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