## 1 Introduction  
Free-space optical (FSO) communication is widely employed in inter-satellite links, satellite-ground links, and communication between various flight platforms and terrestrial stations due to the advantages of high speed, high security, small equipment size, and no requirement of a spectrum license [1, 2, 3, 4]. However, the atmospheric refractive index fluctuates randomly, resulting in an atmospheric turbulence effect [5]. It will severely deteriorate the laser beam and limit the FSO transmission distance or the communication bit rate. Techniques such as adaptive optics [6], aperture averaging [7], error control coding [8], and relaying [9] have been used to mitigate the effects of turbulence and improve the reliability of the FSO system.  
For FSO transmission, higher speed signals suffer more from the influence of atmospheric turbulence. It will perform better if the data are separated into multiple low-speed consequences. Orthogonal frequency-division multiplexing (OFDM), which includes multiple orthogonal sub-carriers [10], can carry a high-speed data stream by dividing it into a series of low-speed sub-carrier signals. Furthermore, coherent modulation formats, such as binary phase shift keying and quadrature phase shift keying (QPSK), have better transmission performance in turbulence channels than intensity-modulated formats [11]. Coherent optical OFDM (CO-OFDM) has exhibited high spectral efficiency and strong anti-interference ability [12, 13, 14]. The complex OFDM series can be easily separated into real and imaginary components and modulated by an in-phase quadrature modulator (IQM) [10]. As a result, it is entirely compatible with conventional coherent FSO communication systems. Using OFDM technology, an FSO communication link is experimentally demonstrated with a distance of 2.5 km and a rate of 10 Gbit/s, where a 3 dB receiver sensitivity improvement is obtained compared to OOK signals [15]. Moreover, a CO-OFDM-FSO scheme with quadrature amplitude modulation (QAM) signals has been proposed to significantly improve the transmission distance and data rate [13]. Furthermore, CO-OFDM with an optical receiving antenna array has been numerically predicted to realize a 20 Gbit/s FSO communication over 4500 km [16].  
Diversity technologies, including spatial diversity, temporal diversity, polarization diversity, and wavelength diversity (or frequency diversity), are widely utilized to increase receiver sensitivity [17]. In principle, OFDM and diversity technology are compatible, and they can be used together to improve the link performance. The outage performance has been improved by using wavelength diversity in an OFDM-FSO system under E-Weibull channels [18]. The sensitivity has been predicted to improve by 6 dB with polarization diversity for an OFDM-FSO link [19]. Spatial diversity is a promising solution to suppress atmospheric turbulence [20]. In particular, spatial diversity reception with multiple receivers has a simple structure and does not need any extra change at the transmitter. The signals collected by all the receivers can be combined using digital signal processing (DSP) of linear combining algorithms, such as the selection combining (SC) algorithm, maximum ratio combining (MRC) algorithm, and equal gain combining (EGC) algorithm [21]. However, OFDM-FSO communications with spatial diversity reception are still limited. It is expected to improve the FSO receiving performance by combining the two kinds of technologies.  
In this paper, we propose to detect the OFDM-QPSK signal using a spatial diversity receiver array in a FSO link in order to improve the receiving sensitivity. The turbulent channel is simulated by the phase screen method and the OFDM-QPSK signal is simulated using the Monte Carlo method to calculate the bit error rate (BER) and the constellation diagram. The sensitivity improvement of spatial diversity is evaluated by using multiple receivers.