  In this paper, we investigate the problem of the joint transceiver and offset
design (JTOD) for point-to-point multiple-input-multiple-output (MIMO) and
multiple user multiple-input-single-output (MU-MISO) visible light
communication (VLC) systems. Both uplink and downlink multi-user scenarios are
considered. The shot noise induced by the incoming signals is considered,
leading to a more realistic MIMO VLC channel model. Under key lighting
constraints, we formulate non-convex optimization problems aiming at minimizing
the sum mean squared error. To optimize the transceiver and the offset jointly,
a gradient projection based procedure is resorted to. When only imperfect
channel state information is available, a semidefinite programming (SDP) based
scheme is proposed to obtain robust transceiver and offset. The proposed method
is shown to non-trivially outperform the conventional scaled zero forcing (ZF)
and singular value decomposition (SVD) based equalization methods. The robust
scheme works particularly well when the signal is much stronger than the noise.
