Channel Characteristics And Their Applications Of The None-Line-of-Sight Optical Wireless Communications Over Broad Spectra

For optical wireless communications(OWC),to achieve high speed communica-tions,wavelength-division multiplexing(WDM)is usually considered where a great many transmitters with different wavelengths and their corresponding photon-electronic detectors with optical filters are employed to increase significantly the transmission rate.When the wavelength number is large,there is massive channel state information over the broad spectrum.However,since the link environments for different wavelengths are the same,the channel state information for all wavelengths is redundant,i.e.,the correlation of the channel state information on different wavelengths is strong.It is im-portant to study how to use this correlation for physical layer design of broad spectra communications inorder to get better performances or lower system complexity.The correlation of channel state information of line-of-sight(LOS)OWC over broad spectra has been proved to exist through the explicit expression of the link gains.However,for none-line-of-sight(NLOS)optical wireless communications,it is difficult to study the correlation since there is no explicit expressions of channel state informa-tion due to the complicated scattering paths of the received photons.We propose the eigenvalue analysis based method for correlation analysis and verify the existance of the strong correlation of both link gain and channel impulse response.We also justfy such correlations by using a single-scattering model.Three applications of the correlation of channel state information are proposed for NLOS OWC systems.The first one is the application on link gain prediction,where the link gains on the entire wavelengths over a broad spectrum are predicted by using a few link gains on some certain reference wavelengths.The linear estimation model as well as the eigen-decomposition of the link gain covariance matrix are employed to derive the expressions of zero-forcing(ZF)and linear minimum mean square error(LMMSE)prediction expressions along with their extimation square error.Moreover,we also analyze the influence of the perturbation of the sampled link gain covariance matrix by using the perturbation theory of statistical matrices.Through strict derivation,we conclude that the LMMSE prediction method hardly suffered from the perturbation while the ZF prediction method is very sensitive to the perturbation.Hence,for the optimal reference wavelengths selection under the LMMSE prediction method,the op-timal reference wavelengths can be obtained by using the exhaustive search of all the conbinations of the reference wavelengths and finding the one with minimum estima-tion square error through the derived expression.However,for the optimal reference wavelengths selection under the ZF prediction method,we should miniize the influence of the perturbation.The second application of the correlation is on power allocation.We consider two power allocation goals,which are the transmission rate and the received signal distor-tion.For each power allocation goal,we consider two kinds of optimization scenarios.The first scenario is that all the wavelengths serve a single-user and we maximize the single-user performance.The second scenario is that each wavelength serves one user and we solve the multi-user fairness problem,i.e.,maximize the performance of the user with the worst performance.In total,four power allocation problems are formulated and solved.Note that there is only one dominant eigenvalue of the link gain covariance ma-trix when simply changing the geometry parameters of the transmission system,which indicates that the link gain ratios are approximately uniform over the broad spectra.Fur-thermore,we can prove that when the link gain ratios are perfectly uniform,different link gains over all wavelengths lead to the same power allocation result for both high signal-to-noise ratio(SNR)and low SNR approximations for all the four power allo-cation problems.Moreover,the losses of using fixed power allocation for the scenario of imperfectly uniform link gain ratios are analyzed and we find that the single-user optimization problems have few performance degradations when using fixed power al-location,while the multi-user optimization problems have significant degradations.The third application is on channel estimation with inter-symbol inferference(ISI).This time we need to consider the correlation of channel impulse response.A novel correlation-based channel estimation method is proposed,where only the reference wavelengths are assigned with pilots and the channel estimates on those wavelengths without pilots are estimated by the channel estimates on the reference wavelengths.Moreover,the pilot pattern optimization is studied for the proposed correlation-based channel estimation method.The results show that the correlation-based channel estima-tion method has a significant gain compared with the conventional channel estimation where all channels are allocated with equal-length pilots.The optimum pilot pattern for the correlation-based channel estimation can further increase the performance by 3dB.