IEICE TRANS. FUNDAMENTALS, VOL.E97–A, NO.1 JANUARY 2014 49 PAPER Special Section on Wideband Systems Performance Analysis of MIMO/FSO Systems Using SC-QAM Signaling over Atmospheric Turbulence Channels * Trung HA DUYEN †a) , Nonmember and Anh T. PHAM †† , Member SUMMARY We theoretically study the performance of multiple-input multiple-output (MIMO) free-space optical (FSO) systems using subcarrier quadrature modulation (SC-QAM) signaling. The system average symbol- error rate (ASER) is derived taking into account the atmospheric turbu- lence eﬀects on the MIMO/FSO channel, which is modeled by log-normal and the gamma-gamma distributions for weak and moderate-to-strong tur- bulence conditions. We quantitatively discuss the inﬂuence of index of refraction structure parameter, link distance, and diﬀerent MIMO conﬁg- urations on the system ASER. We also analytically derive and discuss the MIMO/FSO average (ergodic) channel capacity (ACC), which is expressed in terms of average spectral eﬃciency (ASE), under the impact of various channel conditions. Monte Carlo simulations are also performed to validate the mathematical analysis, and a good agreement between numerical and simulation results is conﬁrmed. key words: free-space optical (FSO) communications, multiple-input multiple-output (MIMO), subcarrier quadrature-amplitude modulation (SC-QAM), atmospheric turbulence, channel capacity 1. Introduction Free-space optical (FSO) communications, also known as optical-wireless communication, is a cost-eﬀective, license- free, highly secured and broadband technique, which has recently received considerable attention for a variety of ap- plications [1], [2]. One of major impairments to the per- formance of FSO systems is the inﬂuence of atmospheric turbulence, which is caused by variations in the refractive index due to inhomogeneties in temperature, pressure ﬂuc- tuations, humidity changes, and motion of the air along the propagation path of the laser beam [3]. The atmospheric turbulence results in irradiance ﬂuctuations in the received signal, i.e., the signal fading, which severely degrades the system performance, especially when the transmission dis- tance is longer than 1 km [4]. Recent studies have shown that, similar to radio com- munications, the eﬀect of fading over FSO links can be signiﬁcantly relaxed by employing multiple-input multiple- output (MIMO) technique with multiple lasers at transmit- ter and multiple photodetectors at receiver. The ﬁrst use of space diversity in FSO systems has been proposed in [5]. In [6] Lee and Chan have derived the outage probability of Manuscript received March 15, 2013. Manuscript revised July 27, 2013. † The author is with School of Electronics and Telecommuni- cations, Hanoi University of Science and Technology, Vietnam. †† The author is with the Computer Communications Lab., Uni- versity of Aizu, Aizuwakamatsu-shi, 965-8580 Japan. ∗ The paper is presented in part at IEEE ICC 2013. a) E-mail: trung.haduyen@hust.edu.vn DOI: 10.1587/transfun.E97.A.49 MIMO/FSO systems over log-normal turbulence channels. This study showed that the power gain of diversity increases as turbulence becomes stronger, and in theory, power gain of up to 25 dB could be achieved when the number of re- ceivers approaches inﬁnity. In [7], [8] Wilson et al. have for- mulated and analyzed symbol-error rate (SER) and bit-error rate (BER) of MIMO/FSO transmissions assuming pulse- position modulation (PPM) and Q-ary PPM in both log- normal and Rayleigh fading channels. In [9] Navidpour et al. have investigated the BER performance of MIMO/FSO links for both independent and correlated log-normal atmo- spheric turbulence channels. In [10], under the assumption of intensity-modulation/direct-detection (IM/DD) with on- oﬀ keying (OOK), a closed-form expression for the BER expression of single-input single-output (SISO) case and ap- proximated closed-form BER expressions of MIMO/FSO links over strong turbulence channels in terms of Meijer’s G-functions have been investigated. Previous studies only focus on MIMO/FSO systems employing OOK and PPM modulation techniques. How- ever, in the presence of atmospheric turbulence, OOK mod- ulation needs an adaptive threshold to achieve its optimal performance [11]. On the other hand, PPM modulation has a poor bandwidth eﬃciency because of the fact that the nar- row pulse is required for the high PPM multiplicities. To overcome the limitations of both OOK and PPM, subcar- rier intensity modulation schemes, such as subcarrier phase- shift keying (SC-PSK) and quadrature-amplitude modula- tion (SC-QAM), have been considered for SISO/FSO sys- tems. FSO system using SC-PSK signaling was ﬁrst pro- posed by Huang et al. [11], and its performance over turbu- lence channels has been extensively investigated [12]–[15]. FSO system using SC-QAM has also gained attention due to its better spectral eﬃciency. In [16], Hassan et al. presented the average SER (ASER) for subcarrier intensity modulated wireless optical communications with general order rectan- gular QAM by using the series expansion of the modiﬁed Bessel function [17]. ASER of general-order rectangular QAM of FSO systems over atmospheric turbulence chan- nels can be found in [18], [19]. Most recently, BER anal- ysis of FSO systems with avalanche photodiode (APD) re- ceiver over atmospheric turbulence channel have been re- ported [20]. However, to the best of our knowledge, the per- formance analysis of MIMO/FSO systems using SC-QAM signaling has not been reported in the literature. In this paper, we therefore present a study on FSO sys- tems employing both MIMO technique and SC-QAM sig- Copyright c  2014 The Institute of Electronics, Information and Communication Engineers