  This paper presents a novel massive multiple-input multiple-output (MIMO)
transmission in beam domain for optical wireless communications. The optical
base station equipped with massive optical transmitters communicates with a
number of user terminals (UTs) through a transmit lens. Focusing on LED
transmitters, we analyze light refraction of the lens and establish a channel
model for optical massive MIMO transmissions. For a large number of LEDs,
channel vectors of different UTs become asymptotically orthogonal. We
investigate the maximum ratio transmission and regularized zero-forcing
precoding in the optical massive MIMO system, and propose a linear precoding
design to maximize the sum rate. We further design the precoding when the
number of transmitters grows asymptotically large, and show that beam division
multiple access (BDMA) transmission achieves the asymptotically optimal
performance for sum rate maximization. Unlike optical MIMO without a transmit
lens, BDMA can increase the sum rate proportionally to $2K$ and $K$ under the
total and per transmitter power constraints, respectively, where $K$ is the
number of UTs. In the non-asymptotic case, we prove the orthogonality
conditions of the optimal power allocation in beam domain and propose efficient
beam allocation algorithms. Numerical results confirm the significantly
improved performance of our proposed beam domain optical massive MIMO
communication approaches.
