On the use of wavelength and time diversity in optical wireless communication systems over gamma–gamma turbulence channels Hector E. Nistazakis n , George S. Tombras Department of Electronics, Computers, Telecommunications and Control, Faculty of Physics, National and Kapodistrian University of Athens, Athens 15784, Greece article info Article history: Received 25 January 2012 Received in revised form 14 March 2012 Accepted 15 March 2012 Available online 6 April 2012 Keywords: Atmospheric optics Optical wireless communications Diversity abstract Optical wireless communication or free space optical systems have gained significant research and commercial attention in recent years due to their cost-effective and license-free high bandwidth access characteristics. However, by using the atmosphere as transmission media, the performance of such a system depends on the atmospheric conditions that exist between transmitter and receiver. Indeed, for an outdoor optical channel link, the existence of atmospheric turbulence may significantly degrade the performance of the associated communication system over distances longer than 1 or even 0.5 km. In order to anticipate this, particular attention has been given to diversity methods. In this work, we consider the use of wavelength and time diversity in wireless optical communication systems that operate under weak to strong atmospheric turbulence conditions modeled by the gamma–gamma distribution, and we derive closed form mathematical expressions for estimating the system’s achievable outage probability and average bit error rate. Finally, numerical results referred to common practical cases are also obtained in order to show that wavelength and time diversity schemes enhances considerably these systems’ availability and performance. & 2012 Elsevier Ltd. All rights reserved. 1. Introduction It is recognized that there is an increasing research and commercial interest for optical wireless communication – or free space optical (FSO) – systems, since they combine license free high bandwidth access and security at low installation and operation cost, [1–4]. As it is for every communication link, the operation characteristics of an FSO link greatly depend on the (optical) channel state, i.e., on the atmospheric conditions in the area between the transmitter and the receiver. In this respect, one of the significant reliability and performance mitigation factors is the atmospheric turbulence, [2,5–8], which, for a typical outdoor line-of-sight, point-to-point optical link, may cause even rapid fluctuations of the propagated signal at the receiver input. It is, therefore, reasonable to expect that outdoor optical channels will appear to have randomly time-varying characteristics due to the so-called scintillation caused by turbulence, [9–13], and in conclusion, it is clear that this turbulence, affecting the optical channel characteristics, degrades the overall FSO systems’ perfor- mance and reliability. In order to combat the atmospheric turbulence deterioration effect on the operation of FSO links, particular attention has been given to diversity methods, which being popular in wireless radio, can be used in optical wireless, as well. In principle, the use of diversity refers to the consideration of multiple copies of the propagated signals in an attempt to overcome a poor transmis- sion media state and enhance the communications systems’ reliability and performance. Diversity can generally be realized in space, in time or in wavelength, [7,14–18]. Using spatial diversity, [14,15], an FSO system incorporates multiple transmitters and receivers at different places that send and receive copies of the same signal, resulting to a decreased probability of error, [7]. In time diversity schemes, [16], the system uses a single transmitter—receiver pair, but the signal is retransmitted at different time slots and the total effective bit rate of the link is decreasing. Finally, when wavelength diversity is employed, [7,17,18], FSO systems use a composite transmitter and the signal is transmitted at the same time at different wavelengths towards a number of receivers [19], each of which detects the signal at a specific only wavelength. In this work, we consider the use of wavelength and time diversity in FSO systems that operate under weak to strong atmospheric turbulence as modeled by the gamma–gamma Contents lists available at SciVerse ScienceDirect journal homepage: www.elsevier.com/locate/optlastec Optics & Laser Technology 0030-3992/$ - see front matter & 2012 Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.optlastec.2012.03.021 Abbreviations: AWGN, Additive White Gaussian Noise FSO: Free Space Optical; BER, Bit Error Rate; CSI, Channel State Information; cdf, cumulative distribution function; iid, independent and identically distributed; IM/DD, Intensity Modulation/ Direct Detection; OC, Optimal Combining; OOK, On–Off Keying; pdf, probability density function; SIMO, Single Input Multiple Output; SNR, Signal to Noise Ratio n Corresponding author. E-mail addresses: enistaz@phys.uoa.gr (H.E. Nistazakis), gtombras@phys.uoa.gr (G.S. Tombras). Optics & Laser Technology 44 (2012) 2088–2094