Optimal space signalling for intensity modulated MIMO optical wireless communications

This paper investigates the design of optimal space signaling for an intensity modulated direct detection multi-input-multi-output optical wireless communication system with independent and non-identically log-normal distributed channel coefficients. In order to optimize both large-scale diversity and small-scale diversity gains with a maximum likelihood detector, the design problem is formulated into a max-min optimization problem with continuous-discrete mixed design variables. Two techniques are proposed to solve the problem: 1) by taking advantage of the full large scale diversity condition, all spatial codewords are properly sorted to simplify the inner minimization problem with the discrete design variables; and 2) a novel geometrically weighted inequality is established to carefully deal with a specific objective function of the power products in the outer maximization problem with the continuous variables. Among all the high dimensional nonnegative space signaling vectors, we rigorously prove that the spatial repetition signaling (RS) with an optimal power allocation is optimal under an average optical power constraint. Simulation results indicate that in a high signal to noise ratio regime, our optimally designed space signaling has better error performance than RS, which is the best space signaling available in literature for this application.