# Performance of SIMO FSO Links over Mixture Composite Irradiance Channels
## 1 Introduction  
The research and commercial interest for free space optical (FSO) systems has rapidly increased over the last few years, due to their inherent characteristics, including license-free high bandwidth access and security along with low installation and operation cost [1]. However, their operation depends strongly on the atmospheric phenomena and conditions that prevail in the region where the transmitter and the receiver are deployed. One of the most significant performance mitigation factors is the atmospheric turbulence effect, which causes rapid fluctuations of the signal irradiance as a result of the variations in the refractive index, due to in-homogeneities in temperature and pressure changes. Furthermore, the receiver irradiance suffers from misalignment-induced fading, also known as pointing errors (PE) effect [2]. That effect consists of two components, i.e., the boresight, which stands for the fixed displacement between the beam center and the center of the detector, and the jitter, which is the random offset of the beam center at the detector plane [3, 4]. In order to combat the impairments mentioned above, particular emphasis has been devoted to the employment of diversity techniques. In principle, the use of diversity refers to the consideration of multiple copies of the propagated signals in an attempt to overcome the poor transmission media state and enhance the system performance. The diversity is realized in space, time, or wavelength. In spatial diversity schemes, the FSO system incorporates multiple transmitters and receivers at different places, which send and receive copies of the same part of the information signal. In time diversity, the system uses a single transmitter-receiver pair, and each specific part of the information signal is retransmittedat different time slots. Finally, when wavelength diversity is employed, the signal is transmitted at the same time, by different wavelengths [4]. In this work, we consider a single-input multiple-output (SIMO) free space optical (FSO) system with wavelength, spatial, or time diversity at the receiver. For the first two cases, a single transmitter is considered, which emits \(M\) copies of the same part of the information signal towards \(M\) receivers. For the time diversity case, the transmitter is assumed to emit the \(M\) copies towards one receiver at different \(M\) time moments. Each copy arrives at the receiver and remains at the buffer of the system until all the \(M\) copies have been received. Hence, in all diversity cases, the information signals propagate through different, or the same path(s), but with different channel characteristics. Therefore, the total information signal at the receiver buffer is composed of \(M\) different versions of the same initial signal. Intensity modulation/direct detection (IM/DD) method with on-off Keying (OOK) or \(L\)-symbols Pulse Position Modulation (\(L\)-PPM) schemes and optimal combining (OC) for signal reception are taken into account [4]. The signals propagate through the turbulent atmospheric channel with additive white Gaussian noise (AWGN) and pointing error effects. After detection at the corresponding receiver, the photodetector converts the optical signals to electrical ones [4]. We assume that the channel between the transmitter and each receiver is memory-less, stationary, and ergodic. The turbulence effect is modeled using the mixture Gamma (MG) distribution that has been suggested in [5] in order to approximate the most frequent but complicated turbulence models, like Gamma-Gamma (GG) and \(M\)alaga distributions. A non-zero boresight (NZB) PE model is considered, using the efficient approximation introduced in [3]. The composite effect of these two impairments is described by another mixture distribution, which readily occurs after combination [5]. In this context, the performance of the SIMO FSO scheme is readily evaluated by deriving novel mathematical expressions for the outage probability (OP) and the average bit error rate (ABER).