Four-beam OAM-based unipotent single-entry code for high-capacity 40 × 16 Gbps FSO links

1 Introduction

In recent years, the demand for high speed data rates and high user capacity has rises due to emerging technology requirements such as the Internet of Things, Artificial Intelligence, Autonomous Vehicle, 6G Network, and Quantum Computing. The increasing number of smartphone and social networking users will lead to a telecommunications bottleneck, which is also a reason for researchers to develop new telecommunications systems to overcome it El-Mottaleb et al. [1]. Free Space Optics (FSO) technology uses light to transmit data in an open space or open air which supports high speed data rates and rapid deployment without the need of physical cable, no disruption of electromagnetic waves Altakhaineh et al. [2]. It operates in the near infrared frequency range, and it’s a promising technology for wireless backhaul broadband connectivity, which can reach several kilometers Alsabah et al. [3]. Furthermore, a recent technology known as Mode Division Multiplexing (MDM) enhances high-speed data transmission and increases channel capacity in optical communication networks by transmitting user data through specific modes in optical fiber. MDM is preferred to be used with Orbital Angular Momentum (OAM) as its suitable to achieve ultra-high channel capacity to subscribers Trichili et al. [4].

Optical Code Division Multiple Access (OCDMA) is a multiple-access technique that employs a unique code for encoding and decoding users’ data. Over the years, various OCDMA codes have been developed, including Modified Double Weight (MDW), Enhanced Double Weight (EDW), Variable Weight (VW), and Fixed Right Shift (FRS) El-Mottaleb and Singh [5]; Liu et al. [6]; Rani et al. [7]; Abd El-Mottaleb et al. [8]. The need to achieve low cross-correlation, high autocorrelation, effective Multiple Access Interference (MAI) suppression, and better overall performance highlights the importance of new coding methods Abdulrahman and Mohamed [9].

OAM denotes a characteristic of electromagnetic waves in which the phase of the wavefront spirals in a helical manner, giving it angular momentum. By twisting the beams, several orthogonal modes can propagate simultaneously through the same optical or wireless channel at the same frequency or wavelength Zhao et al. [10]; Henderson [11]. A vortex beam that carries OAM introduces an exciting new dimension for information encoding in optical and quantum communication technologies. These beams can span an infinite-dimensional Hilbert space, enabling an unlimited number of encoding symbols Wang et al. [12]; Wang [13]; Dai et al. [14]; Wang et al. [15]. In El-Mottaleb et al. [16], a 160 Gbps OCDMA system with hybrid Multi-Mode Fiber (MMF)/FSO was designed and tested under rainy weather conditions. This system uses the Permutation Vector (PV) code by employing four OAM beams, each carrying four OCDMA channels. The findings suggested the attenuation caused by the rain are one of the limiting factor faced in FSO. As reported in Kumari and Mishra [17], a 16 x 10 Gbps OAM FSO transmission were tested under clear air, drizzle and haze weather condition. The system uses four optical carrier frequencies ranging from 193.1 to 193.4 THz, with a 100 GHz channel spacing. Each channel is assigned four distinct LG modes, L G 0,0, L G 0,10, L G 0,20, L G 0,30. The study further indicates that the maximum achievable transmission distance varies across LG modes due to differences in the modal sensitivity to atmospheric attenuation, turbulence, scattering and beam spread in varying weather conditions.

According to Singh et al. [18], This research examines the performance of a hybrid MMF integrated with FSO communication. To conduct the analysis, two geographical locations were selected which is Chandigarh in India and Alexandria in Egypt. The findings indicate that these two locations have different visibility conditions and meteorological data which lead to different levels of attenuation in FSO. In Singh et al. [19], the 120 Gbps channel capacity of an Enhanced Double Weight (EDW) OCDMA system is simulated under various weather conditions, such as Rain, Haze, and Fog. The only downside of this system is that each OCDMA channel has a significant performance gap, making the system unstable.

This research introduces a new OCDMA code, namely, the Unipotent Single Entry (USE) code, which offers better code structure, more substantial Multiple Access Interference (MAI) and PIIN suppression, lower cross-correlation, and higher autocorrelation. This new OCDMA is tested theoretically and through simulations under various weather conditions for high-speed data transmission. Four OAM beams L G 0,0, L G 0,20, L G 0,40, L G 0,60 are used each carrying 40 Gbps. The transmission range and Bit Error Rate (BER) are used as performance metrics of the proposed model. The weather condition considered are Clear Weather, Light Rain (LR), Medium Rain (MR), Heavy Rain (HR), Light Fog (LF), Medium Fog (MF) and Dense Fog (DF).

2 LG modes & orbital angular momentum

A Laguerre–Gaussian (LG) beam is a solution of the paraxial wave equation, which is a form of the Helmholtz equation in cylindrical coordinates ( r , Φ , z ). It describes the shape of a laser beam that has both radial and azimuthal structures, whereas a simple Gaussian beam is circularly symmetric. Generally, the electrical field of an LG beam can be represented by Equation 1 Allen et al. [20]:where r , Φ , z , w ( z ) , z R represent radial coordinate, angular coordinate, direction of propagation along z-axis, waist size of beam at z-distance, and Rayleigh range respectively El-Mottaleb et al. [1]; Allen et al. [20].

u m h r , ϕ , z = 2 m ! π m + | h | ! 1 w z 2 r w z | h | L m | h | 2 r 2 w 2 z × exp − r 2 w 2 z exp i h ϕ exp i c r 2 z 2 z + z R × exp i 2 m + | h | + 1 tan − 1 z z R (1)

OAM is a helical phase of the EM beam in the direction orthogonal to the propagation axis Tamburini et al. [21]. OAM beam are characterized by a spiral phase structure or doughnut shape that are represent as e i h Φ, where h and Φ are the number of 2 π phase shifts and azimuthal angle respectively Olaleye et al. [22]; Merabet et al. [23]. The othogonality of OAM is shown in Equation 2 by comparing two beams u m h and u m ′ * h ′ at z distance.Both beam must have same z distance otherwise the two OAM beam shall overlap which shown in Equation 3 Plick and Krenn [24].The intensity of four OAM beam L G 0,0, L G 0,20, L G 0,40, L G 0,60 with its helical phase is shown in Figure 1.

∫ 0 2 π r d r ∫ 0 ∞ u m h r , ϕ , z u m ′ * h ′ r , ϕ , z d ϕ = δ m , m ′ δ h , h ′ (2)

∫ 0 2 π ∫ 0 ∞ u m h r , ϕ , z u m ′ * h ′ r , ϕ , z ′ r d r d ϕ ≠ 0 (3)

3 OCDMA Unipotent Single Entry (USE) code

Various OCDMA codes have been developed in the past 2 decades. Every code strives to achieve ideal cross-correlation, high auto-correlation, MAI and PIIN suppression, and reduction of design complexity. OCDMA assigns to each user a unique code as a unique identifier, essentially serving as an address Abd El-Mottaleb et al. [8]. The unique code is integrated with the user data through a modulation technique that modulates/pairs the code with the user data. Thus, the modulated data is sent through an optical fiber Ammar et al. [25]. At the receiver, a detection method separates the incoming signals and recovers the data for each user. The receiver compares the recovered signal with the unique identifying signature code of each user to retrieve the user’s data. The low cross-correlation properties of the codes will allow the receiver to distinguish signals from different users in the presence of noise and interference Aljunid et al. [26]. This paper proposes a new coding scheme for SAC-OCDMA called the USE (Unipotent Single Entry) code. The USE code is characterized by the number of users N, the code length L (total number of chips), the code weight w, and the cross-correlation λ c. The code construction is based on four interrelated matrix structures: the lower shift matrix, the identity matrix, the single-entry matrix, and the unipotent matrix. These are combined to produce the final USE code matrix.

First, consider the lower shift matrix L. In linear algebra and spectral theory, let H be a separable Hilbert space. The shift operator S * : H → H defined by S * e n = e n − 1 for n = 1,2,3 , … with respect to the standard basis ( e n ) n = 0 ∞ has a matrix representation called the lower shift matrix L, which contains 1s only on the subdiagonal and 0s elsewhere:

Matrix L is shown as a square matrix with zeros in the first row, ones on the subdiagonal, and zeros elsewhere; dotted boxes and ellipses indicate continuation for larger matrices. Equation is labeled as equation 4.

Next, the n × n identity matrix I n is a square matrix with entries equal to the Kronecker delta (Equation 5);where i , j = 1,2,3 , … , n and n is a positive integer. Explicitly (Equation 6);The unipotent matrix is then obtained by adding the lower shift matrix and the identity matrix (Equation 7);In matrix form:

δ i j = 0 , if i ≠ j , 1 , if i = j . (5)

I = 1 0 0 ⋯ 0 0 1 0 ⋯ 0 0 0 1 ⋱ ⋮ ⋮ ⋮ ⋱ ⋱ 0 0 0 ⋯ 0 1 (6)

U = L + I (7)

Matrix equation labeled L plus I equals a lower triangular matrix with ones on and below the main diagonal and zeros elsewhere, with ellipses indicating continuation for larger matrices. Equation number eight is shown on the right.

A single-entry matrix, denoted J i j ∈ R n × n, has a single element equal to 1 at position ( i , j ) and 0 elsewhere. For the USE code, we specifically require J n 1, which places a 1 at the bottom-left corner:

Mathematical expression showing a matrix J superscript m1, where all entries are zero except the bottom left corner, which is one, indicating a block matrix structure with ellipses and dotted boxes for omitted values. Equation number nine is on the right.

Finally, the USE code matrix is constructed by adding the unipotent matrix and the single-entry matrix (Equation 10);In matrix form:

USE = L + I + J n 1 (10)

Mathematical matrix labeled USE containing ones and zeros with diagonal and off-diagonal elements, ellipses indicating continuation, and the final column ending in one. Equation number eleven in parentheses is aligned to the right.

The USE code then, can be expressed in general form as (Equation 12);where D i i for i = 1,2,3 , … , n represents the elements on the main diagonal, and B i , i − 1 for i = 1,2,3 , … , n represents the elements on the subdiagonal. Thus, the element matrix of the USE code can be described as follows (Equation 13);

USE = D 11 0 0 ⋯ 0 B 21 D 22 0 ⋯ 0 0 B 32 D 33 ⋱ 0 ⋮ ⋮ B 43 ⋱ ⋮ M 0 0 B i , i − 1 D i i (12)

EM = D i i = 1 , for i = 1,2 , … , n B i , i − 1 = 1 , for i = 1,2 , … , n M = 1 , for all n 0 , otherwise (13)

The USE code length is given by L = N ( w − 1 ) + 1, where N = 1,2,3 , … and w ≥ 2. The design mechanism for constructing the USE code is presented in Algorithm 1.

Algorithm 1 Unipotent Single-Entry Code Algorithm for OCDMA System.

Table 1 shows examples of USE code patterns based on the parameters w and N. Table 2 presents a specific example of the USE code for the Even-Even case. The symbol 1 indicates where a light pulse is present, and 0 means no light pulse is transmitted. Each row corresponds to a unique code for a user, and the diagonal pattern of ones represents a coded structure of their respective wavelength. The pattern indicates that the Direct Detection technique is incompatible, as one or two users have non-overlapping chips that cannot be selected. The only solution to this issue is to use the AND subtraction technique. The other parity cases (Odd-Odd, Odd-Even, Even-Odd) follow the same pattern and satisfy the same code length formula L = N ( w − 1 ) + 1.

TABLE 1. USE code patterns based on parameters w and N

TABLE 2. USE Code Construction for w = 4 and N = 6.

4 OCDMA system design

The proposed OCDMA with OAM using FSO as transmission medium is shown in Figure 2. At the transmitter section, a spatial laser is used to generate four OAM beams L G 0,0, L G 0,20, L G 0,40, L G 0,60. This beam assignment is optional, and it depends on which helical phase is intended to be assigned as long as the beams orthogonal with each other Liu et al. [27]. Each beam carries N channels of USE OCDMA, utilizing the code design discussed in the previous section. Table 3 presents the wavelength assignments for the USE code with W = 3, N = 4, and L = 9. The data is modulated with the specified wavelength and transmitted through FSO where different weather condition such as clear weather, rain and fog is considered.

TABLE 3. Wavelength assignment for different users for W = 3 and N = 4 USE OCDMA.

At the receiver, a detection technique used is AND subtraction technique. The AND subtraction detection technique involves dividing incoming signals into two parts. The first part is the main decoder, which features a filter configuration similar to that of the encoder. The second part of the decoder which is subtractive decoder includes AND filter configurations El-Mottaleb et al. [28]. In this technique, signals at different wavelengths using logical AND operation to identify the presence of identical wavelengths or overlapping chips. A subtractor is included just before the photodiode in order to eliminate the overlapping chip from the code intended for use. In this manner, no overlapping chips are present, and only what is intended to be received is at the photodiode Anuar et al. [29]. The optical filter used for this detection is Fiber Bragg-Gratings.

Figure 3 shows block diagram of receiver design for AND subtraction technique. By using AND subtraction technique for USE code, the signal interference cancellation is illustrated in Table 4.

TABLE 4. USE with AND subtraction detection technique interfering signal cancelation illustration.

5 Performance analysis

In this section, a theoretical analysis comparing the USE code with the MDW and EDW codes is presented. This comparison is based on the BER and the number of users. In an optical communication system, the BER threshold for the system to be considered Good is 1 0 − 9 or lower Morsy and Alsayyari [30]. To have a fair assessment of the performance of the USE, MDW, and EDW codes, the same detection technique is used throughout this comparison, which is the AND subtraction technique.

In simulation analysis, the USE code is rigorously evaluated under multiple weather conditions to assess performance and reliability. There are seven types of weather conditions tested, which are clear weather, light rain (LR), medium rain (MR), heavy rain (HR), light fog (LF), medium fog (MF), and dense fog (DF). LR conditions exhibit gentle drizzles that coat things with a light wetness, while MR conditions present moderate droplets and decreased visibility. HR conditions exhibit considerable downpours that may reduce visibility for FSO detection and possibly impact device reliability. LF conditions may impair visibility when viewing objects located at a distance, while MF conditions further influence the visibility. Finally, DF surrounds the immediate environment with very thick fog that almost prohibits visibility, which in turn impacts the detection systems.

5.1 Theoretical analysis

In this section, USE code with AND subtraction technique performance is calculated based on Signal to Noise Ratio (SNR) and Bit Error Rate (BER). The calculation include various types of noise which is shot noise ( I shot ), PIIN ( I PIIN ) and thermal noise ( I t h ). If C f ( i ) denotes the ith element of the fth USE code sequence, the code properties based on AND subtraction technique can be represented by Equation 14, and Equation 15:

∑ i = 1 L C f i C g i = W , f = g 1 , f ≠ g 0 , f ≠ g (14)

∑ i = 1 L C f i C f i ⋅ C g i C f i = 0 , f = g W , f ≠ g 0 , f ≠ g (15)

the power spectral density (PSD) of the received optical signal can be written as following:The unit step function u ( v ) is defined as follows (Equation 17):Based on Equation 16, the PSD is represented by Equation 18

r v = P s r Δ V ∑ n = 1 N d n ∑ i = 1 L C n i u v − v 0 − Δ V 2 L − L + 2 i − 2 − u v − v 0 − Δ V 2 L − L + 2 i (16)

u v = 1 , v ≥ 0 0 , v < 0 (17)

G v = P s r Δ V ∑ N = 1 N d n ∑ i = 1 L C n i u Δ V L (18)

where P s r is the effective power of optical source at the receiver, N is the number of users and L is the code length of USE code. The photocurrent of the receiver I p is defined by Equation 19

I = R ∫ 0 ∞ G v d V (19)

where R is the responsivity of photodetector and ∫ 0 ∞ G ( v ) d V is the total power of the photodiode represented by Equation 20 Liu et al. [6]; Ammar et al. [25].

∫ 0 ∞ G v d v = ∫ 0 ∞ P s r Δ V ∑ n = 1 N d n ∑ i = 1 L C n i u Δ V L d v (20)

Based on each decoder properties, the PSD are integrated into (Equations 21–24):

∫ 0 ∞ G 1 v d v = ∫ 0 ∞ P s r Δ V ∑ f = 1 N d f ∑ i = 1 L C f i C g i u Δ V L d v (21)

∫ 0 ∞ G 1 v d V = P s r w L + P s r L ∑ f = 1 , f ≠ g L C f i (22)

and

∫ 0 ∞ G 2 v d v = ∫ 0 ∞ P s r Δ V ∑ f = 1 N d f ∑ i = 1 L C f i C f i ⋅ C g i C f i u Δ V L d v (23)

∫ 0 ∞ G 2 v d V = P s r L + P s r L ∑ f = 1 , f ≠ g L C f i (24)

the total photocurrent at the photodetector is expressed as follows (Equations 25–27):

I = R ∫ 0 ∞ G 1 v d V − R ∫ 0 ∞ G 2 v d V (25)

I = R P s r w L + P s r L ∑ f = 1 f ≠ g L C f i − P s r L + P s r L ∑ f = 1 f ≠ g L C f i (26)

I = R P s r w − 1 L (27)

from Equations 22 and 24, the shot noise is defined by Equations 28–30: the PIIN is expressed as:wherefrom Equations 32 and 33, when the number of users transmitting bit ‘1′ using the average value ∑ f = 1 , f ≠ g L C f ( i ) ≈ N w L the PIIN can be represented by Equations 34–36 It is important to note that each user sending a bit ‘1’ at any point in time has a probability of 1 2. Consequently, Equations 31 and 36 are expressed as follows (Equations 37, 38):andthe thermal noise is calculated using Equation 39:thus, the SNR is represented by Equation 40 Ogbonda Amadi et al. [31]:

I shot 2 = 2 e B R ∫ 0 ∞ G 1 v d V + ∫ 0 ∞ G 2 v d V (28)

I shot 2 = 2 e B R Δ V L P s r w Δ V + P s r Δ V ∑ f = 1 f ≠ g L C f i + P s r Δ V + P s r Δ V ∑ f = 1 f ≠ g L C f i (29)

I shot 2 = 2 e B R P s r L w + N − 1 + 1 + N − 1 (30)

I shot 2 = 2 e B R P s r L 2 N − 1 + w + 1 (31)

I PIIN 2 = B I 1 2 τ c 1 + B I 2 2 τ c 2 (32)

τ c = ∫ 0 ∞ G n 2 v d V ∫ 0 ∞ G n v d V 2 (33)

I PIIN 2 = B R 2 ∫ 0 ∞ G 1 2 v d V + B R 2 ∫ 0 ∞ G 2 2 v d V (34)

I PIIN 2 = B R 2 P s r 2 N w Δ V L 2 ∑ f = 1 N ∑ i = 1 L C f i C g i + ∑ f = 1 N ∑ i = 1 L C f i 3 C g i (35)

I PIIN 2 = B R 2 P s r 2 N w Δ V L 2 w + 1 + 2 N − 1 w (36)

I shot 2 = e B R P s r L 2 N − 1 + w + 1 (37)

I PIIN 2 = B R 2 P s r 2 N w 2 Δ V L 2 w + 1 + 2 N − 1 w (38)

I t h 2 = 4 K b T n B R L (39)

the SNR for USE systems is written as:

S N R = I 2 I shot 2 + I PIIN 2 + I t h 2 (40)

where χ = 2 ( N − 1 ) + w + 1 and. ϒ = w + 1 + 2 ( N − 1 ) w

S N R = R P s r w − 1 L 2 e B R P s r L χ + B R 2 P s r 2 N w 2 Δ V L 2 ϒ + 4 K b T n B R L (41)

from Equation 41, the BER is obtained by Equation 42

B E R = 1 2 e r f c S N R 8 (42)

5.2 FSO model

The performance of FSO is also affected by various weather conditions. Rain are one of the major factor that can cause deterioration of received signals at the FSO link. The attenuation of FSO caused by rain weather condition is calculated using Equation 43 Singh et al. [19]; El-Mottaleb et al. [32].where β and q are the wavelength-dependent coefficients, α Rain and R represent rain attenuation and rainfall rate (mm/hr), respectively. The value for β is 1.076 while the value for q is 0.67 at 1,550 nm wavelength which based on Singh et al. [33]; Muhammad et al. [34].

α Rain = β R q (43)

For fog condition, the attenuation is calculated using Equation 44 El-Mottaleb et al. [32]:where α Fog is fog attenuation, V is the visibility during foggy weather, λ is the wavelength and δ is size distribution of scattering particle which its value is given by kim and kruse model Marlina et al. [35]; Kim et al. [36]; El-Mottaleb et al. [32].

α Fog = 3.912 V λ 550 n m − δ (44)

δ kim = 1.6 , V > 50 km , 1.3 , 6 km ≤ V ≤ 50 km , 0.16 V + 0.34 , 1 km < V < 6 km , V − 0.5 , 0.5 km ≤ V ≤ 1 km , 0 , V < 0.5 km . (45)

δ kruse = 1.6 , V > 50 km , 1.3 , 6 km ≤ V ≤ 50 km , 0.58 V 1 3 , 0 km < V < 6 km . (46)

Based on Equations 45 and 46, the kim model is more precise compared to kruse since it involves various visibility conditions Marlina et al. [35]. The Kruse model predicts lower attenuation at longer wavelengths, but it does not accurately estimate atmospheric attenuation when visibility is below 1 km. On the other hand, the Kim model states that the wavelength becomes nearly independent when the visibility is lower than 500 m and shows better reflection of dense fog behaviour Rajput and Acharya [37]; Khan et al. [38].

6 Results and discussion

6.1 Theoretical results

The theoretical result for the USE code is compared with previous code such as MDW and EDW code. The fixed parameter for the theoretical calculation is given in Table 5.

TABLE 5. Typical parameters used in the calculation.

The theoretical performance of the USE OCDMA code is assessed using Equations 41 and 42 under back-to-back fiber conditions. This approach simplifies the calculation by excluding factors such as attenuation from weather conditions during signal transmission, allowing for a comparison of code performance. Figure 4 shows the BER versus the number of users for the USE code, compared with the MDW and EDW codes. Figure 4 shows that the USE code’s performance improves as the code weight increases. Higher weight codes inherently provide better BER performance due to their advanced interference-rejection capabilities. The reason for this is their high autocorrelation properties, which helps the system differentiate between users’ signals to minimize effects of MAI. The USE code with w = 5 can support up to 30 users with BER 9.049 × 1 0 − 9, while the EDW code with w = 5 can support up to 24 users with BER 3.925 × 1 0 − 9. The USE code with w = 6 can support up to 47 users with BER 9.918 × 1 0 − 9, whereas the MDW code with w = 6 can support only 34 users with BER 8.225 × 1 0 − 9.

To improve the performance of the USE code, a 4-OAM beam is used to increase user capacity in a high-bit-rate scenario significantly. Figure 5 shows the USE code employing four OAM beams with different code weights. Using 4-OAM beams, the number of users supported by the USE code increases as the weight increase. For W = 4, the USE code achieves a BER of 9.286 × 1 0 − 9 with 66 users. In comparison, W = 5 achieves a BER of 9.049 × 1 0 − 9 with 120 users. For W = 6, the USE code achieves a BER of 9.918 × 1 0 − 9 at 188 users, while for W = 7, a BER of 9.662 × 1 0 − 9 is attained with 267 users. Table 6 shows performance comparison before and after employing OAM beams. Each of OAM Beams is said to be orthogonal if all beam have same z distance. To observe the light distribution in a beam, an average radial intensity is plotted in Figure 6 for L G 00, L G 02, L G 04 and L G 06. The plot shows the normalized radial intensity profiles of four Laguerre–Gaussian (LG) modes: L G 00, L G 02, L G 04 and L G 06. The x-axis represents the radial distance from the beam center in μm, while the y-axis shows the normalized intensity, indicating the distribution of light across the beam cross-section. L G 00 has a single peak at the center, characteristic of a fundamental Gaussian mode with no radial nodes. As the radial mode index increases L G 02, L G 04, L G 06, the intensity peaks shift outward, forming rings farther from the center, and the number of rings corresponds to the radial index. The curves have been normalized, meaning the maximum intensity of each mode is set to 1, allowing easy comparison of their spatial distributions. This behavior shows a larger spatial structure and an increased radial area occupied by the higher-order LG modes.

TABLE 6. Performance comparison before and after employing OAM beams.

6.2 Simulation results

The software used for simulation of USE OCDMA system is Optisystem Version 21. The parameter used for simulation is listed in Table 7.

TABLE 7. Typical parameters used in the Simulation.

In the simulation, the USE code was set with three code weights and four users per OAM beam. The performance of the USE OCDMA system is assessed over 16 channels, as shown in Figure 7. This assessment was done in CW weather conditions to demonstrate the stability of the system for each channel.

The eye diagram for four channels (Ch 1, 5, 9, 13) that was transmitted using the OAM beam L G 00, L G 02, L G 04 and L G 06 is shown in Figures 8a–d. For CW weather conditions, the farthest distance it can reach is 1700 m, which has the acceptable value of BER ≤ 1 0 − 9.

The system was also evaluated under rainy and foggy weather conditions. The eye diagrams for LR, MR, HR, LF, MF, and DF are presented in Figure 9. During light rain, the system can transmit signals up to 900 m under medium rain, the range is reduced to 750 m, and it lowers further to 500 m during heavy rain. The eye diagrams shown in Figures 9a–c illustrate the quality of the eye pattern at the maximum distance achievable (maximum bit error rate before exceeding the threshold) for light rain, medium rain, and heavy rain. In light fog, the system can transmit signals up to 720 m, while in medium fog, this range decreases to 480 m. In conditions of dense fog, the transmission distance is significantly limited to 380 m. Figures 9d–f shows the quality of the eye pattern during foggy weather at the maximum distances achieved.

To further analyze the performance of the USE system under different weather conditions, the BER versus transmission distance graphs are presented in Figures 10 for rainy weather and in Figures 11 for foggy weather.

The graph in Figure 10 shows how the BER increases with distance under different rain conditions. Under light rain, the BER remains very low up to around 700 m and only begins to rise noticeably beyond that distance. Medium rain causes errors to appear sooner, with the BER increasing more rapidly starting around 550–600 m. Heavy rain has the strongest degradation effect where it occurs at a very short distances (around 350–400 m), the BER is already significantly higher, and it climbs steeply as distance increases. Overall, the graph illustrates that harsher weather conditions reduce the effective communication range by causing signal attenuation and more frequent transmission errors.

The plot in Figure 11 shows how the BER increases with increasing FSO link distance under different fog conditions. Dense fog causes the most substantial attenuation, so its BER rises sharply even at short distances (around 300–400 m), indicating rapid signal degradation. Medium fog performs moderately better but still shows a steep BER increase starting near 400–500 m. Light fog performs the best, maintaining very low BER values up to about 500 m before gradually increasing as the distance approaches 750 m. Overall, the figure clearly illustrates the sensitivity of FSO links to fog density, as the denser the fog, the shorter the achievable distance before BER becomes unacceptable.

To provide a more comprehensive evaluation of USE OCDMA system performance, a comparative analysis between this research and earlier studies is provided in Table 8. The findings show that the USE code supports low power consumption, achieves greater transmission distances, supports higher bit rates, and maximizes channel capacity compared to previous work.

TABLE 8. Comparison of current and previous work.

The USE code utilizes a deterministic structure with a controlled weight distribution, resulting in more stable, lower cross-correlation and high autocorrelation values that are essential for minimizing MAI in OCDMA systems. On the other hand, MDW and EDW codes impose structural constraints that limit flexibility in code design because MDW supports only even weights and EDW supports only odd weights. The USE code expands the construction framework by accommodating both odd and even code weights. This increased flexibility enables improved chip placement optimization and greater resilience to distortion caused by weather conditions in FSO channels.

As can be observed, the integration of OAM with USE OCDMA in FSO communication systems is a promising solution to enhance the channel capacity as well as the spectral efficiency. However, practical implementation of these systems faces considerable experimental challenges, including atmospheric turbulence, pointing errors, beam divergence and mode-dependent losses (MDL). MDL can cause unequal attenuation across different OAM modes due to atmospheric turbulence and system imperfections, and imbalanced system performance in practical deployments. These challenges may compromise modal orthogonality, cause power fluctuations, and increase inter-channel interference, which may deteriorate the overall system reliability Zhu et al. [40]; Wang et al. [41]. To mitigate these effects, adaptive optics and digital signal processing techniques can be employed to compensate for turbulence-induced phase distortions and reduce inter-modal crosstalk, thereby enhancing modal stability and preserving the performance of OAM-based FSO communication systems Wang et al. [15]. To implement experimentally, the transmitter generates a Gaussian beam and converted into an OAM mode using a Spatial Light Modulator (SLM), a Beam Splitter (BS), and a Circular-Polarizer lens. In this case, the number of SLMs is determined by the number of OAM modes used, which is four Xu et al. [42]; Wang et al. [15].

On the receiver side, each channel is sorted into distinct OAM modes using an OAM filter, which comprises a log-polar transformer and a convex lens that separates various OAM states into different spatial positions Huang et al. [43]; Berkhout et al. [44]. For the AND subtraction technique, fiber Bragg gratings (FBGs) are employed to filter out undesired spectral components from a targeted optical channel. The optical signal is subsequently detected by a photodetector, which converts it into an electrical signal. This electrical signal is then passed through a Low Pass Bessel filter to shape and refine the signal before being recorded and analyzed using an oscilloscope (Eye Diagram) Feng et al. [45]; Ji et al. [46].

7 Conclusion

This paper proposed and evaluated a newly developed Unipotent Single Entry (USE) OCDMA code integrated with Orbital Angular Momentum (OAM) multiplexing in a Free-Space Optical (FSO) to enhance transmission capacity and improve the Bit Error Rate (BER) of the system performance. The proposed system was evaluated alongside existing multiple-access schemes from previous studies, demonstrating its ability to reduce BER and improve the system’s transmission link. It has been shown that as weight increases, the USE code can support more users while also improving autocorrelation properties. By using four OAM beams, the capacity gained with the USE code is increased by a factor of 300%, further increasing the overall capacity of the USE OCDMA system. Additionally, the system has been simulated under various weather conditions, including rain and fog. The USE OCDMA system continues to successfully deliver commendable performance at a bit rate of 40 Gbps, achieving a range of up to 1700 m in clear weather, 900 m in light rain, 750 m in moderate rain, 500 m in heavy rain, 720 m in light fog, 480 m in medium fog, and 380 m in dense fog. Mode-Dependent Loss (MDL) resulting from atmospheric turbulence is not included in the current model. These impairments were deliberately excluded to maintain a simplified system model and to provide a clear comparison with previous studies under consistent conditions. The proposed system is applicable to next-generation optical wireless networks such as 5G/6G backhaul links, building-to-building communication, and disaster recovery scenarios, where rapid deployment and multi-user access are required. For future work, we recommend incorporating comprehensive real-world data on the city’s weather conditions, atmospheric turbulence and MDL to evaluate the robustness of the USE OCDMA code under realistic free-space optical channel conditions. In addition, adaptive optics and digital signal processing can be employed as a turbulence mitigation technique to enhance overall system performance. Experimental validation of the proposed architecture is also necessary to further demonstrate its feasibility for next-generation high-capacity optical wireless communication networks.

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Footnotes

Edited by: Xinzhong LI, Henan University of Science and Technology, China

Reviewed by: Guoquan Zhou, Zhejiang Agriculture and Forestry University, China

Ahmed C. Kadhim, University of Technology, Iraq