The Impact of Optical Beam Position Estimation on the Probability of Error in Free-Space Optical Communications

Optical beam position on a detector array is an important parameter that is needed to optimally detect a pulse position modulation (PPM) symbol in free-space optical communications. Since this parameter is generally unknown, it is essential to estimate the beam position as accurately as possible. In this paper, we examine that an accurate estimate of the beam position is required in order to minimize the probability of PPM symbol detection error. Furthermore, we employ different estimators/trackers of the beam position (which could be stationary or time-varying), and compare the probability of error performance of the detectors using those estimators. The probability of error is calculated with the help of Monte Carlo simulations for the uncoded 8-PPM and 16-PPM systems, each of which employ photon counting maximum likelihood receivers. It is found out that the probability of error is minimum for the maximum likelihood estimate of the stationary beam position. Moreover, for the dynamically varying beam position, a particle filter with a sufficiently large number of particles provides a close-to-optimal probability of error performance.