Performance investigation of 2 × 20 Gb/s MDM-RoFSO link incorporating spiral-phased Hermite–Gaussian modes under strong weather conditions

This research paper presents a novel high bit rate and spectral efficient 20 Gb/s mode division multiplexed (MDM) radio over free space optical communication (MDM-RoFSO) system. 10 Gb/s MZM/QAM-16-modulated data streams, each from two distinct channels, are transported over two spiral-phased Hermite–Gaussian (HG) laser modes, HG00 and HG01, respectively. These two HG channels are multiplexed using MDM at a 10 GHz RF signal, amplified and transmitted over the atmospheric link at an optical wavelength of 1550 nm. The proposed MDM-RoFSO system is simulated for MZM modulation over two distinct HG modes in clear sky, dense haze, dense fog, and strong rain weather conditions. The performance of the system is evaluated using performance metrics such as BER, eye diagram, Q factor, and link transmission range. The simulation results show that the HG00 mode is more robust and the extended transmission range is achieved from (7 to 24.4) km for (24.4 to 2.98) Q factor for clear sky to strong rain conditions. This transmission range is further extended by the factor of (2.9 to 1.7) km when the QAM-16 modulation is incorporated in composite (HG00 + HG01) mode and then transmitted in similar weather conditions for the acceptable BER of < 10–5. Finally, the simulation results confirm that the QAM-16 modulated composite HG mode is able to mitigate the atmospheric weather conditions and travel a longer transmission distance compared to individual HG mode transmission.


Introduction
Radio over free space optical (RoFSO) communication has demonstrated its utility in ultra-high speed and spectralefficient data transmission in an unguided medium, i.e. free space [1].It has been used to transport large volumes of interference-free secure data in less time with less power consumption over license-free bandwidth.In RoFSO, the radio frequency (RF) signal is used to transmit using an optical carrier through free space as the channel.As a result, RoFSO has emerged as an alternative solution for various applications such as wireless local area networks (WLAN), 5G mobile data transmission, and internet of things (IoT) services [2].However, the RoFSO link has to face various types of atmospheric attenuations due to different weather conditions such as haze, dust, fog, rain, and snow during optical signal transmission [3].The channel models for different weather conditions implemented in this research work have been reported and discussed in "Mathematical model of the proposed optical link" section in detail.To increase the transmission range while maintaining high-speed data transmission under such weather conditions, some major modifications such as modulation techniques, appropriate light source, estimation of the transmitting power levels, selection of transmission wavelength, and appropriate optical detector have to be implemented at the transmitter and receiver side [4].
In adverse weather conditions, FSO systems generally transmit data through adaptive threshold transmission schemes such as On-Off keying modulation.These schemes are not only difficult to implement, but they significantly increase the likelihood of fading errors in received data in bad weather.
In this paper, we implemented a QAM-16 modulation scheme to fix this problem.In adverse weather conditions where the transmission link degrades rapidly, QAM-16 facilitates high data rate transmission while maintaining excellent phase margin.As the QAM order increases, the distance between the constellation points reduces, and the probability of data errors increases.Furthermore, transmission of highorder QAM schemes requires a very high signal-to-noise ratio (SNR) to maintain a threshold SNR level to avoid poor link performance.QAM-16 provides a balance between data throughput and the requisite signal-to-noise ratio below 20 km of transmission range [5].
According to recent research, various multiplexing techniques, such as time division (TDM), wavelength division (WDM) and mode division multiplexing (MDM), have been found highly efficient in increasing transmission range while improving transmission rate and spectral efficiency.Among these approaches, mode division multiplexing (MDM) has been identified as a novel and promising candidate that optimizes spectrum efficiency and data rates and extends the transmission range in FSO transmission systems at acceptable SNR.These spatial laser modes are produced by using a various technique, such as spatial light modulators, photonic crystal fibres [6][7][8].Recently, different studies proposed the implementation of Laguerre-Gaussian (LG) and Hermite-Gaussian (HG) modes in FSO systems employing multiple channels under high attenuation environments such as dense dust, fog, haze and strong rain weather conditions.
The transmission of an OOK-modulated single channel at a data rate of 2.5 Gb/s over various dusty weather conditions was examined.Under dense dust, a link range of less than 0.2 km was achieved for 22 dB transmitted power.It is improved to 1 km in light dust conditions.BER, SNR, and channel capacity were used to evaluate performance.The results demonstrate a minor improvement in FSO system performance under dusty conditions; hence, it is regarded as an ultimate impairment.No multiplexing techniques have been reported to increase transmission range [9].
The 8 × 5 Gb/s channel MDM-FSO system with LG modes transmission was developed for clear sky to rain conditions to achieve the greatest possible link range at a 1550 nm wavelength.The FSO system transported data at a rate of 40 Gb/s for a distance of 3 km in clear weather and 0.650 km in severe rain conditions.Quality data reception has shown that BER performance has improved [10]. 10 Gb/s information was sent at 10 dBm power of employing a modified Duo-binary return to zero modulation (MDRZ) technique for optimal reception at a single channel receiver with an equal gain combining technique.An analysis of optical signal scintillation owing to rain-induced attenuation losses has been examined.For a link range of less than 1 km, Suriza, Carbonnea, Japan, and Samir models were used to estimate rainfall-induced attenuation for a given rainfall rate.An increase in BER, Q factor, and received optical power implies that the MDRZ-based FSO link has improved significantly [11].
A high-speed passive network with a 10 Gb/s FSO hybrid link has also been reported to provide a solution to last-mile bottleneck problems.A passive fibre network of 10-20 km in length was combined with the FSO system.Under strong atmospheric turbulence conditions, the FSO system was capable of transmitting high-speed data over a link range of 0.1-1 km.An MDM has also been integrated into this system to improve the efficiency of the FSO link, employing four LG 00 , LG 01 , LG 10 , and LG 11 laser modes.Among these 4 modes, LG 00 mode has found highly suitable in increasing the link tinge up to 1 km for acceptable SNR [12].
The incorporation of the decision feedback equalization (DFE) technique into the MDM-FSO system improved the link range even more.The system's performance was evaluated in fog, rain, and haze conditions.To compensate for atmospheric attenuation, the MDM-FSO receiver used the minimum mean square error (MMSE) technique in tandem with DFE.The proposed system included three channels, each of which carried 2.5 Gb/s data rates using HG modes.Under medium fog, rain, haze, and clear weather conditions, a transmission rate of 7.5 Gb/s was achieved over 0.40 km, 0.8 km, 1.4 km, and 2 km, respectively.The designed system's simulation results confirmed excellent throughput with the desired BER [13][14].
The performance of the MZM-MDM-FSO system is compared to that of the MZM-MDM-FSO system based on QAM-16 modulation in this proposed research work.To produce a 20 Gb/s-10 GHz optical signal, two independent channels, each carrying 10 Gb/s of data, are modulated with MZM/QAM-16 modulation schemes and transported via two HG (HG 00 and HG 01 ) laser modes at 10 GHz RF signal employing mode division multiplexing."Proposed design and architecture of QAM-MDM-FSO system" section discusses in detail into the mathematical expression and modelling of various HG modes [15].This MDM signal is transmitted at a wavelength of 1550 nm through free space link to assess the effects of different clear sky, dense haze, dense fog, and severe rain conditions."Mathematical model of the proposed optical link" section also discusses and presents the mathematical modelling of atmospheric attenuation produced by these climatic conditions.For strong turbulence, the refractive index structural parameter of the free space link is chosen as C 2 n = 10 −13 m 2∕3 .We use some performance metrics such as BER, eye diagram, quality factor with respect to change in transmission range, and the findings identified finally are compared with the precious research work in "Conclusion" section.The findings confirm the significant improvement in transmission link by using mainly HG 00 laser mode transmission.
"Conclusion" section finally concludes the entire proposed work and its research findings.It also identifies the possible improvements in the existing proposed work.The content of this research paper is finally summarized as illustrated in Fig. 1 in the form of work flow.

Proposed design and architecture of QAM-MDM-FSO system
Figure 2 presents the architectural design of our proposed advanced modulated spiral-phased HG-MDM-based free space optical (FSO) transmission system.Table 1 depicts the proposed system parameters and their corresponding simulation values as per the practical FSO transmission link scenario under different weather conditions for a 5-km link distance.

Fig. 1 Research work organization and workflow
In the proposed system, the spatial HG modes are excited by the spatial laser block at a wavelength of 1550 nm and with a phase noise of-100 dB/Hz and separated into Hermite-Gaussian (HG 00 and HG 01 ) orthogonal modes in the multimode generator (MMG) block as illustrated in Fig. 1.The working principle of this MMG block is illustrated in Fig. 2, where two distinct HG 00 and HG 01 modes can be directly produced by using an end-pumped solid-state laser with an off-axis pumping technique as shown in Fig. 3 [16].The corresponding mode intensity profile of these spiral-phased modes is illustrated in Fig. 4.
As shown in Fig. 2, the output from two pseudo random binary sources (PRBS), each capable of producing 10 Gb/s of information, is encoded into an electrical non-return to zero (NRZ) format, which is further modulated using MZM modulator or advanced QAM-16 modulation schemes.The modulated information's from such two channels is then sent over two orthogonal HG laser modes HG 00 and HG 01 , respectively, which are excited by the spatial CW laser as discussed above.The spatial laser output is directed into the MMG block, which separates out these spiral-phased transverse mode profiles over which phase transformation is applied by the vortex lens with a focal length of 10 mm by changing the focus of the out beam.This applied phase transformation is expressed by Eq. ( 1)   where f is the focal length, m is vortex constant, and n is the refractive index.Figure 3a and c shows the phase of excited modes generated with vortex lens.As presented in Fig. 3, modulated data from channel 1 and channel 2 are transferred over HG 00 (vortex m = 1), HG 01 (vortex m = 3), with a mode spot size of 5 μm [17].
The mathematical expression for the spiral-phased HG mode intensity profile produced by the spatial continuous laser at = 1550 nm is shown in Eq. (2).
In the above equation, H a and H b represent the Hermite polynomials in x and y directions, respectively, where positive integers 'a' and 'b' decide the beam profile.ω o indicates the beam spot size, and R signifies the curvature radius, which varies along the optical link propagation directions due to atmospheric diffraction process.Table 2 summarizes the simulation parameters used in generation of the HG modes profiles.
Figure 4 presents the three mode excitation intensity profiles HG 00 , HG 01 and HG 02 , respectively.Figure 4a, c represents the HG 00 intensity profile in 2-D and 3-D dimension, while Fig. 4b and d depicts the mode profiles of HG 01 and HG 02 , respectively.Because higher-order modes are complex in nature and are not optimal for long-distance optical signal transmission, HG 02 modes are not considered in our proposed system.Figure 5  In the proposed design, this modulator is set to operate in quadrature mode with a 30 dB extinction ratio and a switching bias voltage of 4 V to remove any chirp due to the asymmetric structure.Further, the LiNbO3-MZM-modulated radio signals at 10 GHz are further integrated in the mode division multiplexer (power combiner) block and amplified using an 10 dBm optical boost amplifier (OBA-EDFA) to transmit 20 Gb/s-20 GHz intensity modulated optical signals over a free space optical link with span of 25 km under different weather conditions [19].
To compensate for atmospheric effects, the attenuated signal is amplified by an optical preamplifier (OPA) at the receiver end.A mode selection filter based on the principle of non-interferometric modal decomposition is utilized to distinguish the distinct HG modes.The optical-to-electrical conversion process is then accomplished by an avalanche photodetector.The signal is then demodulated and decoded to restore the original data stream using Gaussian Bessel Low pass filter.Table 1 lists the simulation parameters for the subsystems under consideration [20].This research paper explores the impacts of heavy rain, dense haze/fog and dust with an attenuation coefficient, as listed in Tables 3 and 4, respectively, in the next section.Due to poor visibility, these weather conditions attenuate the transmitted optical signal and therefore reduce the signalto-noise ratio (SNR) over the transmission range.In "Mathematical model of the proposed optical link" section, four mathematical models for clear sky, dense haze, dense fog and strong rain are discussed in detail.Their severity levels, different types, and impact on transmitted optical signals and simulative parameters selected for the proposed system are also explained in detail.

Mathematical model of the proposed optical link
The overall performance of an optical link majorly depends on the external local weather conditions, which are not only unpredictable but also restrict the optical link availability at the receiver end.The atmospheric attenuation due to these adverse weather conditions changes from 20 dB/km for moderate rain to 300 dB/km for very dense fog and snow conditions.However, the optical link equation must include all system losses along with this weather-related attenuation.Starting with transmitted optical power, we have included all the link degradation parameters to identify the received signal intensity at the optical receiver.This received intensity must be compared with receiver sensitivity to identify the link margin.In the sections that follow, we discuss about the different mathematical link models of attenuation that work under different weather conditions [21].

Atmospheric channel losses
Because of absorption and scattering, the FSO channel attenuates the optical field travelling through the atmosphere.The parameter transmittance τ (λ, L) given in Eq. (3) describes the atmospheric attenuation encountered by the transmitted laser power P tx through the link distance of length R.
where λ and P rx represent the transmitted wavelength and received optical power, respectively.The total attenuation coefficient is represented by γ T which is also known as the extinction ratio (in m −1 ) [22].The γ T includes the attenuation contributions from the absorption and scattering of optical energy by aerosols and molecules in the atmosphere.Absorption produces heat as a result of photon propagation interactions with air particles and can be reduced by choosing a wavelength window near 1550 nm [23].Scattering, on the other hand, is a molecular radiusdependent phenomenon that produces an angular redistribution of the optical field.The total attenuation coefficient is given as The first two terms represent the molecule and aerosol absorption coefficients, whereas the latter two terms indicate the molecular and aerosol scattering coefficients, respectively.In dBm, the link budget equation is stated as where P tx (λ, 0) and P rx (λ, R) are the transmitted and received laser power.L opl is the optical loss in transmitter and receiver system, and L p is the pointing loss.L m is the link margin, which includes the losses due to changes in specifications when faulty components are replaced or due to the ageing of the laser source.For transmitter and receiver aperture areas A t and A d , the geometric loss L gl is given by

Haze and fog attenuation
Haze and fog are visibility (v in km)-dependent phenomena that cause more severe link degradation than rain due to smoke (gas) and dust (aerosol) particles suspended in the atmosphere.These particles are responsible for absorption and scattering of the transmitted wavelength, which contributes to total haze and fog attenuation.As discussed earlier, absorption can be ignored at a wavelength of 1550 nm and Eq. ( 7) is used to calculate scattering attenuation in terms of scattering coefficients [24] The particle size distribution can be estimated using Kin's model in Eq. ( 8) (4) T ( ) = mol ( ) + aero ( ) + mol ( ) + aero ( ) Table 3 presents the attenuation coefficient levels under different weather conditions for various particle size dimensions.The performance of link degrades in low visibility scenarios with higher particle concentration and their size than in average visibility.Equation ( 9) is used to compute atmospheric haze attenuation in terms of receiver transmittance τ(R).

Rain attenuation prediction model
Rain is a significant attenuation factor that is highly dependent on the size distribution of the raindrops and has a significant impact on the optical link, primarily due to the scattering effect [11].However, because the transmitted optical wavelength is smaller than that of a raindrop, it has a comparable lower attenuation impact than fog [25].The specific attenuation of the optical link increases as the rain rate R (cms −1 ) increases, given by the following equation: where the constants k and α are frequency, temperature, and drop size distribution-dependent parameters, respectively.The practical values of these parameters along with the severity of the rain attenuation γ and corresponding rainfall intensity R are shown in Table 4 [26].
The performance of the proposed system is investigated using BER, SNR and quality factor.From the calculated received power from Eq. ( 3), the SNR of an APD optical detector can be expressed as Table 1 presented in "Proposed design and architecture of QAM-MDM-FSO system" section defines the simulative values for detector responsivity (R d ), noise density (N 0 ), and receiver noise bandwidth (B).The receiver noise in directdetection systems can be modeled as the quadrature sum of all the noise densities (N 0 ) and is given by Eq. ( 12) where i dark, i thermal and i shot are the average detector dark, thermal and shot noise currents, respectively.In terms of complementary error function, the BER v/s SNR for M-QAM coded optical signal detected at the APD detector can be given as where erfc is the complementary error function.
"Simulation results and discussion" section analyses the simulated findings of the proposed system design under various atmospheric weather conditions.The performance is evaluated on the basis of bit error rate (BER), signalto-noise ratio (SNR) and the quality factor (Q).The chosen signal wavelength for the data transmission is 1550 nm which offers very low molecular absorption due to negligible cross-section of haze, fog and rain particles [27].Therefore, the major contribution considered for our proposed system is mainly due to scattering phenomenon.

Simulation results and discussion
This section examines the simulative performance of the proposed NRZ-MDM and QAM-18-based NRZ-MDM RoFSO links under different atmospheric weather conditions such as clear sky ( = 0.14dB∕km) , dense haze ( = 10.112dB∕km ), dense fog ( = 22.98dB∕km ) and heavy rain ( = 19.28dB∕km ).The qualitative analysis of the simulated result is carried out and compared in terms of performance metrics such as BER, quality factor, eye diagram, SNR, and total link distance achieved under the above stated different weather conditions to achieve a minimum acceptable BER of 10 -5 at the transmitted optical power of 10 dBm.
Figure 6a and 6b shows the BER performance of NRZmodulated MDM-RoFSO link when the HG 00 and HG 01 modes are transmitted for the link distance from 3 to 24 km under clear sky condition with an atmospheric attenuation level of γ = 0.14 B/km.The BER for HG 00 mode increases exponentially with link distance from 6.2 × 10 -16 to 5.3 × 10 -2 and for HG 00 from 1.4 × 10 -2 to 3.3 × 10 -6 .To achieve the minimum acceptable BER level of 10 -5 at the optical receiver, the maximum link distance R max achieved by HG 00 mode transmission is approximately 6.4 km more compared to HG 01 mode.This predicts that the HG 00 mode transmission is more robust compared to HG 01 mode and it achieves the maximum link distance R max = 24.4km under clear sky conditions.The eye-opening height at the optical receiver predicts the maximum quality factor Q max = 4.9 for HG 00 mode and Q max = 4.2 for HG 01 mode reception.As a result, (13) BER = 0.5 erfc � HG 01 mode is found to be more impacted by FSO link attenuation than HG 00 mode in clear sky conditions beyond a link distance of 18 km.The impact of HG 00 and HG 01 modes transmission under sever haze weather conditions with respect to increase in propagation distance is illustrated in Fig. 7a and 7b.The attenuation level in haze weather is dependent on the amount of smoke, dust, and dry particles present in the atmosphere.We chose an attenuation level of γ = 10.112dB/km for the proposed system, which represents a severe level of dense haze.Figure 7a shows that as the link distance of the NRX-MDM FSO link increases from 3 to 24 km, the BER increases from 1.4 × 10 -21 to 3.3 x 10 −4 and from 2.1 × 10 -17 to 5.3 × 10 -3 for HG 00 and HG01 modes transmission respec- tively.The best possible link range for HG 00 and HG 01 modes at the minimum targeted BER level of 10 -5 is R max = 20 km and 15.3 km, respectively.This confirms that HG 00 mode outperforms HG 01 mode by 4.7 km in terms of the propagation distance.Figure 7a  Figure 8a and 8b describes the BER simulation and eye diagram at the optical receiver for transmission of two distinct NRZ modulated modes under dense fog conditions with an attenuation level of γ = 22.98 dB/km.Figure 8a presents the exponential variations of BER for HG 00 and HG 01 modes from 1.8 × 10 -12 to1.18 × 10 -2 and 2.1 × 10 -17 to 4.3 × 10 -2 , respectively.The maximum link distance achieved for HG 00 and HG 01 modes at an acceptable BER of 10 -5 is R max = 11 km and 7 km, respectively.That means the HG 00 mode can reach a 4-km-longer link distance than HG 01 mode under similar fog conditions and perform better.As demonstrated in Fig. 8b, the maximum quality factors received for the two unique modes at the optical receiver are Q max = 4.33 and 2.98, respectively, which again confirms the robustness of HG 00 mode compared to HG 01 in dense fog condition.The proposed NRZ-MDM system achieved almost half and more than half lower link distance at the same acceptable level compared to dense haze and clear sky weather conditions.The opening of the eye height in fog dense weather conditions is the worst among of all the weather conditions examined in terms of Q factor and link propagation distance.In the proposed NRZ-MDM RoFSO system, the received signal quality at the optical receiver for each transmitted HG channel is also evaluated under a strong rain attenuation level of γ = 19.28dB/km as shown in Fig. 9a and 9b.The minimum acceptable BER of 10 -5 is achieved for the maximum link range of R max = 12 km and 10 km for HG 00 and HG 01 modes, respectively.The performance of HG 00 mode transmission is still better compared to HG 01 mode for strong rain condition, but lowest in terms of propagation distance compared to results analyzed earlier for the haze and clear sky conditions.Although the maximum link distance achieved is almost with respect to fog weather conditions.The eye-opening height under strong rain is 4.61 and 3.7 for HG 00 and HG 01 modes, respectively, which demonstrates a significant improvement over dense fog situations but is worse than haze conditions for HG 00 mode.
Table 5 summarizes the performance comparison for the two distinct NRZ-MDM modulated RoFSO links under various weather conditions discussed earlier, corresponding propagation distance and maximum quality factor.The results explain that the proposed system performs best for HG 00 mode transmission under clear sky and achieves a maximum link distance of 24.4 km, while the least distance of 11 km is under dense fog conditions.In contrast, HG 01 mode transmission achieved a maximum link distance of 20 km under clear skies and a minimum link distance of 7 km under dense fog conditions.This clearly concludes that the proposed NRZ-MDM multiplexed system performs best under clear sky and worst under dense fog compared to the other weather conditions.
The BER performance of the proposed QAM-16 modulation-based MDM-RoFSO system is represented in Fig. 10 under different atmospheric weather conditions for the link range of 3 to 25 km.The two QAM-16-modulated channels have been transmitted over the composite HG (HG 00 + HG 01 ) laser mode to evaluate the performance of the FSO link in different weather conditions at acceptable BER of 10 -5 .The results show the significant improvement in transmission link distance when we transmit QAM-16-modulated information over composite HG laser mode in each of the assumed weather conditions with different attenuation levels and are summarized in Table 6.
The transmission distance is increased by the link distance of 1.9 km only when there is dense fog and improves further to 1.7 km when there is a dense haze condition.It is further improved by 2 km under heavy rain scenarios and finally goes up to 2.9 km under clear sky conditions with respect to HG01 mode transmission without QAM-16 modulation scheme.It can be seen that the increase in the optical link distance makes the BER performance worse in all the weather scenarios, and beyond an acceptable BER of 10 -5 , the receiver is not able to detect the received signal.Different BER graphs demonstrate that the Rmax is reached during clear sky conditions, whereas the minimal link distance improvement is achieved during dense haze scenarios.Finally, there is a correlation between the BER and the link distance of data transmission, which can be improved by modulating the two channels with QAM-16 modulation and transmitting them over the composite HG laser mode using an optical boost amplifier at the transmitter side and an optical pre-amplifier at the receiver side.
Table 7 compares the performance of the recently published work to the proposed research work.Recent studies [9][10][11][12][13] have implemented low data rates using conventional modulation methods.Except for Ref. [9], the transmitted power in each reference is nearly 10 dBm.Despite transmitting 22 dBm power in a dusty environment, the system in Ref. [9] only achieves a link distance of less than 0.2 km.Furthermore, with the exception of ref [13], these published works have not evaluated their systems under all weather conditions.However, employing the advanced modulation technique QAM-16 with the same transmitted power of 10 dBm, we were able to achieve a higher transmission range along with the same system parameters implemented by the previous research work under four distinct severe weather conditions.This proves that the proposed system is not only more spectral and power efficient but also provides a greater transmission link range under various weather conditions.

Conclusion
In this paper, we present a novel QAM-16-modulated MDM-RoFSO transmission system to improve information quality and transmission range in free space optical communication.This system employs two independently advanced modulated channels, each carrying 10 Gb/s data and further modulated by the two different Hermite-Gaussian HG00 and HG01 laser modes.These laser modes are combined to form a composite HG mode.These composite modes are amplified by an optical boost amplifier to mitigate the channel impairments before being transmitted over the optical channel.This improves the proposed FSO system's information carrying potential by 20 Gb/s.This model is simulated, and the results are evaluated under a variety of climatic situations, including clear sky, intense haze and fog, and heavy rain.The simulation findings show that by utilizing a QAM-16-based composite HG modulated technique, the optical link transmission range can be increased from 1.7 km to 2.9 km with an acceptable BER of 10.The best results are obtained when the sky is clear, and the worst when there are hazy weather conditions.
In future work, the transmission performance and spectrum efficiency of the proposed system can be investigated by adopting a greater number of higher-order HG laser modes and advanced modulation techniques such as QAM-32/62.In order to mitigate the attenuation losses, the transmitted power should be increased further.Consequently, we recommend this work be investigated under other atmospheric conditions, such as snow and desert conditions.

Fig. 2
Fig. 2 Proposed architecture of HG modes-based FSO transmission link incorporating QAM modulation

Fig.
Fig. Generation of HG mn modes for square vortex array laser represents the combined mode intensity profile of the added HG 00 and HG 01 modes at the output of the power combiner (MDM) block.The spatial mode profiles of distinct optical carrier signals having [10 Gbps-10 GHz] data from two different channels, as shown in Fig.1, are transported over HG00 and HG01 modes using a Lithium Niobate Mach Zehnder ((LiNbO3-MZM))-based optical modulator.The LiNbO3 modulator performs relatively at low voltage compared to other optical modulators as well as being ideally suited for modulating optical signals with data rates greater than 10 Gb/s[18].(2)ab (x, y) =H a also shows that the performance of HG 00 and HG 01 modes is lowered by 4.4 km and 3.3 km compared to clear sky conditions, respectively.The highly distorted eye diagram in Fig. 7b compared to Fig. 6b supports the previously stated statement.The maximum quality factor Q max = 4.81 and 3.73 is achieved corresponding to maximum link distance of R max = 19.2km and 15 km using HG 00 and HG 01 modes transmission, respectively, under a severe haze weather.

Fig. 6 A
Fig. 6 A BER v/s transmission range under clear sky condition for attenuation level of 0.14 dB/ km.B Eye diagram for a HG 00 channel at R max = 24.2km b HG 01 channel at R max = 20 km under clear sky conditions

Fig. 7 A
Fig. 7 A BER v/s transmission range under dense haze condition for attenuation level of 10.112 dB/km.B Eye diagram for a HG 00 channel at R max = 19.2km b HG 01 channel at R max = 15 km under dense haze condition

Fig. 8 A
Fig. 8 A BER v/s transmission range under dense fog condition at attenuation level of 22.98 dB/ km.B Eye diagram for a HG 00 channel b HG 01 channel at R = 11 km under dense fog condition

Fig. 9 A
Fig. 9 A BER v/s transmission range under heavy rain condition at attenuation level of 19.28 dB/km.B Eye diagram for a HG 00 channel at R max = 12 km b HG 01 channel at R max = 10 km under heavy rain condition

Table 1
The designed FSO system parameters

Table 2
Spatial CW laser beam parameters Intensity profile of (HG 00 + HG 01 ) mode at power combiner output

Table 3
Haze and fog conditions and their corresponding attenuation

Table 4
Rain attenuation prediction model for FSO

Table 5
Performance comparison of the proposed system under different weather conditions