In some applications of optical communication systems, such as satellite optical communication and atmospheric optical communication, the optical beam wanders on the detector surface as a result of vibration and turbulence effects, respectively. The wandering of the beam degrades the communication system performance. In this research, we derive a mathematical model of an optical communication system with a detection matrix to improve the system performance for direct-detection pulse-position modulation. We include a centroid tracker in the communication system model. The centroid tracker tracks the center of the beam. Using the position of the beam center and an a priori model of the beam spreading, we estimate the optical power on each pixel (element) in the detection matrix. Using knowledge of the amplitudes of signal and noise in each pixel, we tune adaptively and separately the gain of each individual pixel in the detection matrix for communication signals. Tuning the gain is based on the mathematical model derived in this research. This model is defined as suboptimal, owing to some approximations in the development and is a suboptimum solution to the optimization problem of multiplied by free variables, where are the dimensions of the detection matrix. Comparison is made between the adaptive suboptimum model and the standard model. From the mathematical analysis and the results of the comparison it is clear that this model significantly improves communication system performance.
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