All future access networks will deploy fiber optics technology to provide end users with the required bandwidth to feed all bandwidth-hungry applications. Passive optical networks (PON) are one of the most widely growing access network technologies today [1, 2]. In PONs, an optical line terminal (OLT) delivers high data rates through an optical distribution network (ODN) to devices located in the user premises named optical network unit (ONU). A single OLT can serve between 16 to 128 ONUs at the same time using time division multiple access (TDMA). However, for future applications, TDMA alone is not sufficient. Wavelength division multiple access (WDMA) and optical code division multiple access (OCDMA) are two possible access schemes to be adopted in future access networks to increase both the data rate and the total number of subscribers served [3, 5].
OCDMA is a multi access technique that utilizes codes to distinguish between users that simultaneously access the optical media. Although OCDMA systems can potentially provide very high data rates, these systems suffer from multi access interference (MAI) . MAI mitigation is a crucial part of any OCDMA detection design. Different OCDMA schemes have dealt with MAI mitigation in different ways ranging from simple passive approaches to highly complex coherent procedures . A simple and low cost OCDMA scheme that cancels the MAI at the mean is known as spectral amplitude coding (SAC) OCDMA . The main attributes of the SAC OCDMA is that the code signatures are encoded in spectral domain at the transmitter and the MAI is canceled at the receiver by a differential balanced detector.
Due to their spectral encoding, SAC OCDMA systems require broadband optical sources. Most of the literature have considered broadband incoherent sources such as light emitting diodes (LED) and amplified spontaneous emission (ASE) as SAC sources [8, 18]. Additional to their broadband nature, the low price of these sources makes them a natural choice if SAC OCDMA is ever going to be commercially viable as an access network technology. However, these sources suffer from intensity noise (IN) or phase induced intensity noise (PIIN) which limits their performance to support systems up to hundreds of Mb/s , not to mention the non uniform power distribution of the spectral bandwidth of these sources, which will lead to MAI if not processed by power equalization techniques [20, 21].
In order to overcome the above mentioned limitations of incoherent sources, the use of coherent sources in SAC OCDMA has been considered [22, 26]. It is important to note that coherent sources suffer from beat noise resulting from the laser signals overlapping in frequency . This beat noise, if not mitigated, can result in limiting the performance of SAC OCDMA systems, even more than incoherent sources. Ayotte and Rusch  performed a capacity prediction comparing three different laser source configurations to incoherent sources alone and incoherent sources with forward error correction (FEC). They showed that for highly populated networks, a multi laser source with highly controlled lasers’ central frequencies will provide the best performance. Yoshino et al. countered the beat noise by the use of coherent optical heterodyne detection . The drawback of this scheme is that it requires high phase stabilization between the received signal and the local light signal. In  Yoshino et al. proposed a cost efficient well flattened multi wavelength source that can be used in SAC OCDMA as an alternative to the more expensive multi laser source. In , we proposed the use of wavelength multiplexed SAC OCDMA codes in order to improve the performance of highly populated coherent source SAC OCDMA networks.
In this paper we propose using spatial domain multiplexing to reduce the beat noise in the coherent source SAC OCDMA system. The use of spatial multiplexing is not new to SAC OCDMA. In  spatial multiplexing and 2D codes were used to reduce the PIIN in incoherent systems. By adopting spatial multiplexing we aim to divide the number of overlapping laser signals into two or more groups, where each group of signals is detected by a separate photodiode, leading to a reduction in the beat noise per spectral bin, and the system as a whole.
The rest of this paper is organized as follows; in Section II we show the structure of spatial multiplexing network and its transmitter and receiver. We evaluate our proposed system performance for the three different source configurations in Section III. In Section IV, we verify our proposed scheme through software simulation. Finally, a conclusion highlighting the major advantages and disadvantages of our proposed scheme is given in Section V.
Beat noise is generated at detection by two or more laser sources that have the same central frequency or a central frequency difference that falls within the receiver’s bandwidth. The more the lasers satisfy the above condition, the higher the beat noise would be. The proposed scheme is based on dividing the number of overlapping laser signals into groups, where each group is detected separately by a different photodiode. By doing so, the total number of generated beat signals is reduced, and thus reducing the amount of distortion in the intended signal due to beat noise. For an
The structure of the traditional SAC OCDMA transmitter and receiver are given in Figs. 2(a) and Figs. 2(b), respectively. The receiver structure for our proposed scheme is given in Fig. 3(a). The structure of the SM SAC receiver is simply two balanced detectors connected in parallel. The output of
[FIG. 2.] Structure of the conventional SAC OCDMA. (a) transmitter, (b) receiver. MLS: multi laser source, MZM: Mach-Zehnder modulator, ENC: encoder, DEC: decoder, CDEC: complementary decoder, PD: photodiode.
The purpose of applying spatial multiplexing is to divide the number of overlapping laser signals per spectral bin into two or more groups, where each group is detected by a separate photodiode. Since the beat noise is the resultant of the square law of photo detection, the total number of generated beat signals will be reduced.
In this section, we predict the capacity of our proposed system. In our analysis we follow the same procedure used in .
In our performance analysis we try to find the expressions for the bit error rate (BER) when laser sources are used in SAC OCDMA. However, since there is no analytical expression for the intensity for more than two lasers that vary in phase and polarization, Monte Carlo simulation must be used . The characteristic function of intensity for each spectral bin must be calculated. Using these characteristic functions, an expression for the probability density function can be derived and BER expressions can be found.
In our analysis we consider three different laser source configurations . They are shared multi-laser source, uniformly distributed multi-laser source and controlled multilaser source.
In this case, there is a single centralized multi laser source shared by all users. The central frequencies for the different users for any spectral bin are perfectly aligned (because they come from the same source). However, the phase and polarization angles are random due to the different propagation distances from the centralized source to the users. The phase and polarization angles are assumed to be uniformly distributed in the range [0, 2π]. Fig. 4(a) shows the lasers alignment within a spectral bin in this configuration.
We conducted Monte Carlo simulation to obtain the probability density function (pdf) and the characteristics function for user
The electrical field for a specific realization of phase and polarization
We calculate the empirical distribution of the intensity for 107 different realizations for both phase and polarization. We assume that all the different realizations have the same probability i.e.1/107. The cumulative distribution function can be expressed as:
From the cumulative distribution function, (3), we can find the pdf:
The characteristic function is the Fourier transform of the pdf in (4):
When the number of laser sources is more than five, a good approximation of the characteristic function is obtained from the Gamma pdf instead of the empirical pdf .
Here, each user has its own multi-laser source. The central frequency of each laser for different users will fall within the bin bandwidth (
The characteristic function for each spectral bin is given by :
In the third source configuration, not only are we assuming that each user has its own multi laser source, but that we can control the central frequencies of these laser signals to minimize the beat noise. For any given SAC code there is a maximum number of laser sources
The characteristics function in this case is given by :
Assuming that there is a total number of
We assume that our desired user is first user and is located in the first group. We assume there are
For a specific pattern of
The characteristic functions when the desired user
and the characteristic functions for data “1” are:
The previous calculation of characteristic functions is for a single combination of the data vector
The same applies for Ω
Assuming the number of users sending logical states “0” and “1” obey a binomial distribution, this yields a characteristic function for the desired user sending data “0” for the BD1:
and for BD2:
The same applies for Ω
The electrical outputs of the two balanced detectors are added together to form the final decision statistics of the receiver, which is equivalent to the convolution of the pdfs. To generate the respective pdfs for each characteristic function, a Fourier transform is performed on each of the characteristic functions.
The pdf when the desired user is sending logical state “0”:
and for data “1”:
Using a threshold value γ the BER is calculated from the pdfs by integrating the overlapping tales:
where γ is found numerically.
Firstly, to validate that spatial multiplexing can reduce the beat noise, an arbitrary bin
In order to compare our results with published work, we choose the same operating parameters as in . The data rates are 1.25 Gb/s, 2.5 Gb/s and 10 Gb/s and the optical bandwidth is 30 nm. Two balanced incomplete block design (BIBD) codes are implemented. The first is a code with prime power of 5 (
Figures 6(a) and (b) show the BER versus the number of users at 1.25 Gb/s for the lower and higher cardinality codes, respectively. It can be clearly seen from Fig. 6(a) that the SM SAC outperforms the conventional SAC for all different coherent source configurations. From Fig. 6(a), as an example of the performance improvement, the SM SAC with controlled multi laser source with a standard deviation of 4 GHz for precision of writing the central frequency can support around 25 active users at BER of 10-9 (error free transmission), meanwhile for the same source configuration at the same BER the conventional SAC can only support 10 users. For a precision of 3 Ghz (not shown in the Fig. 6(a)) both SAC and SM SAC supported all the users for a BER of 10-10 , with SM SAC showing better performance than the conventional SAC. Fig. 6(b) shows that the SM SAC will also have higher performance than the conventional SAC for a code with larger weight and higher cardinality. For the uniform multi laser source, the SAC can only support 5 users at BER of 10-9 , while the SM SAC can support 15 users. In the case of the precisely controlled multi laser, we can see for a standard deviation of 0.3 nm of the central frequency the SM SAC can maintain up to 85 active users at BER of 10-12, in the meantime, the conventional SAC can bear just above 65 users at the same BER, a 30% increase.
Figures 7(a) and (b) show the BER versus the active number of users for the same two codes at 2.5 Gb/s, meanwhile Fig. 8 shows the BER versus the number active users for code (
We would like to note that the percentage of improvement obtained by the SM SAC over the conventional SAC depends on the source configuration and the data rate.
The software we used for our simulation is Optisystem. For the simulation we chose the third source configuration, i.e. the precisely controlled multi laser source. We implemented a fourteen user network for both the conventional SAC and SM SAC (two groups), and the network configurations are shown in Figs. 9(a) and (b), respectively. The code used is BIBD code with prime power of 2 (weight=3) multiplexed in the wavelength domain using the technique given in [26, 28]. Table 1 shows the code sequence for the fourteen users.
BIBD wavelength multiplexed code with weight of three
In our design, each transmitter contains a controlled multi laser source. By carefully observing Table 1, we can see that the maximum number of laser sources falling in one spectral bin is three. Since we can control the lasers’ central frequencies, we assigned one of the lasers’ central frequencies to the central frequency of the spectral bin. The other two lasers are placed at 0.2 nm to the right and left of the centralized bin. A visual illustration of the lasers distribution within a given spectral bin is shown in Fig. 10.
The transmitter for both conventional SAC and SM SAC contains three controlled lasers. The default launch power for each laser is 0 dBm. The signals from the lasers are summed up and modulated with the data of a pseudo random bit sequence (PRBS) generator via Mach-Zehnder modulator (MZM) which has an extinction ratio of 30 dB. After modulation, the signals are sent to the network as shown in Figs. 9(a) and (b).
The receiver designs are similar to the designs given in Fig. 2(b) and Fig. 3(a). Fiber Bragg gratings (FBG) filters in reflection are used in the decoder and complementary decoder designs. All the FBGs have 0.6 nm pass bandwidth. The photodiodes for both the conventional SAC and SM SAC receivers are the standard PIN photodiodes. The receiver’s electrical filter is a fourth order Bessel filter with an electrical bandwidth equal to 0.75×data rate.
Figure 11 shows the results for the BER as the number of users is increased from two to fourteen at a data rate of 1.25 Gb/s. It can be seen that both the conventional SAC and SM SAC are able to achieve error free transmission, with some BER improvement on SM SAC compared to conventional SAC for up to eight active users. However, when ten users are active, the conventional SAC transmission is erroneous, with a reported BER of 4.95×10-9 . Meanwhile, SM SAC sustained error free transmission for up to twelve users, and the reported BER was 1.2×10-11 . The eye diagrams for both cases for ten active users are illustrated in Fig. 11, which clearly show the improved quality of the received signal for SM SAC compared to conventional SAC. For a fully populated network (fourteen users in our simulation), both conventional SAC and SM SAC failed to achieve error free transmission. The reported BER for fourteen users for both conventional SAC and SM SAC were 0.6 and 3.49×10-2 , respectively. We would like to note that the very low BER (below 10-20 ) is due to the small number of users (2 to 6 users) where the beat noise is negligible.
The BER at different data rates for ten active users is shown in Fig. 12. SM SAC was able to achieve error free transmission up to 2.5 Gb/s, with a reported BER value of 2.3×10-13 at 2.5 Gb/s. On the other hand, conventional SAC was able to achieve error free transmission at only 155 Mb/s and 622 Mb/s data rates. The eye diagrams at 2.5 Gb/s are given in the figure to qualitatively show the difference in the received signals in both cases. For 10 Gb/s transmission both conventional SAC and SM SAC were unable to retrieve the transmitted data.
By observing Figs. 11 and 12, we can conclude that the obtained results agree with the results obtained via Monte Carlo simulation, and some form of confirmation can be drawn that SM SAC will always outperform conventional SAC at any number of users and at any data rate. To support more active users and to achieve error free transmission at higher data rates, a code with a higher weight (and naturally a larger optical bandwidth) can be used, or by the use of wavelength multiplexed codes.
In conclusion, in this paper we adopted a spatial multiplexing scheme to mitigate the beat noise in coherent source SAC OCDMA network. By applying spatial multiplexing we were able to reduce the beat noise via reducing the total number of generated beat signals per spectral bin. In our analysis we considered three different coherent source configurations. Our results from Monte Carlo simulation showed our proposed scheme outperformed the conventional SAC for all the three different source configurations. A 30% increase in the number of users was reported for a precisely controlled multi laser source at 1.25 Gb/s and reference BER of 10-12 . To back up our results from the Monte Carlo simulation we performed an optical software simulation for fourteen active users for the precisely controlled multi laser source configuration. Results showed that SM SAC was able to achieve error free transmission up to twelve users at a data rate of 1.25 Gb/s. Meanwhile, the conventional SAC scheme could only support eight users at the same data rate. Furthermore, for ten active users the SM SAC was able to maintain error free transmission up to 2.5 Gb/s, while the conventional SAC could only support up to 622 Mb/s.
In order to enable a more active number of users at higher data rates the code space should be divided into more than two groups. However, this will require more optical fibers and photonics devices.