Precoded generalized space shift keying for indoor visible light communications

We consider a visible light communication system with 2 transmit light emitting diodes (LED) and n_r receive photodiodes. An optical generalized space shift keying modulation scheme is considered for the transmission of bits where each LED can be either in ON state or OFF state at a given time. With this set-up, we design in this paper a precoder for this modulation scheme given the channel state information to improve the bit error rate performance of the system. As conventional precoding techniques for radio frequency at the transmitter cannot be applied to the optical intensity channel, we formulate an optimization problem with constraints for this specific channel. An analytical solution for the precoder is derived and the system performance is compared with and without precoder.