None-line-of-sight (NLOS) optical wireless scattering communication over broad spectra can further increase the transmission rate beyond single wavelength scattering communication. A fundamental question is to investigate the link gain correlation over multiple wavelengths, which may lead to more efficient communication design and optimization approaches. We investigate the link gain correlation over multiple wavelengths under varying transmission media environments and transceiver geometries, and show that the link gain vector can be represented in a reduced dimensional space using principle components analysis (PCA). We also justify such correlation properties theoretically through a simplified single-scattering model. The link gain prediction is formulated as a joint continuous and discrete optimization problem, and is transformed into tractable forms. Linear prediction approaches are proposed based on zero-forcing (ZF) and linear minimum mean square error (LMMSE) criteria. It is seen that the LMMSE-based approach generally leads to lower prediction error compared with the ZF-based one, especially for the scenario with large residual eigenvalues of the link gain covariance matrix. We also investigate the link rates on multiple wavelengths, which also exhibit strong correlation for negligible background radiation intensity.