Comparison of phase screen generation methods for the simulation of atmospheric turbulence effects

Abstract

Free-space optical communication (FSOC) systems have recently gained a great deal of attention due to their capability to deliver high-speed data over wireless free-space channel without exhausting sparse radio frequency resources. However, these systems suffer from various channel effects, including absorption, scattering, scintillation, beam wandering, angle-of-arrival fluctuations, and beam spreading. The absorption and scattering reduce the amount of light collected at the receiver and are relatively slowly varying phenomena. On the other hand, scintillation, beam wandering, angle-of-arrival fluctuations, and beam spreading are caused by atmospheric turbulence and limit the performance of FSOC systems even under good weather conditions. Experimental evaluation of atmospheric turbulence effects is highly time-consuming, costly, and not always possible, especially in ground-to-air/air-to-ground links. Computer simulation of atmospheric turbulence allows us to study its impact on the system performance in systematic and easy-to-handle manners. Thus, before real tests of an FSOC system, simulation study needs to be carried out to evaluate and predict the system performance. Random phase screens are essential elements of simulating light propagation through the atmospheric turbulence media. They should reflect theory accurately and also be implementable. In this thesis, I attempt to generate random phase screens by using four methods, fast Fourier transform (FFT) method, subharmonic method, covariance matrix method, and Zernike polynomial method, and compare the performance and simulation time of them. For this purpose, 5000 phase screens are first created by each generation method. The simulation time is also estimated. Then, the values of structure function are evaluated as a function of a distance between two points in the screen. To reduce the statistical fluctuation, the average values are obtained from the 5000 screens. The results show that the FFT method does not accurately generate the phase screen due to lack of low spatial frequency components. The structure function of the phase screens generated by subharmonic method exhibits the values close to the theoretical ones, but they are a few percentages short of the theoretical value even though the size of the screen is very large. Covariance matrix method shows the best performance in terms of accuracy, but it takes a bit longer to generate the screens than FFT and subharmonic methods. It takes the longest time to generate the phase screens using Zernike polynomial method. For example, it takes 75 times longer time than the covariance matrix method when we generate phase screens by using 300 Zernike polynomials. In conclusion, the covariance matrix method generates the phase screens most close to the theory with its simulation time comparable to the other sample-based methods. Therefore, this method would be suitable for simulating atmospheric turbulence for most applications, including FSOC.

Keywords: atmospheric turbulence, phase screens, free-space optics, free-space optical communications, and atmospheric optics