Channel Characterization for Multi-Color VLC for Feedback and Beamforming Design

Visible light communication (VLC) can achieve higher data rate by increasing the number of channels using wavelength division multiplexing (WDM) technology. A fundamental question lies in the channel characterization for multiple colors, to investigate the correlation of different wavelengths. In this paper, theoretical analysis on the correlation is presented based on the multicolor light emitting diode (LED) and optical filter model. Experiments using LEDs of different wavelengths are conducted to observe the correlation of the channel matrix. Based on the experimental results, it is seen that the channel matrix is strongly correlated with a dominant eigenvalue as transmission distance and atmospheric condition change. Based on the low-rank feature of the channel matrix, we propose to project and quantize it in a low-dimensional space. Channel quantization design based on principal component analysis (PCA) is proposed such that the channel vector quantization can be transformed to scalar quantization. We also apply the one-dimensional channel quantization to the beamforming design, where the solution from the quantized channel matrix mostly shows loss lower than 1% compared with the optimal solition to the original problem.