Precoded Optical Spatial Modulation for Indoor Visible Light Communications

This paper proposes a precoded optical space-domain index modulation scheme for indoor visible light communications, which is based on the optimization of the minimum Euclidean distance of optical spatial modulation (OSM) with real-valued modulation constellations. We find that the precoding matrix design can be formulated as a non-convex quadratically constrained quadratic program (QCQP), whose solution is generally intractable. To tackle this problem, we first consider the case of two optical transmit antennas (<inline-formula> <tex-math notation="LaTeX">$N_{t}= 2$ </tex-math></inline-formula>) in the precoded OSM and derive a closed-form solution for arbitrary <inline-formula> <tex-math notation="LaTeX">$M$ </tex-math></inline-formula>-order pulse amplitude modulation (PAM). Based on the derived solutions and the error vector reduction method, we then propose a low-complexity iterative (LCI) algorithm to identify the precoding matrix for the setup <inline-formula> <tex-math notation="LaTeX">$N_{t}> 2$ </tex-math></inline-formula>. To strike a flexible complexity-BER (bit error rate) tradeoff, we propose a successive convex approximation (SCA)-assisted matrix-based optimization method to transform the non-convex QCQP problem into a series of linear convex subproblems, which can be solved by low-complexity solvers. Simulation results show that these proposed algorithms are capable of substantially improving the system error performance compared with conventional OSM systems. Besides, a symbol-based SCA algorithm is introduced and it is shown to outperform the matrix-based SCA and the suboptimal LCI algorithm in terms of the BER.