A Performance Analysis of a Hybrid OCDMA-PON Conﬁguration Based on IM / DD Fast-OFDM Technique for Access Network

: The purpose of this article is to propose a new configuration based on OCDMA and Fast-OFDM techniques for access network applications. A hybrid intensity modulation with direct detection, fast orthogonal frequency-division multiplexing–code division multiplexing access (IM / DD Fast-OFDM-CDMA) system is analytically and numerically evaluated for an amplifier-free access network. Therefore, system performance is analytically investigated in terms of bit error rate / Q-factor as a function of simultaneous users, fiber length and launched optical power. Firstly, the proposed analytical model includes the overlapping effect among OFDM subcarriers, the peak-to-average power ratio (PAPR), and multiple access interference (MAI). Secondly, a simulation setup is performed, allowing four simultaneous users operating at 40 Gb / s in a passive optical network (PON) context. Furthermore, a power budget analysis is made between IM / DD Fast-OFDM-CDMA, all-optical IM / DD OFDM-CDMA (IM / DD AO-OFDM-CDMA) and OCDMA wavelength division multiplexing (OCDMA-WDM) configurations. It is shown that at 40 Gb / s and by using 2D-hybrid coding (2D-HC), the maximum achievable transmission-reach of IM / DD Fast-OFDM-CDMA is 142 km, which is 34 km and 60 km higher than those provided by the IM / DD AO-OFDM-OCDMA and OCDMA-WDM PON configurations, respectively.


Introduction
Orthogonal frequency-division multiplexing (OFDM) is an emerging technology in optical fiber communications due to its inherent advantages, which include simplified digital signal processing for channel estimation and the compensation of linear fiber-induced impairments, such as chromatic dispersion and polarization-mode dispersion [1]. OFDM is essentially a method of encoding digital data on multiple carrier frequencies, harnessing the (inverse) fast Fourier transform (IFFT) [2], and is widely used in wireless local area networks (802.11 a/g) and wireless metropolitan area networks (802.16 d).
In the wireless domain, OFDM's advantages also include the support of several multiple access schema (e.g., time-division multiplexing access (TDMA), frequency-division multiplexing access (FDMA), code-division multiplexing access (CDMA)) and the compensation of multipath propagation [3,4]. In wireline communications, OFDM has been implemented in asynchronous digital subscriber lines (ADSLs) and digital video broadcasting (DVB). On the other hand, CDMA is a multiplexing scheme based on the user code signature with great potential for providing bandwidth allocation, maximization of network user capacity and security enhancement. Further, CDMA offers simple network management with great capacity to support asynchronous bursty traffic, low latency access, transparency to overlaid protocols and high network flexibility [5]. Hybrid OFDM-CDMA systems have been reported in the On the OLT block, the received signal is converted from optical to electrical thanks to the optical demodulator. Then, the generated signal is multiplied by the desired signature provided by the OCDMA decoder, and the Fast-OCDMA subcarrier decoder is applied to restore the symbol. Finally, the symbol is de-mapped to restore the emitted user data.

Analytical System Model
The signal-to-noise ratio (SNR) expression as a function of simultaneous PON users can be expressed as follows: where S is the received signal (i.e., corresponding to the transmitted symbol) and σ is the noise variance. In our model, the noise variance includes MAI and subcarriers overlapping, which can be defined as follows: where is related to 2D-HC codes and given by [23]: In Equation (3), and are the average probability hit of chips related to 2D-HC and the prime number, respectively. In this study, we also consider the photo-detector noise (N ).
In fact, 2D-HC is built as follows: the maximum-length (ML) sequence is employed for the wavelength hopping, and the prime number is used for temporal spreading (i.e., examples of seven 2D-HC codes are described in Table 1, where {1, 2, 3, 4, 5, 6, 7} symbolize the wavelengths { , , , , , , } and [23]). The 2D-HC code is defined with respect to wavelength hoping Hj and temporal spreading Si as shown in Table 1 the different code sequences SiHj where i vary from 0 to 4 and j vary from 0 to 3).  On the OLT block, the received signal is converted from optical to electrical thanks to the optical demodulator. Then, the generated signal is multiplied by the desired signature provided by the OCDMA decoder, and the Fast-OCDMA subcarrier decoder is applied to restore the symbol. Finally, the symbol is de-mapped to restore the emitted user data.

Analytical System Model
The signal-to-noise ratio (SNR) expression as a function of simultaneous PON users can be expressed as follows: where S is the received signal (i.e., corresponding to the transmitted symbol) and σ 2 is the noise variance. In our model, the noise variance includes MAI and subcarriers overlapping, which can be defined as follows: where σ 2 MAI is related to 2D-HC codes and given by [23]: In Equation (3), H and P are the average probability hit of chips related to 2D-HC and the prime number, respectively. In this study, we also consider the photo-detector noise (N 0 ).
Appl. Sci. 2020, 10, x FOR PEER REVIEW 4 of 14 S0H1 30000000 20000000 70000000 00000000 00000000 10000000 00000000 S2H1 50000000 40000000 20000000 00000000 00000000 30000000 00000000 S4H1 20000000 10000000 60000000 00000000 00000000 70000000 00000000 S1H2 10000000 70000000 50000000 00000000 00000000 60000000 00000000 S3H2 40000000 30000000 10000000 00000000 00000000 20000000 00000000 S0H3 60000000 50000000 30000000 00000000 00000000 40000000 00000000 S2H3 70000000 60000000 40000000 00000000 00000000 50000000 00000000 Figure 2 represents the implementation of the OCDMA encoder and decoder based on the 2D-HC S0H1 sequence. As shown in Figure 2, the 2D-OCDMA encoder and decoder are composed of the WDM multiplexer, time delay, Bessel filter and WDM de-multiplexer. One major drawback related to single-band (SB) and multi-band (MB) OFDM systems is their sensibility to fiber nonlinear effects due to the high PAPR of OFDM signals [24]. In fact, even in SB OFDM, four-wave mixing (FWM) happens among electronic OFDM subcarriers due to its multicarrier nature producing inter-subcarrier interference (ICI) [25]. As long as the cyclic prefix is a timeshifted copy of a part of the OFDM signal in the "observation" period, the transmitted time domain waveform inside this period for one OFDM symbol can be expressed by Equation (4): where and represent the input symbol and the subcarrier number of the classical OFDM symbol, respectively.
Since the frequency gap between subcarriers is reduced to half ( ) for the Fast-OFDM symbol, the signal becomes [26]: The kth OCDMA encoder produces the user signature as follows: where and represent the code length and the time chip period, respectively. At the input of the optical modulator, the electrical signal can be written as follows: One major drawback related to single-band (SB) and multi-band (MB) OFDM systems is their sensibility to fiber nonlinear effects due to the high PAPR of OFDM signals [24]. In fact, even in SB OFDM, four-wave mixing (FWM) happens among electronic OFDM subcarriers due to its multi-carrier nature producing inter-subcarrier interference (ICI) [25]. As long as the cyclic prefix is a time-shifted copy of a part of the OFDM signal in the "observation" period, the transmitted time domain waveform inside this period for one OFDM symbol can be expressed by Equation (4): where X k and N represent the input symbol and the subcarrier number of the classical OFDM symbol, respectively.
Since the frequency gap between subcarriers is reduced to half ( 1 2T s ) for the Fast-OFDM symbol, the signal becomes [26]: The kth OCDMA encoder produces the user signature as follows: where F and T c represent the code length and the time chip period, respectively.

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At the input of the optical modulator, the electrical signal can be written as follows: In order to make a comparison between the transmitted signals in the cases of the Fast-OFDM-CDMA configuration and the AO-OFDM-CDMA and OCDMA-WDM systems, we introduce Equations (8) and (9), respectively, as follows: where s 1 (t) represents the transmitted signal in the case of the AO-OFDM-CDMA configuration.
where s 2 (t) represents the transmitted signal in the case of the OCDMA-WDM configuration. Meanwhile, the PAPR is determined by Equation (8), as follows: where max(|s(t)| 2 ) and E(|s(t)| 2 ) are the maximum and the mean of the Fast-OFDM symbol, respectively. A good way to characterize the PAPR is to use the complementary cumulative distribution function (CCDF) of Pc, which is expressed as Pc = Pr{PAPR > a p }. Pc is defined as the probability that PAPR overtakes a particular value of a p . In the latter case, the variance of subcarriers overlap is defined in Equation (11).
The effects of PAPR and nonlinearities on the system performance are added through the variance of the OFDM subcarriers overlapping. In addition, we consider the particular case in Equation (10) in order to minimize PAPR and simplify the calculations.
The bit-error-rate (BER) expression is derived from the SNR expression in Equation (1), as follows [17]: where M is defined as the modulation order. Table 2 shows the simulation parameters deployed for the continuous wave laser (CW laser) transmitter, the G.652 SSMF optical channel and the OCDMA signature parameters. Furthermore, to meet the high-standard optical communication system requirement, we consider forward error correction (FEC limit) and Q-limit for the BER and Q-factor metrics, respectively.   As shown in Figure 3, the three PON configurations can support up to 180 simultaneous users with a BER value less than 10 −4.5 (i.e., less than the typical FEC limit of 3.8 × 10 −3 ) when 2D-Hybrid codes are used as the OCDMA signature. Furthermore, it is shown that the IM/DD Fast-OFDM-CDMA outperforms both the AO-OFDM-OCDMA and OCDMA-WDM systems in terms of BER as a function of simultaneous users. Further, at 100 simultaneous users, the IM/DD Fast-OFDM-CDMA configuration improves the system performance by factors of 10 −0.5 and 10 −1.5 , in terms of BER, compared to AO-OFDM-OCDMA and OCDMA-WDM, respectively.  As shown in Figure 3, the three PON configurations can support up to 180 simultaneous users with a BER value less than 10 −4.5 (i.e., less than the typical FEC limit of 3.8 × 10 −3 ) when 2D-Hybrid codes are used as the OCDMA signature. Furthermore, it is shown that the IM/DD Fast-OFDM-CDMA outperforms both the AO-OFDM-OCDMA and OCDMA-WDM systems in terms of BER as a function of simultaneous users. Further, at 100 simultaneous users, the IM/DD Fast-OFDM-CDMA configuration improves the system performance by factors of 10 −0.5 and 10 −1.5 , in terms of BER, compared to AO-OFDM-OCDMA and OCDMA-WDM, respectively. As demonstrated by Figure 4, the three PON configurations fulfill the FEC limit for a fiber length up to 180 km. Further, at an SSMF length of 100 km it is shown that the Fast-OFDM-CDMA system outperforms AO-OFDM-CDMA and OCDMA-WDM by 10 −1.5 and 10 −1 in terms of BER, respectively. Finally, the Fast-OFDM-CDMA and AO-OFDM-CDMA systems present the same BER at a fiber length equal to 200 km. Figure 5 presents the log(BER) as a function of launched optical power for the Fast-OFDM-CDMA system compared to AO-OFDM-CDMA and OCDMA-WDM at K = 2. As depicted in Figure  5, the IM/DD Fast-OFDM-CDMA system outperforms both the AO-OFDM-CDMA and OCDMA-WDM PON configurations. Furthermore, it is shown that at a launched optical power of 0 dBm, the AO-OFDM-OCDMA and OCDMA-WDM systems have the same Q-factor, equal to 2.5 dB. However, at 0 dBm, Fast-OFDM-CDMA improves the system performance by a Q-factor equal to 2.5 dB compared to AO-OFDM-OCDMA and OCDMA-WDM. On one hand, AO-OFDM-CDMA has a better system performance compared to OCDMA-WDM, while the launched power is less than 0 dBm. On the other hand, for a launched optical power greater than 2 dBm, the OCDMA-WDM PON configuration upgrades AO-OFDM-CDMA in terms of Q-factor. Additionally, the latter PON configurations provide a Q-factor above the Q-limit (i.e., equal to 6 dB) when the optical launched power exceeds 4 dBm.  Figure 5 presents the log(BER) as a function of launched optical power for the Fast-OFDM-CDMA system compared to AO-OFDM-CDMA and OCDMA-WDM at K = 2. As depicted in Figure 5, the IM/DD Fast-OFDM-CDMA system outperforms both the AO-OFDM-CDMA and OCDMA-WDM PON configurations. Furthermore, it is shown that at a launched optical power of 0 dBm, the AO-OFDM-OCDMA and OCDMA-WDM systems have the same Q-factor, equal to 2.5 dB. However, at 0 dBm, Fast-OFDM-CDMA improves the system performance by a Q-factor equal to 2.5 dB compared to AO-OFDM-OCDMA and OCDMA-WDM. On one hand, AO-OFDM-CDMA has a better system performance compared to OCDMA-WDM, while the launched power is less than 0 dBm. On the other hand, for a launched optical power greater than 2 dBm, the OCDMA-WDM PON configuration upgrades AO-OFDM-CDMA in terms of Q-factor. Additionally, the latter PON configurations provide a Q-factor above the Q-limit (i.e., equal to 6 dB) when the optical launched power exceeds 4 dBm.     As shown in Figure 6, a pseudorandom binary sequence (PRBS) is used to generate a random bit user, then followed by an NRZ generator, followed by a 16-QAM generator and finally a Fast-OFDM subcarrier modulator is putted at the end of the first pipeline. A Mach-Zehnder modulator (MZM) is used to convert the electrical signal to an optical one based on a continuous wave (CW) laser source. The output signal of the MZM modulator will be multiplied by the signature generated by the 2D-OCDMA encoder. Finally, the output signal from the 2D-OCDMA encoder will be sent towards the optical channel.    As shown in Figure 6, a pseudorandom binary sequence (PRBS) is used to generate a random bit user, then followed by an NRZ generator, followed by a 16-QAM generator and finally a Fast-OFDM subcarrier modulator is putted at the end of the first pipeline. A Mach-Zehnder modulator (MZM) is used to convert the electrical signal to an optical one based on a continuous wave (CW) laser source. The output signal of the MZM modulator will be multiplied by the signature generated by the 2D-OCDMA encoder. Finally, the output signal from the 2D-OCDMA encoder will be sent towards the optical channel.  As shown in Figure 6, a pseudorandom binary sequence (PRBS) is used to generate a random bit user, then followed by an NRZ generator, followed by a 16-QAM generator and finally a Fast-OFDM subcarrier modulator is putted at the end of the first pipeline. A Mach-Zehnder modulator (MZM) is used to convert the electrical signal to an optical one based on a continuous wave (CW) laser source. The output signal of the MZM modulator will be multiplied by the signature generated by the 2D-OCDMA encoder. Finally, the output signal from the 2D-OCDMA encoder will be sent towards the optical channel.

Figures 6 and 7 represent the ONU and the OLT implementation, with the Optisystem simulator version 17, respectively.
On the OLT side, a 2D-OCDMA decoder is used to eliminate the user signature as depicted in Figure 7. Then, an APD photodetector is employed to convert the optical signal into an electrical one. In addition, a Fast-OFDM subcarrier demodulator followed by a 16-QAM decoder is useful to recover the received symbol as a user bit. In our simulation setup, the system provides 10 GHz spacing between 9 channels, with a 40 Gb/s signal capacity (25 GS/s sampling rate) per-channel, using 16-QAM. The OFDM block is composed of 64 electronic subcarriers (only 5 Ghz spacing among subcarriers is used thanks to the Fast-OFDM technique), a cyclic prefix of 2% to eliminate inter-symbol interference, 10 pilot subcarriers for carrier recovery and digital-to-analog/analog-to-digital converter clipping ratio, and quantization bits set at 13 and 10 dB, respectively. For Fast-OFDM-CDMA on this setup, 9 electrical subcarriers are also considered, supporting 4 simultaneous users in the network. The 5th middle channel is investigated, which suffers the most from nonlinear crosstalk effects, while the launched optical power per channel/optical subcarrier was fixed at the optimum 2 dBm for both cases of downstream link. The PRBS generated bits were 219-1, and hard-error decoding was performed at the receiver to calculate the BER. The CW laser, Fast-OFDM modulator, MZM modulator and related APD detector for IM/DD Fast-OFDM-CDMA were simulated at an aggregate bit rate of 40 Gb/s. The developed Fast-OFDM bloc, as well as the 2D-OCDMA block, was implemented in the Optisystem ® simulator environment (electrical and optical components with SSMF). It should be noted that phase noise and frequency offset have been considered here using three OFDM pilot subcarriers. Our system setup considered 1000 symbols per subcarrier. The adopted SSMF parameters for signal transmission over an 80 km length are the following: fiber nonlinear Kerr parameter, CD, CD-slope, fiber loss and differential group delay (DGD) of 1.1 W −1 km −1 , 16 ps/nm/km, 0.06 ps/km/nm 2 , 0.2 dB/km and 0.2 ps/km, respectively. Likewise, in order to recover the phase after the photodetector, a low pass Bessel filter is used after the photodetector in the setup. In addition, a Bessel optical filter is employed before the photodetector at the third optical window to preserve the received signal phase shape.
As shown in Figure 8, the eye diagrams for four users generated by the Optisystem ® BER analyzer are open, indicating the feasibility of our hybrid IM/DD Fast-OFDM-CDMA system in the PON context operating at 40 Gb/s. However, the eye becomes more closed when the number of users is raised; this is due to the MAI, which is considered as the most dominant degradation factor of OCDMA system. dBm for both cases of downstream link. The PRBS generated bits were 219-1, and hard-error decoding was performed at the receiver to calculate the BER. The CW laser, Fast-OFDM modulator, MZM modulator and related APD detector for IM/DD Fast-OFDM-CDMA were simulated at an aggregate bit rate of 40 Gb/s. The developed Fast-OFDM bloc, as well as the 2D-OCDMA block, was implemented in the Optisystem ® simulator environment (electrical and optical components with SSMF). It should be noted that phase noise and frequency offset have been considered here using three OFDM pilot subcarriers. Our system setup considered 1000 symbols per subcarrier. The adopted SSMF parameters for signal transmission over an 80 km length are the following: fiber nonlinear Kerr parameter, CD, CD-slope, fiber loss and differential group delay (DGD) of 1.1 W −1 km −1 , 16 ps/nm/km, 0.06 ps/km/nm 2 , 0.2 dB/km and 0.2 ps/km, respectively. Likewise, in order to recover the phase after the photodetector, a low pass Bessel filter is used after the photodetector in the setup. In addition, a Bessel optical filter is employed before the photodetector at the third optical window to preserve the received signal phase shape.
As shown in Figure 8, the eye diagrams for four users generated by the Optisystem ® BER analyzer are open, indicating the feasibility of our hybrid IM/DD Fast-OFDM-CDMA system in the PON context operating at 40 Gb/s. However, the eye becomes more closed when the number of users is raised; this is due to the MAI, which is considered as the most dominant degradation factor of OCDMA system.

Power Budget Analysis
The cost performance of the IM/DD Fast-OFDM-CDMA system is calculated as the optical power budget using an APD and a CW laser at OLT and ONU, respectively, as shown in Figure 9. Table 3 presents the power budget calculation related to the proposed hybrid system configuration with 4 dBm and 15 dBm emitted average powers, corresponding to the local and long reach access network [27], respectively.
For the connector attenuation, four connectors are required in total to relay each component in the link, as shown in Figure 8 (i.e., a connector is needed to connect ONU, SSMF, splitter 1 × 16, SSMF and OLT), and if we consider that each connector has a loss of 0.4 dB [28], we get a total connector attenuation in the link in the order of 4 × 0.4 = 1.6 dB. In addition, each splitter 1 × 16 introduces a loss equal to 12 dB. On the one hand, it is shown that the maximum reachable distance between the ONU and OLT for the Fast-OFDM-CDMA system is equal to 112 km and 167 km for the lower case and the upper case, respectively. Likewise, we show that the proposed hybrid system can reach a long-reach PON distance of 167 km using an emitted average power of 15 dBm.

Power Budget Analysis
The cost performance of the IM/DD Fast-OFDM-CDMA system is calculated as the optical power budget using an APD and a CW laser at OLT and ONU, respectively, as shown in Figure 9.  Table 3 presents the power budget calculation related to the proposed hybrid system configuration with 4 dBm and 15 dBm emitted average powers, corresponding to the local and long reach access network [27], respectively. For the connector attenuation, four connectors are required in total to relay each component in the link, as shown in Figure 8 (i.e., a connector is needed to connect ONU, SSMF, splitter 1 × 16, SSMF and OLT), and if we consider that each connector has a loss of 0.4 dB [28], we get a total connector attenuation in the link in the order of 4 × 0.4 = 1.6 dB. In addition, each splitter 1 × 16 introduces a loss equal to 12 dB. On the one hand, it is shown that the maximum reachable distance between the ONU and OLT for the Fast-OFDM-CDMA system is equal to 112 km and 167 km for the lower case and the upper case, respectively. Likewise, we show that the proposed hybrid system can reach a long-reach PON distance of 167 km using an emitted average power of 15 dBm. Table 4 presents the power budget comparison related to the proposed hybrid system configuration compared to the OCDMA-WDM and AO-OFDM-CDMA systems.
Moreover, with a 10 dBm average launched optical power, our hybrid system increases the maximum achievable transmission reach to 142 km, compared to 108 km for AO-OFDM-CDMA. As a result, our hybrid Fast-OFDM-CDMA system can improve the total power budget with an   Table 4 presents the power budget comparison related to the proposed hybrid system configuration compared to the OCDMA-WDM and AO-OFDM-CDMA systems. Moreover, with a 10 dBm average launched optical power, our hybrid system increases the maximum achievable transmission reach to 142 km, compared to 108 km for AO-OFDM-CDMA. As a result, our hybrid Fast-OFDM-CDMA system can improve the total power budget with an increment equal to 6.8 dB (i.e., the power budget passed from 21.6 to 28.4 dB), as compared to the AO-OFDM-OCDMA PON configuration. Table 5 summarizes the relevant 2D-OCDMA-PON systems. To make a fair comparison among our IM/DD Fast-OFDM-CDMA and the other proposed systems in the literature, we consider various features, such as the coding scheme, cardinality (i.e., number of users), performance measured metrics (i.e., BER and Q-factor), system components and reachability distance. As shown in Table 5, various 2D-OCDMA codes are proposed for PON applications, such as hybrid codes (2D-HC), prime hop system (2D-PHS) and 2D permutation vectors (2D-PV) codes. We can also see that when the bit rate is less than 40 Gb/s, the system authorizes a high cardinality, for instance in the 2D-OCDMA-WDM, 2D-OCDMA, 2D-PV and Fast-OFDM-CDMA PON configurations. Nonetheless, for a bit rate equal to 100 Gb/s, the number of simultaneous users is reduced to 5 and 15 for the IMDD OOFDM-CDMA and CO-OFDM-CDMA systems, respectively. As a conclusion, the IM/DD Fast-OFDM-CDMA system outperforms the AO-OFDM-CDMA, CO-OFDM-CDMA, IMDD OOFDM-CDMA and 2D-PV systems in terms of cardinality and reachability as well.

Conclusions
A 40 Gb/s IM/DD Fast-OFDM-CDMA system was analytically and numerically demonstrated using 2D-OCDMA HC codes for an amplifier-free access network. Our hybrid IM/DD Fast-OFDM-CDMA system was based on a breakthrough analytical model that accounts for OFDM subcarriers overlapping, MAI and PAPR. It was shown that our proposal outperforms both the IM/DD AO-OFDM-OCDMA and 2D-OCDMA-WDM PON configurations in terms of system performance. Indeed, at 0 dBm, IM/DD Fast-OFDM-CDMA improves the Q-factor by 2.5 dB compared to AO-OFDM-OCDMA and OCDMA-WDM. On the other hand, the numerical simulation results showed the implementation feasibility of our hybrid system operating at 40 Gb/s in the PON configuration via open eye diagrams. Power budget analysis revealed that at a launched optical power of 10 dBm and with 16 simultaneous users, our proposed technique can improve the total power budget by 6.8 dB compared to IM/DD AO-OFDM-OCDMA. This leads to an extension of the maximum achievable distance of up to 142 km, compared to 108 km and 82 km for IM/DD AO-OFDM-OCDMA and 2D-OCDMA-WDM, respectively. The future directions for the extension of the access network could be the integration of new emergent technologies, such as multi-meter waves [31] and time domain equalizers, based on the OFDM technique [32], to extend the reachability distance and integration of 5G/6G non orthogonal multi-access (NOMA) in order to connect local and metropolitan networks to the broadband global access network. Finally, although an access network based on the OCDMA-PON configuration preserves data integrity, securing the access network will be a big challenge for researchers in the near future, as regards preserving data confidentiality and privacy against various attacks and threats by using Blockchain technology (BCT) and machine learning (ML)-based solutions [33].
Funding: This research received no external funding.

Conflicts of Interest:
The authors declare no conflict of interest.