On the Performance of Spatial Modulations Over Multimode Optical Fiber Transmission Channels
Abstract
In this paper we analyze the performance of coded and uncoded spatial modulations over multi-mode fiber optic channels with Mode-Dependent Loss (MDL) under Maximum Likelihood (ML) and Zero-Forcing (ZF) detection schemes. We focus on multi-dimensional modulations that satisfy certain orthogonality criteria such as the TAST codes. In particular, we link the post-detection Signal-to-Noise Ratio (SNR) to the Orthogonality Defect Factor (ODF) of the equivalent channel matrix by deriving their closed-form expressions as well as characterizing their statistical properties. Using the post-detection SNR and ODF properties, we develop upper and ad-hoc tight bounds on the error probabilities, which illustrates how these “orthogonal” spatial modulations mitigate the MDL under both ML and ZF detection. The obtained properties also allow us to propose a modification to the detection algorithm such that it still achieves essentially optimal performance but at a much smaller cost than exhaustive or tree search algorithms. The theoretical results are validated numerically and by simulations.