  Visible light communication (VLC) is an attractive subset of optical
communication that provides a high data rate in the access layer of the
network. The combination of multiple inputmultiple output (MIMO) with a VLC
system leads to a higher speed of data transmission named as MIMO-VLC system.
In multi-user (MU) MIMO-VLC, a LED array transmits signals for users. These
signals are categorized as signals of private information for each user and
signals of public information for all users. The main idea of this paper is to
design an omnidirectional precoding to transmit the signals of public
information in the MUMIMO-VLC network. To this end, we propose to maximize the
achievable rate which leads to maximizing the received mean power at the
possible location of the users. Besides maximizing the achievable rate, we
consider equal mean transmission power constraint in all LEDs to achieve higher
power efficiency of the power amplifiers used in the LED array. Based on this
we formulate an optimization problem in which the constraint is in the form of
a manifold and utilize a gradient method projected on the manifold to solve the
problem. Simulation results indicate that the proposed omnidirectional
precoding can achieve superior received mean power and bit error rate with
respect to the classical form without precoding utilization.
