Upper Burst Error Bound for Atmospheric Correlated Optical Communications Using an Alternative Matrix Decomposition

Abstract

Atmospheric optical communication has been receiving considerable attention recently for use in high data rate wireless links (Arnon, 2003; Haas et al., 2002; Juarez et al., 2006; Zhu & Kahn, 2002). Considering their narrow beamwidths and lack of licensing requirements as compared to microwave systems, atmospheric optical systems are appropriate candidates for secure, high data rate, cost-effective, wide bandwidth communications. Furthermore, the atmospheric optical communications are less susceptible to the radio interference than radio-wireless communications. Moreover, free space optical (FSO) communication systems represent a promising alternative to solve the “last mile” problem, above all in densely populated urban areas. However, even in clear sky conditions, wireless optical links may experience fading due to the turbulent atmosphere. In this respect, inhomogeneities in the temperature and pressure of the atmosphere lead to variations of the refractive index along the transmission path. These random refractive index variations produce fluctuations in both the intensity and the phase of an optical wave propagating through this medium. Such fluctuations can lead to an increase in the link error probability limiting the performance of communication systems. In this particular scenario, the turbulence-induced fading is called scintillation. If the receiving aperture size in these optical systems, D0, can be made larger than the correlation length, d0, then the received irradiance becomes a spatial average over the aperture area and the scintillation level measured by the detector begins to decrease. This effect is known as aperture averaging (Andrews & Phillips, 1998). Unfortunately, it could be neither practical nor desirable to satisfy this condition, especially in diversity receivers, so we will assume that D0 < d0 throughout this chapter. Finally, weather-induced attenuation caused by rain, snow and fog can also degrade the performance of atmospheric optical communication systems in the way shown in (Al Naboulsi & Sizun, 2004; Muhammad et al., 2005), but are not considered in this chapter. Spatial diversity reception is a good proposal in order to mitigate the adverse effect of the scintillation on the transmitted signal. Nevertheless, many researchers assume in a first approach that turbulence-induced fading is uncorrelated at each of the optical receivers 20