circ}\) as predicted in Section 2.3, hence a minor rotation has a huge impact on the \(SNR\) near \(\theta=45\,^{\circ}\).  
Bit-Error Rates can also be predicted based on the measured distributions of the matched filter outputs using Equation (14) [22]. However, as the \(SNR\) is significantly high in this setup, the numerical solutions of this equation result in 0, except at \(\theta=45\,^{\circ}\), where the predicted BER based on the measured distributions of \(R\) equals \(8\times 10^{-2}\). This again corresponds to intuition due to the symmetry at \(\theta=45\,^{\circ}\), which causes \(\mathrm{T_{X1}}\) and \(\mathrm{T_{X2}}\) to be indistinguishable. This predicted value is still considerably better than the theoretical expected BER of 0.5 as a minor misalignment has a significant impact on \(SNR\). Please note that no error correction was applied in the executed measurements. In less favourable conditions, such as lower transmit power or greater link distance, the \(SNR\) can drop considerably compared to the presented measurements. In this case, the BER will rise meaning bit errors are much more likely to occur and error correction or detection is essential.  
Figure 9: Illustration of the matched filter output for \(T_{b}=250\,\mathrm{\upmu s}\) and \(\theta=0\,^{\circ}\) using setup A [17].  
Figure 11: _Cont_.  
Figure 10: Measured distribution and least square error (LSE) fit of \(R\) for transmitted \({}^{\prime}1^{\prime}\)-bits (top) and \({}^{\prime}0^{\prime}\)-bits (bottom) at \(\theta=0^{\circ}\) for \(T_{b}=250\,\upmu\)s using setup A [17].