Access Type

Open Access Dissertation

Date of Award

January 2010

Degree Type

Dissertation

Degree Name

Ph.D.

Department

Electrical and Computer Engineering

First Advisor

John Liu

Abstract

Statistics are studied for signal detection in optical communication systems operating through the atmosphere. Optical communication systems with which this study is concerned are those that employ intensity modulation and direct detection. Atmospheric turbulence, which is fluctuations in the atmosphere's optical index of refraction, is a hindrance to optical wireless communications because of the signal fades, called scintillation, it causes at the optical receiver. In order to mitigate the deteriorative effect of turbulence on the communications system, the signal length and detection threshold for the signal detector must be properly chosen.

In this study, mathematical models for photoelectron generation in the receiver's photodiode and for the atmospheric turbulence channel enable the derivation or numerical calculation of the probability of miss, which is crucial for determining the signal length and detection threshold. The two commonly used types of photodiodes are the p-i-n photodiode and the avalanche photodiode. A light source of constant intensity impinging upon a photodiode will generate a photoelectron count which is a Poisson process for a p-i-n and a follows the McIntyre-Conradi distribution for an avalanche photodiode. In this study, the Webb distribution will be used as an approximation for the McIntyre-Conradi distribution. When the light intensity is itself a random process, as is the case for the received optical intensity after traveling through atmospheric turbulence, the photoelectron count will be a doubly (or conditional) stochastic process. To model the effect atmospheric turbulence, three different probability distributions are utilized to describe the received optical intensity. These are the lognormal distribution, valid for weak turbulence, the gamma-gamma distribution, valid for a range of turbulence strengths and the exponential distribution, valid for the saturation regime of signal scintillation.

With these models, the probability of miss is derived or numerically calculated. Simulations are provided to verify derived formulae for the probability of miss. Applying results in this study, a system designer can determine appropriate signal length and detection threshold settings in order to meet system specifications for signal detection.

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