  With the capability of reconfiguring the wireless electromagnetic
environment, intelligent reflecting surface (IRS) is a new paradigm for
designing future wireless communication systems. In this paper, we consider
optical IRS for improving the performance of visible light communication (VLC)
under a multiple-input and multiple-output (MIMO) setting. Specifically, we
focus on the downlink communication of an indoor MIMO VLC system and aim to
minimize the mean square error (MSE) of demodulated signals at the receiver. To
this end, the MIMO channel gain of the IRS-aided VLC is first derived under the
point source assumption, based on which the MSE minimization problem is then
formulated subject to the emission power constraints. Next, we propose an
alternating optimization algorithm, which decomposes the original problem into
three subproblems, to iteratively optimize the IRS configuration, the precoding
and detection matrices for minimizing the MSE. Moreover, theoretical analysis
on the performance of the proposed algorithm in high and low signal-to-noise
rate (SNR) regimes is provided, revealing that the joint optimization process
can be simplified in such special cases, and the algorithm's convergence
property and computational complexity are also discussed. Finally, numerical
results show that IRS-aided schemes significantly reduce the MSE as compared to
their counterparts without IRS, and the proposed algorithm outperforms other
baseline schemes.
