1 Introduction

The growth of mobile subscriptions and online video streaming, including Netflix, games, cloud computing, and video conferencing has led to a rise in bandwidth usage (Thangappan et al. 2020). The extensive utilization of the Internet has resulted in a significant increase in the need for high-speed broadband services. The proliferation of network traffic and applications has resulted in a latency between the central office and end users. To deliver high bandwidth, dynamic connectivity, and energy efficiency, radio frequency (RF)and optical fiber cable (OFC) -based, 5th generation (5G) networks are utilized (Kumari 2022). On the other hand, the current telecommunications infrastructure lacks bandwidth and high data rates. Thus, communication networks using OFCs and optical wireless communication (OWC) like FSO are essential for high capacity, security, and fast data delivery to end users (Singh et al. 2021).

Nowadays, researchers are exploring new technologies to improve the capacity of OFC backbones due to the increasing demand for data transmission. To boost transmission capacity, it is crucial to develop a multi-dimensional passive optical network system (PON), given the rapid rise of information traffic globally as per Shannon's limit (Qian et al. 2011). The current optical data transmission methods that employ OFC, such as single mode fibers (SMFs), will eventually hit their capacity limits (Bai et al. 2012; Essiambre et al. 2010). While several approaches such as Time Division Multiplexing (TDM) (Harstead et al. 2019), Wavelength Division Multiplexing (WDM) (Zhou et al. 2022), and Frequency Division Multiplexing (FDM) (Armstrong 2009) are employed in OFC using SMFs, the rates of data transmission and spectrum efficiency are deemed unsatisfactory. As a result, the use of multimode fiber cable (MMFC) has become more common due to its high bandwidth.

FSO communication system is a promising alternative for end-users seeking high capacity and transmission speeds. It allows traffic signals to be transmitted wirelessly in free space between aligned transmitters and receiver units using optically modulated signals (Le and Pham 2022; Mohsan et al. 2023). It has several advantages including high-speed data transmission, providing large bandwidth with license-free spectrum, immunity to electromagnetic interference, low power consumption, and application in metropolitan areas. These benefits make FSO communication a viable alternative for resolving data traffic issues (Kantarci and Mouftah 2012). On the other hand, the effect of different weather conditions like rain, fog, snow, and dust storms cause attenuation which deteriorates the quality of received signal leading to high BER (Kaur and Singh 2015; Chaudhary et al. 2020).

Therefore, the utilization of MMF in conjunction with FSO communication will lead to an increase in transmission capacity and ability to be accessible everywhere. For further capacity enhancement, researchers introduce one or more multiplexing techniques like Polarization Division Multiplexing (PDM) (Chaudhary et al. 2020; Armghan et al. 2023b; Choyon and Chowdhary 2023), OCDMA (Armghan et al. 2023a; Armghan et al. 2023b), orthogonal frequency division multiplexing (OFDM) (Chowdhary and Choyon 2023a) and mode division multiplexing as OAM (Singh et al. 2023a, b) and Hermite Gaussian (HG) beams (Abd El-Mottaleb et al. 2023).

OCDMA is a method that lets several users share a channel. Unlike conventional techniques such as Time Division Multiple Access (TDMA) or Frequency Division Multiple Access (FDMA), which allocate time or frequency resources, OCDMA utilizes distinct code sequences for individual users. These unique codes allow for the simultaneous transmission of several signals using the same wavelength, enabling communication without the need for dividing time or frequency. OCDMA is characterized by the allocation of distinct code sequences to individual users, which improves security and reduces interference by utilizing orthogonal or low cross-correlation codes (El-Mottaleb et al. 2019).

MDM is a contemporary technology that allows high-speed data transfer in optical communication networks (Xie et al. 2015). The simultaneous transmission of independent channels is achieved in MDM through the utilization of eigen modes. In MDM modes, beams like OAM and HG are employed for enhancing the transmission capacity. OAM modes, along with other orthogonal modes, are well-suited for transmitting information in optical communication systems. The orthogonal nature of these modes enables efficient multiplexing and de-multiplexing processes with minimal inter-channel crosstalk (Xie et al. 2015). Moreover, OAM beams exhibit a distinct donut-shaped intensity pattern, and as they propagate, their phase undergoes a helical rotation. To further enhance the transmission capacity of a hybrid MMF/ FSO system, the combined utilization of both OCDMA and OAM beams can be employed.

1.1 Literature review

Currently, multiple research studies have explored the individual application of MDM or OCDMA in FSO only, OFC only, and hybrid OFC/FSO. Additionally, there are studies using other multiplexing techniques like PDM and OFDM. Authors in (Abd El-Mottaleb et al. 2023) proposed a hybrid MMF/FSO using four HG modes and Dual Polarization (DP) states. The findings showed a successful reception rate of 80 Gbps overall capacity. An MDM system was employed in the transmission of hybrid MMF and FSO communication in (Kumari et al. 2023). The results revealed that after reaching a length of 100 m in MMF and a range of 2070 m in FSO, a transmission capacity of 80 Gbps was attained in two separate modes. The authors in (Kodama et al. 2014) introduced an OFC system based on using MDM that utilized Linearly Polarized (LP) modes with OCDM system. This system achieved a data transmission rate of 80 Gbps over 2 km utilizing a two-mode fiber. The MDM was utilized in an FSO system in (El-Mottaleb et al. 2023). Two OAM beams were utilized, with each beam carrying three independent channels encoded using a fixed right shift coding in the OCDMA system. A total transmission capacity of 60 Gbps was attained. The study presented in (Sarangal et al. 2021) described an FSO system based on OAM beams with OCDMA system. The system utilized an identity-type matrix zero cross correlation code and an overall capacity of 120 Gbps achieved at 1.750 km FSO propagation range. The performance of the proposed FSO system, based on using different modulation schemes, is evaluated under the effect of strong turbulence in (Choyon and Chowdhary 2023). Chowdhary and Choyon proposed a high-speed-FSO system based on using Alternate Mark Inversion (AMI) modulation scheme with two multiplexing techniques, PDM and Wavelength Division Multiplexing (WDM) (Chowdhary and Choyon 2023a). The findings achieved an overall capacity of 320 Gbps.

All the previous studies did not use OAM beams with OCDMA system that utilized PV code in a hybrid MMF-FSO system. Accordingly, in our paper, the main objectives are:

  1. a.

    Proposing a 160 Gbps transmission system of MMF-FSO system using four OAM beams (\({LG}_{\mathrm{0,0}}\), \({LG}_{\mathrm{0,20}}\), \({LG}_{\mathrm{0,40}}\), and \({LG}_{\mathrm{0,60}}\)), each carries four OCDMA channels assigned with four distinct PV code sequences.

  2. b.

    Investigating the system performance for various MMF lengths under CA at a fixed FSO range of 5 km.

  3. c.

    Evaluating the system performance under the effect of different rain conditions in terms of BER and eye diagrams while considering a fixed MMF length of 1 km.

In this paper, a new hybrid MMF/FSO communication system is proposed using OAM beams with OCDMA codes. Four OAM beams are utilized, each of these beams carries four OCDMA channels assigned with four different PV code-sequences resulting in 16 channels. 10 Gbps is assigned to each OCDMA channel, resulting in an overall capacity of 160 Gbps. The system incorporates two transmission channels: MMF and FSO. The performance is evaluated under two scenarios. The first scenario involves varying the MMF length with a fixed FSO range of 5 km, considering CA weather conditions. In the second scenario, the MMF length is kept constant at 1 km, and the impact of different rain conditions and FSO ranges is examined. Finally, BER, transmission distance, and eye diagrams are the parameters that are used for evaluating the performance of the proposed model.

The subsequent structure of the paper is as follows. Section 2 describes the proposed model based on OAM beams and OCDMA system with a concise overview of OAM beams and PV code. The performance analysis of the system is presented in the same section. Section 3 presents the simulation findings together with the corresponding analysis followed by the main conclusion in Sect. 4.

2 Proposed model based on OAM beams and OCDMA system

The proposed model consists of transmitter, channel, and receiver as given in Fig. 1. Both OAM beams and OCDMA are generated in the transmitter. Firstly, four OAM beams are generated from a spatial continuous wave (CW) laser.

Fig. 1
figure 1

Schematic diagram for the hybrid MMF/FSO system that leverages OAM multiplexing with OCDMA systems utilizing PV codes

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The electric field intensity of the LG beam is given as (Xie et al. 2016)

$$E\left(\rho ,\varphi ,z;l,p\right)=\sqrt{\frac{2n!}{\pi \left(p+\left|l\right|\right)!}}\frac{1}{\omega (z)}{\left[\frac{\rho \sqrt{2}}{\omega (z)}\right]}^{\left|l\right|}{L}_{l,p}\left[\frac{{2\rho }^{2}}{{\omega }^{2}(z)}\right]\times exp\left[\frac{{-\rho }^{2}}{{\omega }^{2}(z)}\right]exp\left[\frac{-ik{\rho }^{2}z}{2\left({z}^{2}+{{z}_{R}}^{2}\right)}\right]\times exp\left[i\left(2p+\left|l\right|+1\right){tan}^{-1}\frac{z}{{z}_{R}}\right]{\text{exp}}(-il\varphi )$$
(1)

where l and p indicate mode numbers that represent radial and azimuthal directions. Symbols \(\rho\), \(\varphi\), and z are radial, angular, and propagation in Z-direction (cylindrical coordinate system), respectively. \({z}_{R}\) is Rayleigh range, \(k\) is the wave number (2 \(\pi\)/\(\lambda\)), and \(\omega (z)\) is the size of beam waist at distance z that can be expressed as (Xie et al. 2016)

$$\omega (z)\hspace{0.17em}=\hspace{0.17em}{\omega }_{o}\sqrt{1+{\left(\frac{z}{{z}_{R}}\right)}^{2}}$$
(2)

Finally, \({L}_{l,p}\) is the LG polynomial.

In this study, the four OAM beams used are \({LG}_{\mathrm{0,0}}\), \({LG}_{\mathrm{0,20}}\), \({LG}_{\mathrm{0,40}}\), and \({LG}_{\mathrm{0,60}}\), which have intensities profiles having the donut shape given in Fig. 2.

Fig. 2
figure 2

Intensity profiles of a \({LG}_{\mathrm{0,0}}\), b \({LG}_{\mathrm{0,20}}\), c \({LG}_{\mathrm{0,40}}\), and \({LG}_{\mathrm{0,60}}\)

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The OAM beams are classified as types of structured light designed to transmit data in specific patterns. In the proposed work, each OAM beam is responsible for carrying data for four OCDMA channels in a distinctive helical pattern while propagating in the channel. As for OCDMA channels, four different PV code-sequences are used. The PV code is one of the OCDMA codes that is characterized by having zero cross-correlation. Its construction is based on four steps as follows:

Step 1: Generation of one dimension vector (V) having one column and number of rows equivalent to the number of OCDMA channels (N). Additionally, this V vector follows a linear transformation as to be represented in a matrix form as (Singh et al. 2022)

$$V=\left(\begin{array}{c}{v}_{1}\\ {v}_{2}\\ .\\ .\\ {v}_{N}\end{array}\right)=\leftrightarrow [{\text{L}}({v}_{1}),{\text{L}}({v}_{2}), \dots ,\mathrm{ L}({v}_{N})]$$
(3)

where \({v}_{1}\),\({v}_{2}\), …., \({v}_{N}\) are the standard unit basis of \({R}^{N}\) in which \(R\) is the real number, and \({R}^{N}\) is the space of N- tuples of \(R\) that forms \(V\).

Step 2: Conduct permutation theory in a manner where the PV represents a 1-D vector with dimensions (1 × N), consisting of integer "1" entries across N positions. Hence, it can be asserted that the permutation matrix, P, and PV are interchangeable (Singh et al. 2022)

$$P = \left[\begin{array}{c}1\\ 2\\ .\\ .\\ N\end{array}\right]\leftrightarrow [{\text{L}}({v}_{1}),{\text{L}}({v}_{2}), \dots ,\mathrm{ L}({v}_{N})] =\left(\left(\begin{array}{c}1\\ 0\\ .\\ .\\ 0\end{array}\right);\left(\begin{array}{c}0\\ 1\\ 0\\ .\\ 0\end{array}\right);\dots ;\left(\begin{array}{c}0\\ 0\\ .\\ .\\ 1\end{array}\right)\right)$$
(4)

Step 3: Generate the PV code for arbitrary values of N and \(\upomega\) (code weight) by exploring all possibilities of PV code configurations. This is achieved by replicating each vector [L(\({{\text{v}}}_{1}\)), L(\({{\text{v}}}_{2}\)), …, L(\({{\text{v}}}_{{\text{N}}}\))] \(\omega\) times.

The PV code consists of a \(N\)×K matrix (K is the PV code sequence length) given as (Singh et al. 2022)

$$\mathrm{PV code }= {\left({R}^{N}|P\right)}_{ N\times K}$$
(5)

where P is a permutation vector utilized to permute the columns of the matrix.

All potential P configurations can be calculated utilizing the subsequent formula (Singh et al. 2022)

$$P\mathrm { possibilities }=\frac{(\omega N)!}{(\omega !\left(K-N\right)!)}$$
(6)

where the relation between K, \(\omega\), and N is (Singh et al. 2022)

$$K = \omega \times N$$
(7)

One of the P possibilities is considered in this study which is given in Table 1. The associated wavelengths for the PV code sequences with OAM beam are also outlined in Table 1.

Table 1 Channels with corresponding LG beams, polarization states, and wavelengths
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Each OCDMA channel carries a data rate of 10 Gbps. The data is initially generated using a Pseudo-Random Bit Sequence Generator (PRBSG), followed by a Non-Return-to-Zero (NRZ) modulator. Subsequently, the data is optically modulated to the corresponding OCDMA channel through a Mach–Zehnder Modulator (MZM).

In addition, an MDM multiplexer (MUX) merges the 16 channels of the signals obtained after the MZM from the four LG beams, before transmitting them over the channel. Here, hybrid MMF/FSO channels are used, so, the optical signal is first propagating in MMF channel and then FSO channel. In FSO channel, CA and different rain conditions are considered. The attenuation of 0.14 dB/km is considered for CA (Abd El-Mottaleb et al. 2023).

As for rainy weather, the atmospheric attenuation, \(\propto\), can be expressed as (Muhammad et al. 2005)

$$\propto =1.07{{R}_{rainfall}}^{0.67}$$
(8)

where \({R}_{rainfall}\) is the rate of the rainfall with values of 7.22 × 10-4 cm/s, 1.11 × 10-3 cm/s, and 2.22 × 10-3 cm/s for LR, MR, and HR, respectively (Kaur and Singh 2015). The lower value of rainfall intensities gives lower attenuation.

The power of the received signal after propagating through the FSO channel is expressed as (Muhammad et al. 2005; Singh et al. 2022)

$${{P}_{rx}=P}_{tx}{\left(\frac{{D}_{rx}}{{D}_{tx}+\theta L}\right)}^{2}{10}^{\frac{-\propto L}{10}}.$$
(9)

where \({P}_{tx}\) is the transmitted power in dBm, \({D}_{rx}\) is the diameter of transmitter aperture in cm, \({P}_{rx}\) is the receiver power in dBm, \({D}_{rx}\) is the diameter of receiver aperture, \(\theta\) is the beam divergence angle, and \(L\) is the FSO range.

The received signal is then demultiplexed by a spatial demultiplexer into four signals according to the OAM beams. Then, each OAM beam is splitted into four branches to decode the required channel. Each branch consists of two fiber Bragg gratings (FBGs) having wavelengths same as that used in the transmitter, a positive-over-intrinsic (PIN) photodetector (PD) to convert signal back to the electrical domain. It has a small size and can detect the signal rapidly with high efficiency, a low pass filter (LPF) to block unwanted signal, and a BER analyzer to show the performance of the received signal.

The performance of the proposed model is evaluated in terms of BER, propagation range, and eye diagram. Since the BER is contingent on the signal-to-noise-ratio (SNR), it is essential to first delve into the discussion of SNR. It is expressed in terms of shot noise, \({\sigma }_{shot}^{2}\), and thermal noise, \({\sigma }_{thermal}^{2}\), as (Singh et al. 2023a, b)

$$SNR= \frac{{\left({I}_{P}\right)}^{2}}{{{\sigma }_{shot}}^{2}+{{\sigma }_{thermal}}^{2}}$$
(10)

where \({I}_{P}\) is the received current at PD which is given by (Singh et al. 2023a, b)

$${I}_{P}=\frac{\mathcal{R}{P}_{rx}{B}_{o}\omega }{K}$$
(11)

where \(\mathcal{R}\), and \({B}_{op}\) are the PD responsivity and the optical bandwidth, respectively.

\({{\sigma }_{shot}}^{2}\) and \({\sigma }_{thermal}^{2}\) are given by (Singh et al. 2023a, b; Willner et al. 2015)

$${{\sigma }_{sn}}^{2}= 2 {q}_{e} {\upsilon }_{e}{I}_{P}$$
(12)
$${{\sigma }_{th}}^{2}= \frac{4{k}_{B}T{\upsilon }_{e}}{{R}_{L}}$$
(13)

where \({q}_{e}\), \({\upsilon }_{e}\), \({k}_{B}\), are electron charge, electrical bandwidth which has a value of 0.75 × data rate in Hz, and Boltzmann constant, respectively. \({R}_{L}\) denotes receiver load resistance and has a value of 1030 \(\Omega\) and \(T\) is the receiver noise temperature (300 K).

Now, based on Gaussian distribution, the BER is given in terms of SNR as (Singh et al. 2023a, b)

$$BER=0.5 erfc\left(\frac{\sqrt{SNR}}{2\sqrt{2}}\right)$$
(14)

where erfc is the error complementary function.

3 Results and discussion

The proposed system uses four OAM beams; each carries four OCDMA channels. The system is simulated using Optisystem Software ver. 19 and the obtained results are plotted using Matlab Software with the parameters given in Table 2 (Singh et al. 2021; Bai et al. 2012; Zhou et al. 2022; Armghan et al. 2023b; Abd El-Mottaleb et al. 2023).

Table 2 Simulation parameters (Singh et al. 2021; Bai et al. 2012; Zhou et al. 2022; Armghan et al. 2023b; Abd El-Mottaleb et al. 2023)
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In this section, the results are presented in two subsections. The first one explores the system performance under a fixed FSO range of 5 km and CA weather, with an investigation into various lengths of MMF. In contrast, the second one maintains a fixed MMF length of 1 km, evaluating performance under different rain conditions and different FSO ranges.

3.1 Effect of MMF lengths at a fixed FSO range and CA condition

Figure 3 depicts the BER performance for channels 1, 2, 3, and 4, transmitted using OAM beams \({LG}_{\mathrm{0,0}}\), \({LG}_{\mathrm{0,20}}\), \({LG}_{\mathrm{0,40}}\), and \({LG}_{\mathrm{0,60}}\), respectively, under different lengths of MMF and CA weather. Additionally, the eye diagrams for these channels at a total transmission distance of 6.2 km (5 km FSO range + 1.2 km MMF length) are displayed in Fig. 3. The information signal reaches up to 1.2 km of MMF lengths with a BER < \({10}^{-6}\). Since the threshold value of BER is \({10}^{-2.5}\), all the information transmitted on these beams is successfully received. Moreover, longer MMF lengths result in a degradation in BER performance compared to shorter lengths. Furthermore, as every channel carries 10 Gbps, accordingly, the overall capacity achieved is 160 Gbps.

Fig. 3
figure 3

log(BER) for four OAM beams of MMF/FSO system using PV codes versus MMF length under CA

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3.2 Effect of FSO ranges under different rain conditions and fixed MMF length

In this subsection, the performance is investigated under CA and different rain conditions (LR, MR, and HR). Here, a fixed MMF length of 1 km is considered.

3.2.1 Performance under CA

The CA weather condition exhibits very low attenuation, specifically 0.14 dB/km, which minimally impacts the signal quality during propagation in the FSO channel. Consequently, the proposed model enables all the 16 channels transmitted on four distinct beams to achieve an extended FSO range with lower BER, as illustrated in Fig. 4. For simplicity, we present results for four channels transmitted on various OAM beams. The results in Fig. 4 demonstrate that the proposed model can cover an FSO range of 5.5 km, in addition to a 1 km MMF distance, with a log(BER) \(\sim\) - 5. Furthermore, the wide eye opening at this range (1 km MMF + 5.5 km FSO range) signifies a robust reception of information.

Fig. 4
figure 4

log(BER) for four OAM beams of MMF/FSO system using PV codes versus FSO range under CA

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3.2.2 Performance under rainy weather

Figure 5 illustrates the BER performance of channels 1 (transmitted on 1 (transmitted on \({LG}_{\mathrm{0,0}}\)), 2 (transmitted on \({LG}_{\mathrm{0,20}}\)), 3 (transmitted on \({LG}_{\mathrm{0,40}}\)), and 4 (transmitted on \({LG}_{\mathrm{0,60}}\)), for the proposed model, under LR, MR, and HR conditions after traversing a 1 km distance in the MMF. It is observed that as the rainfall intensity increases, the FSO span decreases, which is anticipated as HR induces the highest attenuation. At a log(BER) of nearly -5, all the channels have an FSO range of 1.62 km under LR, which decreases to 1.2 km under MR and further reduces to 0.77 km under HR. Additionally, the four channels eye spectra at a 1 km MMF and 1.6 km (LR), 1.2 km (MR), and 0.8 km (HF) FSO show that an overall information data transmission of 40 Gbps is successful. Furthermore, the proposed model performance is limited to fiber nonlinearities and noise.

Fig. 5
figure 5

log(BER) for four OAM beams assigned with PV codes under different rain conditions; a \({LG}_{\mathrm{0,0}}\), b \({LG}_{\mathrm{0,20}}\), c \({LG}_{\mathrm{0,40}}\), and \({LG}_{\mathrm{0,60}}\)

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Table 3 summarizes the overall transmission distance for the four channels that are transmitted on four distinct OAM beams with log(BER) \(\sim\) 5 under different weather conditions.

Table 3 Overall transmission distance for four channels transmitted on four distinct OAM beams under various weather conditions at log(BER) \(\sim\) 5
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Finally, our proposed MMF/FSO using PV code using four OAM beams achieves an overall capacity of 160 Gbps at overall distances of 6.5, 2.62, 2.2, 1.77 km under CA, LR, MR, and HR, respectively.

4 Conclusion

Given the increasing demand for high-speed data transmission systems, addressing the surge in data traffic has become a pressing concern. To tackle this issue, this paper introduces a new hybrid MMF/FSO system that leverages OAM multiplexing with OCDMA systems utilizing PV codes. Each OAM beam carries 40 Gbps, modulated on four OCDMA channels assigned with PV code sequences. Utilizing four OAM beams (\({LG}_{\mathrm{0,0}}\), \({LG}_{\mathrm{0,20}}\), \({LG}_{\mathrm{0,40}}\), and \({LG}_{\mathrm{0,60}}\)), enables the overall capacity of 160 Gbps. The performance of the optical signal during propagation in the FSO channel is evaluated under CA and different rain intensities. The results reveal that the system achieves the longest transmission distance of 5.6 km (1.2 km MMF + 5 km FSO span) under CA weather. Conversely, the proposed system achieves a shorter distance of 1.77 km (1 km MMF + 0.77 km FSO span) under heavy rain. These ranges are achieved below the threshold BER value of \({3.8\times 10}^{-3}\). The proposed MMF/FSO system with a capacity of 160 Gbps offers several advantages compared to other FSO systems. Firstly, it utilizes two channels, MMF and FSO, enabling data transmission in challenging geographic locations where fiber cable installation is difficult. This ensures data availability everywhere. Additionally, the system employs four OAM beams, effectively multiplying the utilization of the same wavelength and enhancing transmission capacity to accommodate the rapid growth of traffic. Furthermore, the use of OCDMA code, specifically PV code, enables multiple channels to transmit data simultaneously with a high level of security. This allows for efficient and secure data transmission using different code sequences. Finally, the system performance is evaluated under various rain conditions, considering practical values of beam divergence angle, receiver and transmitter aperture diameters. This evaluation ensures that the proposed model is suitable for implementation in 6G applications. Consequently, we recommend that our model can be applied to hybrid wired/wireless optical networks with high transmission rates and to emerging PONs applications such as smart railway stations and health care systems. For future work, we suggest considering more different weather conditions and atmospheric turbulence effects.