Optical Spatial Modulation for FSO IM/DD Communications With Photon-Counting Receivers: Performance Analysis, Transmit Diversity Order and Aperture Selection

This paper investigates two pulse-based Optical Spatial Modulation (OSM) schemes as cost-efficient solutions for multi-aperture Free-Space Optical (FSO) communications with Intensity-Modulation and Direct-Detection (IM/DD). Namely, we consider Optical Space Shift Keying (OSSK) where information is encoded in the index of the pulsed optical source and Spatial Pulse Position Modulation (SPPM) where additional bits determine the position of the transmitted optical pulse resulting in higher transmission rates. A performance analysis is carried out over gamma-gamma channels with the exact Poisson photon-counting detection model. Exact Symbol Error Probability (SEP) expressions, simple upper bounds and the achievable transmit diversity orders are derived for both the open-loop and closed-loop scenarios. Based on the presented performance analysis, a transmit aperture selection scheme capable of maximizing the transmit diversity order is proposed for OSSK and SPPM in the closed-loop case. Results show that for open-loop OSSK, open-loop SPPM and closed-loop OSSK, the transmit diversity order does not depend on the severity of scintillation unlike the closed-loop SPPM case.