Performance Analysis of Hybrid PDM-SAC-OCDMA-Enabled FSO Transmission Using ZCC Codes

: The need for a high-speed transmission network has become essential due to the exponential increase in trafﬁc. In this paper, a free-space-optics (FSO) link modelled by integrating two multiplexing techniques, i


Introduction
Optical code division multiple access (OCDMA) transmission has recently become very popular in the field of optical communication systems. It can allow multiple users to access the same channel using the same spectrum simultaneously, with a high level of security using a unique code [1][2][3][4]. SAC is used with OCDMA as it can eliminate the existence of multiple access interference in OCDMA due to the cross-correlation property of OCDMA codes that affect system performance. SAC-OCDMA codes are classified into two types: codes that have zero cross-correlation where no MAI exists and codes that have cross-correlation equal to or less than one. Zero-cross correlation codes use direct detection techniques while others use suitable detection techniques such as AND-subtraction, complementary subtraction, and single photodiode (SPD) detection techniques [5,6].
Nowadays, optical-wireless-communication (OWC), also known as free-space-optics (FSO) communication, is preferred over radio frequency (RF) communications [7,8]. It provides high speed data transmission, secure communication, no electromagnetic waves exist, and it does not require a license [9]. Additionally, it can be installed everywhere as it uses the atmosphere as a medium to transmit the information signal between transmitter and receiver; as such, it requires a line of sight (LOS) link [10,11]. FSO networks provide high bandwidth wireless communication links that are desirable for meeting the demand of bandwidth hungry applications including social networking websites, video-conferencing events, high-definition television, cloud computing, and over-the-top platforms such as Amazon prime and NETFLIX, etc. Since FSO communication has many advantages, it can be applied in next generation applications that require high transmission speeds, such as the transmission of data between high altitudes platforms and optical ground stations (requires data transmission greater than 100 Gbps), fixed wing aircraft and hospitals (requires data transmission greater than 1 Gbps), and quadcopter drones and residential buildings, as shown in Figure 1.
Appl. Sci. 2023, 13, x FOR PEER REVIEW 2 of transmitter and receiver; as such, it requires a line of sight (LOS) link [10,11]. FSO n works provide high bandwidth wireless communication links that are desirable for me ing the demand of bandwidth hungry applications including social networking websit video-conferencing events, high-definition television, cloud computing, and over-the-t platforms such as Amazon prime and NETFLIX, etc. Since FSO communication has ma advantages, it can be applied in next generation applications that require high transm sion speeds, such as the transmission of data between high altitudes platforms and opti ground stations (requires data transmission greater than 100 Gbps), fixed wing aircr and hospitals (requires data transmission greater than 1 Gbps), and quadcopter dron and residential buildings, as shown in Figure 1. However, various external weather conditions (fog, dust, and snow) cause opti beam attenuation, further affecting the received signal and causing degradation in its p formance [12][13][14].
Recently, the demand for high transmission capacity has become essential due to t expeditious rise in the number of internet, mobile, and online video gaming users. convoy this growth, researchers use one or more multiplexing techniques integrated FSO transmission systems, such as orthogonal frequency division multiplexing (OFDM with SAC-OCDMA [14], polarization division multiplexing (PDM) with SAC-OCDM [15,16], and SAC-OCDMA with orbital angular momentum (OAM) [17] for capacity e hancement.
In our present work, a novel SAC-OCDMA with PDM in FSO transmission usi zero-cross-correlation code (ZCC) is proposed. This code has a simpler construction th the other codes that have been discussed for use in FSO systems. Six users, each carryi 20 Gbps binary information, are transported on two different orthogonal polarized las signals ( and ). Each user is assigned a different ZCC code sequence. The sy tem performance under external weather conditions is considered. These conditions a clear weather (CW), light-fog (LF), medium-fog (MF), heavy-fog (HF), and different sno fall conditions, including wet snow fall (WSF) and dry snow fall (DSF). Log(BER), Q-fa tor, and eye diagrams are used for evaluating the performance of the proposed model. However, various external weather conditions (fog, dust, and snow) cause optical beam attenuation, further affecting the received signal and causing degradation in its performance [12][13][14].
Recently, the demand for high transmission capacity has become essential due to the expeditious rise in the number of internet, mobile, and online video gaming users. To convoy this growth, researchers use one or more multiplexing techniques integrated in FSO transmission systems, such as orthogonal frequency division multiplexing (OFDM) with SAC-OCDMA [14], polarization division multiplexing (PDM) with SAC-OCDMA [15,16], and SAC-OCDMA with orbital angular momentum (OAM) [17] for capacity enhancement.
In our present work, a novel SAC-OCDMA with PDM in FSO transmission using zero-cross-correlation code (ZCC) is proposed. This code has a simpler construction than the other codes that have been discussed for use in FSO systems. Six users, each carrying 20 Gbps binary information, are transported on two different orthogonal polarized laser signals (X Polar and Y Polar ). Each user is assigned a different ZCC code sequence. The system performance under external weather conditions is considered. These conditions are: clear weather (CW), light-fog (LF), medium-fog (MF), heavy-fog (HF), and different snowfall conditions, including wet snow fall (WSF) and dry snow fall (DSF). Log(BER), Q-factor, and eye diagrams are used for evaluating the performance of the proposed model.
The rest of the paper is ordered as follows. Section 2 shows previous studies conducted using different multiplexing techniques in FSO communication systems. Section 3 explains general FSO channels affected by attenuation due to various climate conditions and the code construction of ZCC, followed by a description for the proposed PDM-SAC-OCDMA-enabled FSO system in Section 4. Performance analysis and results are presented, respectively, in Sections 5 and 6. Finally, conclusion is given in Section 7.

Literature Review
In this section, a literature review focused on different multiplexing techniques used in FSO communication systems will be presented.
OFDM is incorporated into an FSO system using four-level-quadrature-amplitude modulation (4-QAM), as reported in [18]. A transmission capacity of 10 Gbps under clear and fog weather conditions is reported, and the results are obtained for single channel. In [15], SAC-OCDMA using enhanced double weight (EDW) code enabled by PDM is used in FSO transmission and the performance is estimated under clear weather, haze, fog, and rain conditions. Six channels assigned with different EDW code sequences are used. Each carry 10 Gbps and an overall capacity of 60 Gbps is achieved. Additionally, in [19], authors proposed hybrid SAC-OCDMA with PDM using permutation vector (PV) code. Eight channels are used and each carry 20 Gbps of information data. Clear sky, fog conditions, different dust storm events, and different snowfall rates are the weather conditions considered. A high transmission capacity of 160 Gbps achieved, but this code has a significant code length that require more components for code generation. In [17], SAC-OCDMA with two Laguerre Gaussian OAM is used in the FSO transmission link and the performance is investigated under various fog and dust storm conditions. The OCDMA technique using fixed right shift (FRS) code that has unity cross-correlation is used, so the SPD detection technique is required to cancel the MAI between users. Six channels are used, each carrying 10 Gbps of data, and the data are transmitted on two different OAM beams. An overall 60 Gbps transmission capacity is reported. A SAC-OCDMA with PDM is proposed in an FSO transmission in [16]. Ten channels are used. Each is assigned a random diagonal (RD) code sequence and carries 10 Gbps of data. The performance of the system is evaluated under the effect of clear sky and different fog conditions and a 100 Gbps transmission capacity is reported. In [20], a dense wavelength division multiplexing (DWDM) is used in a hybrid FSO and single mode fiber (SMF) communication system. Different fog conditions and clear sky weather conditions are considered, and shorter FSO propagation ranges are reported in the results. The OFDM technique with (4-QAM) is used with SAC-OCDMA in an FSO transmission system in [14]. Three channels are used, and each is assigned three different EDW codes. An SPD detection technique is used to cancel MAI that exist as EDW code has unity cross correlation. Clear sky, haze conditions, rain conditions, and fog conditions are considered and a 45 Gbps transmission capacity is reported. In [21], spectral slicing wavelength division multiplexing (SS-WDM) is used in FSO systems. Sixteen channels are used: each carries 1.25 Gbps of information data. The tropical weather conditions in southern India are considered and an approximately 25 Gbps transmission capacity is reported. In [22], the two multiplexing techniques, PDM and SAC-OCDMA are used in the FSO transmission communication system. The diagonal permutation shift (DPS) code is used with an SPD detection technique as this code has unity cross correlation. Different weather conditions such as rain, different fog levels, and different dust storms are considered and a 60 Gbps transmission capacity is reported. In [23], four Laguerre Gaussian OAM beams are used with a SAC-OCDMA system in an FSO transmission system. The three SAC-OCDMA channels are assigned with a DPS code and transmitted on four different OAM beams, each carrying 20 Gbps of information data. Weather conditions (different snowfall rates, different dust storms and tropical weather conditions) of different Indian and Saudi Arabia cities are considered and a 120 Gbps overall transmission capacity is reported. In [24], the FSO communication system based on the use of two multiplexing techniques; PDM and SAC-OCDMA are proposed. Five channels are used, and each is assigned an RD code; each channel carries 5 Gbps of information data that are transmitted on two polarization states. Weather conditions (clear sky and different fog conditions) are considered. An overall transmission capacity of 50 Gbps is reported. In [25], the mode division multiplexing (MDM) technique is used in an FSO transmission communication system. One channel is transmitted on two different modes. Weather conditions (clear sky and different fog conditions) are considered. A successful transmission of 10 Gbps is reported. In [26], the WDM technique is used in an FSO transmission system based on using binary shift keying (BSK) modulation. Four channels are used: each carries 1.56 Gbps of information data. Clear sky, different rain conditions, and different fog conditions are considered and a 6.24 Gbps overall transmission capacity is achieved.

Weather Conditions and OCDMA Code
In this section, a brief description about the two weather conditions and the construction of the OCDMA code used in this work (ZCC) will be given.

Attenuation Caused by Fog and Snowfall Conditions
The various changes in weather conditions have an impact on the information signal in the FSO channel while it is propagating through it. In this study, CW, LF, MF, HF, WSF, and DSF weather conditions were considered. When tiny smoke particles are suspended in the air, fog is formed, and it varies from LF to HF depending on particle size and visibility (R) range. The fog attenuation coefficient, γ (dB/km), can be given as in [27]: where λ indicates the wavelength in nm and p is the size distribution of the scattering particle. According to the Kim model, this can be calculated as in [27]: (2) Table 1 shows attenuation coefficients caused by different fog conditions. Table 1. Different fog conditions with their corresponding attenuation coefficient [27,28].

Fog Conditions LF MF HF
Attenuation coefficient (dB/km) 10 18 27 Snowfall has a significant impact on the LOS link and causes attenuation that differs according to the snowfall rate. The attenuation caused by snowfall, ∝ (dB/km), is mathematically calculated as in [29]: where S in mm/hr refers to the snowfall rate. Alternatively, m and n are parameters that are given as in [29]: n = 1.38, and m = 5.42 × 10 −5 λ + 5.49 in the case of DSF n = 0.72, and m = 1.02 × 10 −4 λ + 3.78 in the case of WSF (4) Table 2 shows attenuation coefficient for different snowfall types. Table 2. Different snowfall conditions with their corresponding attenuation coefficient [30].

ZCC Code Construction
The ZCC code is characterized by number of users (U), the code length (N), code weight (W), and zero cross-correlation. The basic matrix U × N of ZCC code with W= 1 is given as in [31]: To obtain ZCC code with W = 2 from basic matrix M, we perform a transformation as in [32,33]: where D consists of diagonal pattern with alternate column zeros matrix.
In this study, we use ZCC code with W = 2. According to T, the matrix of ZCC code with W = 2 will be: The relation between N, U, and W is given as in [34]: Figure 2 illustrates the diagram describing the proposed PDM-SAC-OCDMA-enabled FSO system. It comprises three main parts: the transmitter, the FSO channel, and the receiver. The transmitter consists of multiple continuous-wave laser (CWL) sources, a ZCC code encoder, information data, and an optical modulator. In information data, the pseudorandom-bit-sequence (PRBS) generator with a non-return-to-zero (NRZ) on-off keying (OOK) modulator are used for generating 20 Gbps of information data. CWL sources are used for generating the wavelengths corresponding to the ZCC code as given in Table 3. Each user required two CWL sources for generating the optical codes equivalent to the presence of bit "1". As an example, user one has ZCC code sequence "000101", so two CWL lasers are used with wavelengths "λ 4 and λ 6 ". The two polarization states, X Polar and Y polar , are delivered from the CWL source (0 • azimuthal angle for X Polar and 90 • azimuthal angle for Y polar ). The ZCC code encoder is formed by combining the wavelengths that are generated from the CWL according to the corresponding code sequence assigned to each user. The electrical information stream is then modulated into the optical signals produced by the CWL source using a Mach-Zehnder modulator (MZM). After being combined by a PDM combiner, the information of the six users is transmitted to the FSO channel. The information signals of the six users are then transmitted through the FSO channel. At the receiver, a PDM splitter is used to split the signal into X Polar signals and Y polar signals. To convert the information signal back to its original electrical signal, a p-type, intrinsic, n-type (PIN) photodetector is used. A low-pass filter (LPF) is then used to block unwanted signals, followed by a BER analyzer to visualize the received signal's BER, Q-factor, and eye diagram.

Performance Analysis
The current reaching the PIN photodetector for the required user is expressed as in [33]: where ℛ is the responsivity of PIN photodetector and is the received power which in FSO transmission is expressed as in [27]: where represents the transmitted power, is the attenuation due to weather conditions ( in the case of fog and ∝ in the case of snowfall), is the diameter of receiver aperture while is the diameter of transmitter aperture, is the range of the signal transmitted in the FSO channel, and Ø represents the beam divergence. The SNR is expressed as in [33,34]:

Performance Analysis
The current reaching the PIN photodetector for the required user is expressed as in [33]: where R is the responsivity of PIN photodetector and P Rx is the received power which in FSO transmission is expressed as in [27]: where P Tx represents the transmitted power, β is the attenuation due to weather conditions (γ in the case of fog and ∝ in the case of snowfall), d Rx is the diameter of receiver aperture while d Tx is the diameter of transmitter aperture, L is the range of the signal transmitted in the FSO channel, and Ø represents the beam divergence. The SNR is expressed as in [33,34]: where e and B e are charge of electron and electrical bandwidth, respectively, k B is Boltzmann constant, T abs refers to absolute temperature of receiver noise, and R Load is the load resistance of receiver. The BER is given as in [27]: Alternatively, the Q-factor is given as in [27]:

Simulation Results
The computed results for PDM-SAC-OCDMA-enabled FSO transmission are given in this section. The parameter values considered during simulations performed on Optisystem software are given in Table 4 [5,21,24,28]. Log(BER), Q-factor, various FSO spans, and eye diagrams are considered for evaluating the performance of our proposed model. The results are divided into four parts as follows.

Impact of Clear Weather on PDM-SAC-OCDMA-Enabled FSO System
The attenuation of CW is 0.14 dB/km [28]. This is small when compared to attenuation caused by severe weather conditions such as fog and snow. As such, it has little effect on the signal transmission. The impact of various propagation ranges on the performance of six users of the proposed PDM-SAC-OCDMA-enabled FSO system in terms of log(BER) is shown in Figure 3. It is seen that all six users, who are transmitted on two different polarization states (users 1, 2, and 3 are transmitted on X polar and users 4, 5, and 6 are transmitted on Y polar ), can propagate up to 10 km with log(BER) values varying between −12.55 and −9.24. Figure 4 depicts the Q-factor versus FSO link for different users in our proposed model. It should be noted that users 1 and 4, who transmit their dataon X polar and Y polar , respectively, reached a propagation range of 10 km with nearly the same Q-factor (6). A higher Q-factor of ∼7 is obtained at the same range for users 3 and 6. Users 2 and 3 have a Q-factor of 6.7 at 10 km.
The eye patterns at 10 km propagation range for users 1, 2, 3, 4, 5, and 6 are displayed in Figure 5. From the results in Figures 3-5, we can see that user 3 and user 6, using the same code, performed better than other users (1, 2, 4 and 5). The main reason for the better performance of these channels is that they have the same code (101000). As such, they are occupied at the first point of the spectrum, leading to higher optical signal to noise ratio and so better log(BER). The other channels experience significant noise interference from neighboring channels due to the FBG bandwidth and reflectivity. Therefore, the size of eye diagrams for user 3 and user 6 are different than the other users. The large eye opening suggests a successful received signal at a 10 km FSO link with 120 Gbps overall transmission capacity.  Figure 4 depicts the Q-factor versus FSO link for different users in our p model. It should be noted that users 1 and 4, who transmit their dataon and respectively, reached a propagation range of 10 km with nearly the same Q-facto higher Q-factor of ~7 is obtained at the same range for users 3 and 6. Users 2 and a Q-factor of 6.7 at 10 km.   Figure 4 depicts the Q-factor versus FSO link for different users in our p model. It should be noted that users 1 and 4, who transmit their dataon and respectively, reached a propagation range of 10 km with nearly the same Q-facto higher Q-factor of ~7 is obtained at the same range for users 3 and 6. Users 2 and a Q-factor of 6.7 at 10 km. The eye patterns at 10 km propagation range for users 1, 2, 3, 4, 5, and 6 are di in Figure 5. From the results in Figures 3, 4, and5, we can see that user 3 and user the same code, performed better than other users (1, 2, 4 and 5). The main reason noise ratio and so better log(BER). The other channels experience significant noise interference from neighboring channels due to the FBG bandwidth and reflectivity. Therefore, the size of eye diagrams for user 3 and user 6 are different than the other users. The large eye opening suggests a successful received signal at a 10 km FSO link with 120 Gbps overall transmission capacity.

User#1
User#2 User#4 User#5 User#3 User#6 (a) (b) . Table 5 lists the performance results of the six users of the PDM-SAC-OCDMA-enabled FSO transmission at 10 km under clear weather conditions.

Impact of LF, MF, and HF on PDM-SAC-OCDMA-Enabled FSO System
As seen in Table 1, different levels of fog cause different attenuation, varying from low attenuation caused by LF to high attenuation caused by HF. Accordingly, the effects of this different attenuation on the performance of the proposed model in terms of Log(BER) and Q-factor versus different FSO ranges are given in Figures 6 and 7,  Table 5 lists the performance results of the six users of the PDM-SAC-OCDMA-enabled FSO transmission at 10 km under clear weather conditions.

Impact of LF, MF, and HF on PDM-SAC-OCDMA-Enabled FSO System
As seen in Table 1, different levels of fog cause different attenuation, varying from low attenuation caused by LF to high attenuation caused by HF. Accordingly, the effects of this different attenuation on the performance of the proposed model in terms of Log(BER) and Q-factor versus different FSO ranges are given in Figures 6 and 7, respectively. A shorter range provides a high performance than a longer range, while the best performance is achieved under LF conditions. The log(BER) and Q-factor for User 1 at 1.6 km are −9.26 and 6.09 under LF, respectively, while under HF, this range is decreased by 0.85 km at approximately the same log(BER) and Q-factor values. respectively. A shorter range provides a high performance than a longer range, while the best performance is achieved under LF conditions. The log(BER) and Q-factor for User 1 at 1.6 km are −9.26 and 6.09 under LF, respectively, while under HF, this range is decreased by 0.85 km at approximately the same log(BER) and Q-factor values.

Impact of WSF and DSF on PDM-SAC-OCDMA-Enabled FSO Transmission
Furthermore, the performance of the six users of the PDM-SAC-OCDMA-enabled FSO transmission is studied under snowfall conditions. From Figures 8 and 9, the proposed model can reach propagation range under WSF longer than that reached under DSF. This result is expected as DSF causes higher attenuation than WSF. As an example, the FSO link achieved under WSF for User 1 is 1.2 km with log(BER) of −10.99 and Q-factor of 6.70. Under DSF, and at the same values of log(BER) and Q-factor, the range is decreased to 0.255 km.This result is expected as DSF has a large attenuation value when compared to WSF.
The computed performance values at 1.2 km under WSF and 0.26 km under DSF for the six users are given in Table 7. The comparison between using our proposed SAC-OCDMA-based PDM using ZCC code and other SAC-OCDMA-based PDM using different codes is given in Table 8.

Impact of WSF and DSF on PDM-SAC-OCDMA-Enabled FSO Transmission
Furthermore, the performance of the six users of the PDM-SAC-OCDMA-enabled FSO transmission is studied under snowfall conditions. From Figures 8 and 9, the proposed model can reach propagation range under WSF longer than that reached under DSF. This result is expected as DSF causes higher attenuation than WSF. As an example, the FSO link achieved under WSF for User 1 is 1.2 km with log(BER) of −10.99 and Qfactor of 6.70. Under DSF, and at the same values of log(BER) and Q-factor, the range is decreased to 0.255 km .This result is expected as DSF has a large attenuation value when compared to WSF.  The computed performance values at 1.2 km under WSF and 0.26 km under DSF for the six users are given in Table 7.

Impact of WSF and DSF on PDM-SAC-OCDMA-Enabled FSO Transmission
Furthermore, the performance of the six users of the PDM-SAC-OCDMA-enabled FSO transmission is studied under snowfall conditions. From Figures 8 and 9, the proposed model can reach propagation range under WSF longer than that reached under DSF. This result is expected as DSF causes higher attenuation than WSF. As an example, the FSO link achieved under WSF for User 1 is 1.2 km with log(BER) of −10.99 and Qfactor of 6.70. Under DSF, and at the same values of log(BER) and Q-factor, the range is decreased to 0.255 km .This result is expected as DSF has a large attenuation value when compared to WSF.  The computed performance values at 1.2 km under WSF and 0.26 km under DSF for the six users are given in Table 7.

Conclusions
A novel FSO transmission that uses SAC-OCDMA with PDM for capacity enhancement is reported. Three users, each with a different ZCC code, are transmitted on X Poalr state, carrying 60 Gbps of information data. In addition, three additional users carrying 60 Gbps of information data assigned with the same three distinct ZCC codes are transmitted on Y Poalr state simultaneously. The proposed system is simulated considering different climate conditions (CW, LF, MF, HF, WSF, and DSF), and its performance is investigated in terms of log(BER), Q-factor, and eye diagrams. The results show that our proposed model can reach 10 km under CW, while for different fog conditions this range is decreased to 1.6 km (LF), 1 km (MF), and 0.76 km (HF). Additionally, FSO ranges of 1.2 km under WSF and 0.26 km under DSF are achieved. These ranges are considered at log(BER) ≤ 10 −9 and Q-factor ≥ 6. Consequently, we suggest our proposed PDM-SAC-OCDMA-based FSO system for use in next generation high-speed applications and in remote areas. Furthermore, the proposed FSO transmission can be used for high-capacity wireless networks required for beyond 5G and 6G access networks. In this work, we have not considered cross-polarization effects due to FSO channel and practical, imperfect PDM combiner/splitter while performing simulations. In future works, the proposed FSO system will be experimentally validated to take into consideration real-time FSO channel imperfections and losses.