Average symbol error rate analysis of reconfigurable intelligent surfaces-assisted free-space optical link over log-normal turbulence channels

ABSTRACT


INTRODUCTION
Free space optical communication systems are where free space acts as a communication channel between transceivers that are line of sight (LOS) for the successful transmission of optical signals. The critical advantage of free-space optical (FSO) is flexibility in designing optical network architectures at very high speeds, at tens and hundreds of Gbit/s rates [1]. Atmospheric propagation factors, for example, fog, haze, snow, and rain, are the most critical disadvantages. The deployment of FSO systems faces some challenging problems: negative effects scattering, turbulence, absorption, and even misalignment between transmitter and receiver. A new procedure was presented in [2]- [7] for deriving the statistical distribution of pointing errors and turbulence in current works.
Currently, deploying optical relay nodes is the only possible resolution to the obstruction problem. This approach is expensive and inconvenient because of additional hardware deployment [8]- [12], [13]- [17]. Reconfigurable intelligent surfaces (RIS) are electromagnetic devices with electronically controllable characteristics. RIS able to refract, extinct, scatter or reflect the incoming signal by influencing the incoming signal's phase, polarization, and amplitude. RIS module design is based on its application. The RIS module includes multiple mirrors on a planar array. It directs the incoming signal toward a targeted area and reconfigures the transmission channel [18]- [24]. It helps wireless networks have many benefits over vying technologies. Besides, RIS consumes low power and is constructed with electronically controllable components. Therefore, it has become an area of current research interest. Materials for reconfigurable metasurfaces often have optical properties modulated by an optical stimulus, mechanical, thermal, or external electrical. Conductive oxide materials, for example, indium tin oxide (ITO) in Figure 1. It includes four layers, i.e., a metal-semiconductor conductive oxide-metal (Au-Al2O3-ITOAu) setup. Upon applying a positive (negative) voltage bias, the free charges of the ITO layer accumulate (deplete) at the semiconductor-ITO interface. This variation of the charge accumulation layer causes a significant change in the refractive index of the ITO layer, which in turn alters the phase of the reflected electromagnetic waves. Similarly, graphene has been shown to exhibit significant charge carrier-dependent modulation for THz to near Infrared radiation (IR) wavelengths if an electrical field is applied [25].
This study introduces a theoretical investigation of the average symbol error rate (ASER) analysis of RIS-assisted FSO link. We theoretically analyze the ASER of signal-to-noise ratio (SNR) of RIS assisted FSO link over log-normal turbulence channels. The remainder of the study is presented as the following. Section 2 shows system descriptions and channel models. Section 3 presents the closed-form statistical analysis. The numerical results and discussions are shown in section 4. Finally, the study is included in section 5.

SYSTEM AND CHANNEL MODELS 2.1. System model
The RIS-assisted FSO link environment under study is presented in Figure 2. Nodes S and D are the source and destination nodes, respectively. The signal is from node S. After the signal reflects on a RIS element, it is transmitted to D. S and D do not directly link because of obstructions. The RIS module is placed at an appropriate position in the building. It reflects the incoming signal. Besides, it assures that transferred light reaches the receiver without being blocked. We assume that both transmitted and reflected channels exhibit weak turbulence levels, and the light intensity over them undergoes the same attenuation level. It is also assumed that, at each receiving end, the detectors face similar pointing errors. In the case under study, we assume there are no pointing errors.

The log-normal channel
Because of atmospheric conditions, one optical wave beam is deformed when it moves via the atmosphere. Three main signal factors impair the FSO link: atmospheric turbulence, attenuation, and pointing errors. The atmospheric turbulence caused by the irradiance fluctuation represents signal scintillation. Many models have been proposed for representing the atmosphere-induced turbulence. For weak turbulence conditions, h(t) is considered a spontaneous process according to log-normal distributions. The probability density function (pdf) of the irradiance intensity in the weak turbulent is given by [14].
where is the scintillation index, and is defined at [13] In these equations, = √ 2 /4 where, = 2 / is optical wave number, is wavelength, is link distance, is radius of a circular receiving aperture, 2 is Rytov variance. Assuming that spherical wave propagation is defined: In [10], 2 is the refractive-index structure parameter.

CLOSED-FORM STATISTICAL ANALYSIS 3.1. End-to-end SNR
We assume the following: i) RIS module has a reflective function only, ii) the light cannot move through the RIS, and iii) the channel phases' perfect knowledge at the destination and RIS. The detected signal is determined as (5) [21]: where is symbol energy, is S-RIS, is RIS-D, is characterizes the RIS element with being its amplitude reflection coefficient and its induced phase [5], [14], is transmitted symbols, is received symbols, is additive white Gaussian noise at the destination The main goal is to reflect the original signal in such a way as to optimize signal reception at the D position. It can do by end-to-end SNR maximization. The value of SNR is computed by (6) [24]: where ̄= 0 is the average SNR in both S-RIS and RIS-D sub-channels, and 0 is the noise power spectral density.

PDF of the end-to-end SNR
The overall system's gain is , where the quantity is deterministic in contrast to and , which are random variables. Denote ( ), the SNR's PDF. It is evaluated as [26]. where (⋅) is PDF of the S-RIS, (⋅) PDF of the RIS-D.
We are assuming that weather conditions are constant. The channel' parts are represented by a distribution combination of turbulence levels and pointing errors. The resulting unified PDF, ( ) is expressed as (8) [27]: where ∈ {ℎ, }. We sequentially substitute by and in (8), and obtain ( ) and ( ) respectively as (9), (10): where ̄ is average value of the SNRs and ̄ is average value of the SNRs . From (7), (9), and (10), the end-to-end SNR's PDF ( ), is computed as (11).

ASER ANALYSIS
We consider the ASER of FSO system that uses SC-QAM over atmospheric disorder. It is computed as (13) [17]: where ( ) is the conditional error probability (CEP). For using SC-QAM modulation, the CEP presented as (14):

NUMERICAL RESULTS AND DISCUSSION
This section presents numerical results for RIS-assisted FSO systems' ASER analysis utilizing rectangular quadrature amplitude modulation and an avalanche over weak atmospheric turbulence channels modeled by a log-normal distribution. We use expressions that are derived in previous sections. ASER is computed as a transmitted optical power's function, . This approach assures fair comparison. Many different operating conditions are investigated when the performance analysis: link distance, transmitted optical power, and rectangular quadrature amplitude modulation schemes. We can see the parameters of the analysis in Table 1. We analyze the average SNR versus ASER with different link distances, transmitted optical power, and QAM scheme. Figures 3 and 4 show the mathematical results of the scenarios. The causes can be explained: while the quadrature-to-in phase decision distance ratio decreases by increasing the modulation level. Therefore, the ASER of the FSO system will become worse. So, when using the high modulation level and still ensuring a low ASER, it must increase the transmitted optical power.  Figure 5 shows that ASER is an average electrical SNR function for different QAM schemes. We consider the case with RIS and without RIS. The ASER declines with the growth of the SNR, RIS-assisted, and reduces QAM schemes. The influence of the RIS-assisted on the system's performance is much more influential in high SNR regions than in low regions. Simulation results and analytical results are closed agreement.

CONCLUSION
This study analyzes the ASER of RIS-assisted FSO system using the QAM modulation scheme over log-normal atmospheric turbulence channels. We propose theoretical expressions for RIS-assisted FSO systems considering different transmitted optical power, link distance, and QAM modulation scheme. It can see a significant improvement if deploying the RIS technique. That solves the LOS transmission problem. The numerical results pointed out that using RIS with transmitted optical power' proper selection improves the system significantly. In this study, the QAM schemes reach the best ASER of the system. ISSN: 2088-8708 