On the Performance of Spatial Modulations over Multimode Optical Fiber Transmission Channels

In this paper, we analyze the performance of coded and uncoded spatial modulations over multi-mode fiber optic channels with the mode-dependent loss (MDL) under the maximum likelihood (ML) and zero-forcing (ZF) detection schemes. We focus on the multi-dimensional modulations that satisfy certain orthogonality criteria such as the Threaded Algebraic Space-Time (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 illustrate how these 'orthogonal' spatial modulations mitigate the MDL under both the ML and ZF detection schemes. The obtained properties also allow us to propose a modification to the detection algorithm such that it still achieves an essentially optimal performance but at a much smaller cost than exhaustive or tree search algorithms. The theoretical results are validated numerically and by simulations.