Training Receivers for Repetition-Coded MISO Outdoor Visible Light Communications

In this paper, we consider a multiple-input single-output (MISO) outdoor visible light communications (VLC) system in which the channel state information (CSI) at the receiver side is unknown and where the channel coefficients are independent and lognormal distributed. For such a system, we propose to take advantage of the repetition coding scheme in the space dimension and to add a fixed nonzero pilot bit to the head of the block to ensure the reliable blind estimation of channel coefficients. Then, a symbol-by-symbol maximum-likelihood (ML) receiver with linear complexity for the repetition-coded MISO outdoor VLC is developed, and the bit error performance is derived by integrating the conditional error function on the dominant decision region. It is proved that the training ML receiver can assure full-diversity achievement. In addition, optimal power allocation between the pilot bit and data bits is proven to be a concave problem, and an optimal power allocation scheme is presented. Simulation results demonstrate that the training receivers can achieve full diversity and that the optimal power allocation scheme can improve the error performance significantly.