This paper investigates the performance limits of pulse position modulation (PPM) optical communication systems using multi-pixel single-photon detectors (SPDs) under the constraint of detector dead time. A detailed analytical framework is developed by modeling the temporal detection behavior of SPDs as a Markov process, capturing the effects of dead time across consecutive PPM symbols. Closed-form expressions are derived for slot-wise detection probabilities, symbol transition matrices, and symbol error rate (SER) under maximum-likelihood detection. To enhance spectral and energy efficiency, a probabilistic shaping scheme is introduced and optimized using a truncated Blahut-Arimoto algorithm, allowing the transmitter to adapt its symbol distribution to the nonlinear detection characteristics of the SPD array. The proposed model is validated through extensive Monte Carlo simulations, demonstrating excellent agreement with theoretical predictions. Results show that probabilistic shaping significantly improves communication sensitivity, reducing the required number of photons per bit by up to 25% in photon-starved or high-noise regimes.

Free-space optical (FSO) satellite communication systems face distinct challenges depending on link topology, as horizontal or inter-satellite links (ISLs) operate above the atmosphere, uplink (UL) channels experience atmospheric turbulence near the transmitter, and downlink (DL) channels suffer primarily from geometric losses. This paper presents a comprehensive analysis of low Earth Orbit (LEO) satellite communication links employing single-photon detectors (SPDs) to address photon-starved conditions under various FSO channel impairments. We develop comprehensive channel models for DL, ISL, and UL that capture the combined effects of atmospheric turbulence, attenuation, pointing errors, angle-of-arrival (AoA) blockage, and geometric spreading. To further enhance performance in high-data-rate scenarios, we investigate multi-pixel SPD arrays and derive analytical expressions for error-rate performance that include detector dead time and dark counts. Our theoretical models are validated through extensive Monte Carlo simulations, showing strong agreement with predicted results. The findings highlight the benefits of spatial diversity in multi-pixel SPDs, demonstrating notable gains over single-pixel configurations. Finally, we provide key insights into optimizing link parameters: receiver aperture, link distance, detection efficiency, modulation order, and beam divergence for robust, high-sensitivity photoncounting FSO satellite communication.

Single-photon detector (SPD)-based communication systems, and in particular those employing superconducting nanowire single-photon detectors (SNSPDs), are playing an irreplaceable role in scenarios such as quantum communication and deep-space communication. Due to the high cost of experimental equipment, establishing a theoretical framework to analyze the performance of SPD-based systems has become an effective and low-cost solution. However, due to the unique detection mechanism of SPDs and the decisive impact of dead time, there is currently no analytical framework suitable for evaluating the performance of high-speed communication systems with SPDs. To fill this gap, we propose an analytical framework tailored to SPD-based pulse-position modulation (PPM) systems, based on a Markov detection model, and use this framework to evaluate the system’s symbol error rate and achievable symbol rate. The framework demonstrates significant advantages over simulations and experiments, particularly in its ability to predict theoretical performance limits. Based on this framework, we reveal unique characteristics of the SPD-based PPM system, such as channel asymmetry and detection dependence. In addition, optimization guidelines for three representative system configurations are provided.

The optical communication system using pulse position modulation (PPM) and superconducting nanowire single-photon detectors (SNSPDs) has attracted considerable attention for deep space applications as it enables high speed data transmission at extremely low average signal power. The deadtime of SNSPD is a critical factor in such systems because it primarily affects the signal detection efficiency. This becomes even more crucial in high-speed systems, where the deadtime can span several symbol periods. We employ the Markov chain model to characterize the high-speed PPM-SNSPD system and investigate its behavior. Analytical expressions for symbol transition probabilities are derived to characterize system-level metrics, including the symbol error rate and achievable code rate. Analysis shows that deadtime introduces memory to the PPM-SNSPD channel, resulting in channel asymmetry. Through experimental verification and simulations, we confirmed the effectiveness of our analysis. In addition, a set of new log-likelihood ratio (LLR) expressions is proposed based on the new model. Compared with the commonly used Poisson LLR expression, our proposed LLR expressions show more than 0.5 dB performance gain.