A closed-form expression for the average capacity of the heterodyne differential phase shift keying (DPSK) free-space optical (FSO) communication systems over gamma-gamma turbulence channels is derived by considering the effect of pointing errors. Numerical results show the average capacity can be evaluated with the effect of atmospheric turbulence conditions, beamwidth and jitter variance. Meanwhile, these results verify the accuracy of our mathematical analysis. This work can be helpful for the heterodyne DPSK FSO communication system designer.Introduction: Outdoor free-space optical (FSO) communication systems have received significant attention in recent years [1, 2]. The system always suffers from atmospheric turbulence and pointing errors. Turbulence-induced fading is known as scintillation and is caused by variations of the refractive index. Furthermore, thermal expansion, dynamic wind loads and weak earthquakes result in the sway of high-rise buildings, which causes vibrations of the transmitter beam, so the effect of misalignment (pointing errors) occurs between the transmitter and receiver. Most studies on the combined effect of atmospheric turbulence and pointing errors are based on the intensity modulation/direct detection (IM/DD) [1,2]. Although direct detection is the main detection method for FSO systems, heterodyne detection can overcome the thermal noise and has been proposed as an important detection method [3]. In [3,4], Kamran and Tsiftsis have, respectively, studied the bit error rate (BER) performance for the heterodyne differential phase shift keying (DPSK) FSO systems in the gamma-gamma (GG) and K channel without considering the effect of pointing errors. In the presence of pointing errors, Harilaos et al. have evaluated the BER of heterodyne DPSK FSO systems over the GG channel [5]. The majority of these earlier works focus on the analysis of BER. However, average capacity is another important parameter for communication systems [6,7]. In [6], the average capacity of IM/DD FSO systems has been evaluated depending on the turbulence conditions, link length and operation wavelength. In [7], the average capacity of direct detection FSO systems has been investigated by considering the effect of atmospheric turbulence conditions, beamwidth, detector size, jitter variance and transmitted optical power. In this Letter, our theoretical model considers the average capacity in closed-form solution for the heterodyne DPSK FSO communication systems over GG turbulence channels with the combined effect of atmospheric turbulence and pointing errors. This closed-form expression of average capacity is presented by considering the effect of atmospheric turbulence conditions, beamwidth, and jitter variance.
