# Optical Beam Position Estimation and Tracking in Free-Space Optical Communications

#### Abstract

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 therefore essential to estimate the beam position as accurately as possible. In this thesis, we examine different algorithms that are used to estimate and track the beam position which could be either stationary, or time-varying. We use different estimators (Centroid, Template-Matching and Maximum Likelihood) and trackers (Kalman and particle filters) for stationary/dynamic beam position scenarios, and compare their performance in terms of mean-square error and computational complexity. Simulation results indicate that for various signal-to-noise ratios and detector array configurations, the maximum likelihood estimator achieves the lowest mean-square error performance of the three stationary beam position estimators. For tracking with particle filters, the greater the number of particles used for the purpose of tracking, the superior the mean-square error performance. However, the better performance of the maximum likelihood estimator, and the particle filters employing a larger number of particles, comes with the overhead of larger computational complexity. Furthermore, we also argue that an accurate estimate of the beam position is required in order to minimize the probability of PPM symbol detection error in an uncoded free-space optical communication system, and we use an argument based on the Chernoff bound in order to verify this. Moreover, we verify the probability of error minimization argument with the help of Monte Carlo simulations. From the simulations, we find out that probability of error increases monotonically with mean-square error achieved by a given estimator. Hence, the estimators that perform well in terms of mean-square error will also achieve better performance in terms of the probability of error criterion. Lastly we present some ideas for future work.

#### Degree

Ph.D.

#### Advisors

Bell, Purdue University.

#### Subject Area

Electrical engineering

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