Bit Error Rates for Focused General-Type Beams

Abstract

Using the scintillation index of general beam formulation, bit error rate (BER) is investigated for focused Gaussian, cos-Gaussian, cosh-Gaussian and annular beams in weak atmospheric turbulence. We have employed our previously derived formulation of the scintillation index of these beams by Rytov method. Rytov method scintillation theory is known to yield accurate results for focused beams on horizontal paths under certain regions. Therefore we find the scintillation indices of the mentioned beams for the valid region. Using the log-normal distributed intensity, BER values versus signal-to-noise ratio (SNR) are calculated for Gaussian, cos-Gaussian, cosh-Gaussian and annular beams. In our study, the focal lengths (radius of curvature) of all the mentioned focused beams are equal to the propagation distance. The improvement of BER is observed for variations of propagation length, source size and wavelength of operation. Based on these parameters, BER values of Gaussian, cos-Gaussian, cosh-Gaussian and annular beams are compared. BER values we found for the focused Gaussian, cos-Gaussian, cosh-Gaussian and annular beams decrease with increasing source sizes. Likewise, BER values of focused Gaussian, cos-Gaussian, cosh-Gaussian and annular beams decrease with increasing wavelength. The focused annular beam attains the lowest BER value for small source sizes and long propagation distances. Moreover, BER for focused beams is compared with their collimated counterparts. We observe that focused beams have lower BER values than the collimated beams on horizontal paths. Our formulation can easily be extended to cover corresponding higher order beams, however in this paper we concentrate mainly on the zero order beams.