Pulse position modulation, which is a modulation method obtained from the on-off keying (OOK) after encoding, has the characteristic of a high energy efficiency ratio, which increases peak optical power by reducing the duty cycle to overcome the adverse effects of factors such as atmospheric turbulence and dark counts on the signal. It also increases the signal-to-noise ratio, giving it better channel interference immunity, which is important in a wide range of applications in atmospheric and even deep-space optical communications. In pulse position modulation communication systems, classical receivers usually use direct detection to detect pulse position modulated signals, and their bit error rate (BER) performance is limited to the standard quantum limit (SQL). However, in quantum theory, their counterparts, which can obtain more information than classical communication systems, increase the BER performance to the Helstrom limit. However, there is a lack of relevant studies on the effects of practical factors on the BER performance of pulse position modulated quantum-enhanced receivers. In this study, we analyze the effects of the main practical factors, interference visibility, dark counts, and detection efficiency on the BER performance of a single pulse position modulated joint detection quantum-enhanced receivers based on 4-PPM (PPM, pulse position modulation) signal modulation. We also provide a theoretical reference for the subsequent development of quantum-enhanced receiver design and experiments.

First, the structure of the joint detection quantum-enhanced receiver system for pulse position modulated signals is introduced. Second, a decision-tree model of the corresponding feedback control strategy is established, from which the theoretical BER performance of the joint detection quantum-enhanced receiver is obtained. Then, the effects of practical factors such as interference visibility, dark counts, and detection efficiency on the system performance are analyzed by Monte Carlo simulation and compared with SQL, the Helstrom limit, and the ideal performance of the receiver to determine the influence mechanisms of various practical factors.

The simulation results show that as the average number of photons increases, the non-ideal interference visibility causes the bit error to first decrease and then increase, and its minimum point value is positively correlated with the interference visibility (Fig. 3). The existence of dark counts causes the bit error rate to converge to a fixed value, which is a monotonically decreasing function of dark counts (Fig. 4). Moreover, the non-ideal detection efficiency causes the bit error rate to decrease exponentially and the deceleration rate to increase with the detection efficiency (Fig. 5).

In the experiment, by adjusting the moderate numbers of average photons of input signals and the intensity and polarization of the local oscillator to obtain high interference visibility, and applying the single photon detector with high detection efficiency and low dark count, the BER performance of the single-pulse position modulation quantum-enhanced receiver can be improved under practical conditions while saving energy. In future, this approach could also be extended to multipulse position modulation to further determine the effects of practical factors on pulse position modulation at higher code rates. Meanwhile, the development of a suitable feedback strategy to reduce uncertainties in the conditional pulse nulling strategy could reduce the probability of code-word judgment errors.