## 1 Introduction  
The increasing requirement for high data rates, low cost, and improved security over recent years has given rise to the employment of terrestrial free-space optics (FSO) as a potential technology for point-to-point communications. FSO systems are characterized by a plethora of prominent advantages, including, among others, unlicensed operation, small power consumption, immunity with respect to multipath dispersion, and electromagnetic interference, as well as flexibility for deployment and re-deployment due to their compactness and the rather low installation cost [1; 2]. However, the propagation of optical beams is impaired by several deleterious effects that overwhelmingly emerge from the varying nature of the atmospheric medium. Absorption (mainly due to molecules of water, carbon dioxide, and ozone), aerosol scattering (mainly due to fog particles), and the dispersion of group velocity often attenuate the signal to a certain degree. Additionally, refractive index variations along the propagation path originate from the very complex atmospheric turbulence process, and result in the so-called scintillation effect, which causes rapid fluctuations in the irradiance of the optical signal at the receiver side. Furthermore, FSO links suffer from misalignment effects between transmitter and receiver terminals, leading to intensity variations in the received signals as well [2]. In the context of FSO communications, several modulation formats have been proposed and implemented, including on-off keying (OOK), pulse-position modulation (PPM), and subcarrier intensity modulation (SIM) [3]. By assigning data from different users to different subcarriers, SIM systems can achieve a higher capacity or throughput than OOK and PPM schemes with comparatively lower bandwidth than PPM. However, this comes at the cost of increased transmitter power and cross-talk [4]. On the other hand, if SIM techniques are applied, some degradation of the error performance has to be taken into consideration due to the non-perfect synchronization of the carrier frequency and phase [5]. Indeed, from a practical point of view, it is very hard to obtain an accurate estimation of the phase of the received signal [6]. This difficulty is to a large extent due to phase noise, which is a stochastic process normally described by a Tikhonov distribution [7]. The impact of turbulence, along with pointing errors and phase noise, on subcarrier phase shift keying (PSK) performance has recently attracted some attention in the open literature. [PERSON], [PERSON] and [PERSON] in [7] applied a phase-locked loop (PLL) for phase noise compensation over strong turbulence conditions described by a K distribution. Additionally, the bit error rate (BER) performance of a subcarrier binary PSK (BPSK) system with Tikhonov and gamma-gamma models was investigated in [6] by [PERSON]. On the other hand, the BER of subcarrier BPSK and quadrature phase shift keying (QPSK) solutions was derived by [PERSON] et al. in [3] by assuming phase effects determined by a Tikhonov distribution and weak turbulence conditions using a lognormal model. More recently, [PERSON] and [PERSON] in [5] complemented the study of [PERSON] et al, [3], via a gamma-gamma turbulence model in the presence of zero boresight pointing errors and phase noise. Considering an \(M\)-ary subcarrier PSK FSO system, they derived approximate closed-form average symbol error probability (ASEP) expressions, which turned out to be accurate enough over a wide signal-to-noise ratio (SNR) range. Regarding the distance dependency of fading impairments in FSO systems, which are induced by combined turbulence and misalignment effects, we understand that shorter hops between nodes relate to a weaker amount of fading compared to the total end-to-end link. Consequently, the use of relays in FSO systems is an effective method to extend the coverage distance and lessen the negative effects of fading [8; 9].