Introduction
The growing popularity of the internet and the need for the simultaneous use of network services by multiple subscribers has brought about the need for network providers to provide high and stable bandwidths across multiple channels [1,2]. To satisfy this increasing demand for data usage, technologies based on optical communications (such as passive optical networks (PONs)) have been proposed due to the advantages they offer over radio frequency based communication systems such as high speeds and large bandwidths [3]. A variant of the PON, the wavelength-division multiplexing (WDM) PON; where each subscriber is assigned a different channel/wavelength, is seen as the most promising choice for a reliable access network [4]. A WDM PON has attributes such as high security, sufficient capacity (able to satisfy bandwidth demands) and being easily upgradeable but its high equipment cost and complicated operation (especially in the access network) makes its practical deployment problematic. Methods involving the use of low-cost transmitters have been proposed to alleviate this problem [5–7]. To realize multiplexing and demultiplexing in WDM systems, it is common to use devices based on arrayed waveguide grating (AWG) due to their low chromatic dispersion. However, due to the cost and intricacy of AWG-based devices, other multiplexing techniques such as free-space diffraction-grating have been proposed [8].
Optical fiber communication links (combined with dense WDM) have been used to obtain transmission speeds greater than 1 Tb/s (in the network core) but the high setup cost of fiber in the access region and lack of flexibility is currently diverting attention to free-space optical (FSO) communication systems. FSO communication systems are increasingly gaining recognition due to the advantages they offer such as low cost, simplicity, immunity to electromagnetic interference, flexibility and no licensing requirements [3,9–11]. Thermal inhomogeneity, due to refractive index changes, in the atmosphere results in atmospheric turbulence [11,12] which causes fluctuations in the transmitted optical signal power and negatively affects the performance of FSO communication systems [11,13]. The effect of atmospheric turbulence becomes even more severe in long distance communication [14,15].
An optical amplifier (OA) has the ability to adjust its gain to new power levels by providing higher gains to lower input powers and lower gain to higher input powers [16]. This attribute of the OA has been shown in an earlier work to improve the system bit error rate (BER) in a turbulent atmosphere with unknown channel state information when a non-adaptive decision threshold is used at the receiver [16]. OAs can naturally be integrated with WDM systems since a single OA can concurrently amplify signals at different wavelengths within the gain region [17]. In choosing a gain flat (at least in the small signal regime) OA for FSO communication system, it is important to ensure the gain dynamics are fast enough to track fluctuations in the atmosphere. While the gain dynamics in both erbium-doped fiber amplifiers (EDFAs) and semiconductor OAs (SOAs) are fast enough to track the atmospheric turbulence fluctuations, EDFAs are preferable for WDM systems since they do not introduce gain crosstalk (from cross-gain modulation) into the system. Furthermore to continue to benefit from the turbulence mitigation, while avoiding gain crosstalk, it is necessary to ensure that individual channels saturate independently. This will be harder to achieve with an SOA than with an EDFA [18–20]. Crosstalk occurs in communication systems either due to optical component imperfections or power transmission between different channels caused by nonlinear effects [21]. It is particularly common in WDM networks due to the presence of multiple wavelengths and the effect is further exacerbated in FSO communication systems due to atmospheric turbulence [22]. In the upstream of WDM FSO communication systems, where the desired and crosstalk signals are assumed to follow independent paths, the fluctuations caused by atmospheric turbulence in both the desired and crosstalk signals poses a major limitation to system performance [8].
In Ref. [23], a 32×10 Gbps WDM FSO link limited by snow and rain weather was proposed and compared with existing WDM FSO links while a WDM FSO link employing multibeam and single beam technologies were compared in Ref. [24] under hazy and clear weather conditions. The power efficiency of different single-line and mixed-line rates were compared in Ref. [25] where an investigation was also carried out to ascertain the trade-off between power and spectral efficiency in a WDM network. In Ref. [26], the performance of M-ary quadrature amplitude modulation WDM FSO link limited by atmospheric turbulence and optical nonlinearity was studied and a WDM FSO link employing optical amplifiers (with hybrid arrangement) is shown in Ref. [27] to improve and increase the received signal power and maximum achievable link length respectively. The impact of interchannel crosstalk in non-amplified and amplified FSO communication systems was investigated in Refs. [8,28]. In Ref. [8] where the on–off keying (OOK) modulation format was used, an adaptive decision thresholding scheme was assumed at the receiver and the OAs used in Refs. [8] and [28] were only operated in the unsaturated gain regime. In this paper, a direct detection scheme with non-return-to-zero OOK modulation is considered and a Monte Carlo (MC) simulation approach is also used to analyze the upstream of WDM FSO communication systems using adaptive and non-adaptive decision thresholding schemes. For amplified systems, results are obtained for instances where the OA gains are either in the fixed or saturated gain regime. Additionally, results are also shown for instances where a power control algorithm (PCA) ensures that at any receiving instant, the same turbulence-free powers (equal to the power received from the farthest transmitter) are received by both receiving lenses. In a more general sense (i.e., for any WDM system where it is assumed that all the receiving lenses are situated at the same location), the PCA is actualised by turning down the powers of all the transmitters (except the farthest transmitter; which is used as reference).
After this introductory part, the statistical model used to describe atmospheric turbulence-induced fading in the WDM FSO communication system is described in Section 2. Section 3 describes the upstream transmission of a WDM FSO communication system. Section 4 describes the WDM FSO communication system modeling and BER analysis. The results of the MC simulations for the WDM FSO communication system are presented in Section 5 and a conclusion is provided in Section 6.
Channel statistics
where represents the parameter used to describe the varying atmospheric turbulence-induced channel gain (or loss). The variance of the natural logarithm of the irradiance is given as [11]
where represents the Rytov variance used to characterize the different atmospheric turbulence regimes and it is given as [29]
where represents the refractive index structure parameter, represents the length of the FSO link and represents the optical wave number where represents the optical wavelength.
System configuration
A practical WDM FSO system is made up of many wavelengths, and signals on each wavelength is limited by the contribution of crosstalk from signals on all other wavelengths. It is however noteworthy that crosstalk effects from adjacent wavelengths are more critical than those from further separated wavelengths. Therefore, two WDM channels are considered in this paper to generate the fundamental understanding of how such a system operates and can be modeled. Clearly the multi-wavelength case is more complex but basic understanding of how it will work can come from this underpinning. Note that a single crosstalk channel (two WDM channels) is applicable where a worst-case performance analysis (combining multiple crosstalk signals into a single wavelength and modeling such as a single crosstalk) is carried out. Figure 1 shows a WDM FSO communication system model where both TX 1 and TX 2 can transmit either desired or crosstalk signals (with the two wavelengths assumed to have a channel spacing of 100 GHz on the ITU-T grid [32]). This means that at RX 1, TX1 and TX 2 are seen as the desired and crosstalk transmitter respectively and at RX 2, TX 2 and TX 1 are seen as the desired and crosstalk transmitter respectively. In Fig. 1, both the desired and crosstalk signals are sent through lenses into the atmosphere. Note that while propagating through the atmospheric channel, the desired and crosstalk signal paths are assumed (with proper alignment) to be independent of each other such that they do not interact either in the atmosphere or at the receiving lenses. After both signals are collected by their respective receiving lenses (which are assumed to be at the same location, e.g., rooftop), they are multiplexed and amplified before onward transmission through a feeder fiber. At the receiving end, the signals are demultiplexed and received by their respective receivers. Interchannel crosstalk (the crosstalk type considered in this paper) is caused by imperfections in the demultiplexer and it is more severe in WDM FSO communication systems due to the fluctuations in the crosstalk signal [8,28].
System modeling and BER analysis
For computational convenience, a MC simulation technique is used to model the WDM FSO communication system. With the MC simulation approach, the BER analysis (with respect to the ‘desired signal’ receiver) is first carried out for a random sample after which averaging takes place over all the samples to obtain the average BER. By assuming that the desired and crosstalk signals (each transmitted with signal power for ) are propagated in a clear atmosphere, the total loss in the FSO link where represents the LN random variable describing the fluctuations due to atmospheric turbulence and ; which represents the turbulence-free fixed path loss () is given as [28]
where represents the receiving lens diameter and represents the beam diameter due to diffraction alone where represents the transmitter beam divergence angle. represents the atmospheric attenuation in the FSO link where represents the atmospheric attenuation factor. The signal power at the receiving lens . The multiplexed signals are amplified by an OA with gain and amplified spontaneous emission (ASE) power spectral density (PSD) , where is the noise figure, is the Planck constant and is the frequency of the optical carrier. The instantaneous optical signal power at the OA input is implicitly related to the OA gain as shown below [22]
where and represents the internal saturation power and the small signal gain of the OA respectively. At the decision circuit, the mean desired signal current level at the sampling instant is given as
where the desired signal power in a ONE . represents the desired signal power at the input of the desired signal receiving lens (), represents the feeder fiber loss, represents the extinction ratio and the desired signal power in a ZERO . The responsivity where is the quantum efficiency and is the electronic charge. Also, the mean crosstalk signal current level at the sampling instant is given as
where the crosstalk signal power in a ONE , where represents the crosstalk signal power at the input of the crosstalk signal receiving lens (), represents the extra loss experienced when the demultiplexer couples the crosstalk signal with the desired signal photodiode and the crosstalk signal power in a ZERO . The total noise current variance is given as [8]
where the signal-spontaneous beat noise is given as
where the receiver noise equivalent bandwidth, and is the bit rate. The crosstalk-spontaneous beat noise is given as
where represents the ASE PSD at the signal receiver (but at or near the crosstalk wavelength). The spontaneous-spontaneous beat noise is given as
where is the number of polarization states parameter and is the optical band pass filter (OBPF) bandwidth. The ASE shot noise is given as
and the total shot noise (due to the desired and crosstalk signals) is given as
The instanteneous BER (i.e., obtained after a single MC iteration) is given as [16]
where represents the decision thresholding scheme used at the receiver. For an adaptive decision threshold, it is given as
and for a non-adaptive decision threshold (a fixed value equal to the long-term average of the desired and crosstalk signal powers), it is given as
where represents the trials count, represents the total number of trials used for the MC simulation, the desired signal power at the receiver and the crosstalk signal power at the receiver . The average BER is then given as
Results and discussion
The parameters used for the MC simulations are shown in Table 1. It is assumed that the saturated operation integrates the effect of ASE noise, responds freely and uses complete saturation characteristics. Also, a non-saturable OA () is called a fixed gain OA and a saturable OA ( = 5 dBm) is called a saturated gain OA. A sensitivity of -23 dBm analogous to a BER of is used to calculate the receiver thermal noise current (i.e., A) [13]. Note that all the transmitters and receivers used in this analysis are assumed to have the same beam divergence angle and lens diameter respectively. The desired signal transmitting lens is assumed to be pointed directly at and the crosstalk signal transmitting lens is assumed to be pointed directly at . For brevity sake, the desired signal is referred to as ‘signal’ and the crosstalk signal is referred to as ‘crosstalk’. Results are obtained for the weak ( = 10−15 m−2/3) turbulence regime.
The WDM FSO communication systems considered includes non-amplified systems with an adaptive decision threshold (NOAADT), non-amplified systems with a non-adaptive decision threshold (NOANADT), fixed gain amplified systems with an adaptive decision threshold (FOAADT), fixed gain amplified systems with a non-adaptive decision threshold (FOANADT) and saturated gain amplified systems with a non-adaptive decision threshold (SOANADT).
Tab.1 Parameters used for the simulations |
| parameter | symbol | value |
|---|---|---|
| desired signal wavelength | 1550.12 nm | |
| crosstalk signal wavelength | 1550.92 nm | |
| bit rate | 2.5 Gb/s | |
| OBPF bandwidth | 76 GHz | |
| noise figure | 5 dB | |
| quantum efficiency | 0.8 | |
| extinction ratio | 10 dB | |
| transmitted optical power (maximum permitted) | 10 dBm | |
| OA small signal gain | 25 dB | |
| feeder fiber length | 20 km | |
| feeder fiber loss | 0.2 dB/km | |
| atmospheric channel loss | 0.2 dB/km (clear air) | |
| receiving lens diameter | 4 cm | |
| beam divergence angle | 1 mrad |
In all cases considered, results are obtained for instances where and are only affected by and respectively. Since the feeder fiber length is assumed fixed, any reference to link lengths refers to the lengths of the FSO link. Note that and represents the length of the signal and crosstalk links relative to the positions of and (both at 0 km). For instance, longer and mean lower signal and crosstalk powers respectively.
Figure 2 shows the BER curves for different WDM FSO communication systems when = 15 dB. The BER curves are obtained for instances when = . In Fig. 2(a) where a PCA is not applied, the NOAADT, NOANADT, FOAADT, FOANADT and SOANADT are able to achieve a BER of at 0.82 km, 0.6 km,>2 km, 0.82 km and 0.87 km respectively. In Fig. 2(b) where a PCA is applied, the NOAADT, NOANADT, FOAADT, FOANADT and SOANADT are also able to achieve a BER of at 0.82 km, 0.6 km,>2 km, 0.8 km and 0.91 km respectively. As expected, Figs. 2a and 2b shows that the PCA has no significant impact on system performance when the signal and crosstalk link lengths are always equal.
Figure 3 shows the average BER values obtained without a PCA for different and when = 30 dB. The benefit of including an amplifier in a WDM FSO communication system is highlighted by comparing the systems with an adaptive decision threshold (i.e., NOAADT and FOAADT). In the FOAADT, a BER of less than is attainable when and is 2 km compared to the NOAADT where BER values higher than are obtained for the same link length. Also, a BER of less than is always achievable with the FOAADT when and is about 2 km and more than 0.1 km respectively. This is a huge improvement on the NOAADT where BER values less than can only always be achieved when is less than 0.5 km.
For the systems with a non-adaptive decision threshold (NOANADT, FOANADT and SOANADT), amplification is also advantageous and has more significant effect on system performance (especially for turbulence mitigation) when the OA is operated in the saturation regime. For instance, among the three systems, the longest link lengths achieving a BER of (i.e., 1 km and = 2 km) were obtained with the SOANADT. This shows the importance of using a saturated OA with a non-adaptive decision threshold. For any particular , the system performance is naturally expected to improve as increases (i.e., lower crosstalk power). However some instances in Fig. 3 show a reduction in system performance as increases. This can be attributed to an increase in atmospheric turbulence effects due to longer link lengths. In other words, while the crosstalk adversely affects the performance of WDM FSO communication systems, the system performance also largely depends on the turbulent state of the atmosphere.
Figures 4 shows the capability of various WDM FSO communication systems (with = 30 dB and target BER= 10−12) when and are varied. In Fig. 4, 0 m indicates that the transmitter is placed just in front of the receiver and 2000 m indicates that the transmitter is placed at a distance of 2000 m from the receiver. Note that when = 0 m and = 2000 m, the crosstalk signal is almost negligible and when = 2000 m and = 0 m, the desired signal is almost negligible. Also, the shaded areas in Fig. 4 show the link lengths at which the target BER is met. In the NOAADT shown in Fig. 4(a) where a PCA is not applied and the target BER is met when <880 m and >80 m. When <80 m, a <620 m is required to achieve the target BER. When a PCA is applied in Fig. 4(b), the target BER is met when <640 m and <960 m. While the target BER is also met at other link lengths (<880 m and <880 m) in Fig. 4(b), the target BER is not met when >1040 m for all considered. This is because the PCA ensures that even when = 0 m (desired signal transmitter placed just in front of the receiver) and >1040 m (crosstalk signal transmitter placed at a link length>1040 m from the receiver), the received signal power is set to the received crosstalk power, leading to errors. In the NOANADT shown in Fig. 4(c) where a PCA is not applied and the target BER is met when <560 m for all considered. As expected, this performance is lower than the NOAADT performance shown in Fig. 4(a) due to the non-adaptive decision threshold used in Fig. 4(c). When a PCA is applied in Fig. 4(d), the target BER is met when <400 m and <880 m. The target BER is also met at other link lengths (<120 m and <960 m). The errors observed in Fig. 4(b) due to the PCA are also observed in Fig. 4(d) where the target BER is not met when >960 m for all considered. Compared to Fig. 4(a), the advantage of amplification is observed in the FOAADT shown in Fig. 4(e) where a PCA is not applied. In Fig. 4(e), the target BER is met when >160 m for all considered. Also, when <80 m, the target BER is met when <880 m. In contrast to Figs. 4(b) and 4(b) where the PCA limited the system performance, the target BER is met for all and considered when a PCA is applied in Fig. 4(f). This shows that amplification is needed for the PCA to have a beneficial impact on system performance. In the FOANADT shown in Fig. 4(g) where a PCA is not applied and the target BER is met when <640 m for all considered. Also, the target BER is met when <800 m and >80 m. When a PCA is applied in Fig. 4(h), the target BER is also met when <640 m for all Dxt considered but compared to Fig. 4(g), Fig. 4(h) shows an increased performance when = 0 m and a reduced performance when = 2000 m. This means that the PCA becomes less beneficial with increased link lengths. The benefit of using a gain saturated amplifier for turbulence mitigation is observed in the SOANADT shown in Fig. 4(i) where a PCA is not applied. Compared to the NOAADT (where the target BER is not met at >880 m for all considered), improved system performance is observed in Fig. 4(i) where the target BER is met at = 1040 m and = 2000 m. When a PCA is applied in Fig. 4(j), an increased performance is observed at reduced and a reduced performance is noticed at increased . These results align with results in Fig. 4(h) and it further proves that while the PCA benefits amplified system, it would impair system performance with increased link lengths.
Fig.4 Capability of WDM FSO communication systems ( = 30 dB and target BER= 10-12). (a) NOAADT, no PCA; (b) NOAADT, with PCA; (c) NOANADT, no PCA;(d) NOANADT, with PCA; (e) FOAADT, no PCA; (f) FOAADT, with PCA; (g) FOANADT, no PCA; (h) FOANADT, with PCA; (i) SOANADT, no PCA; (j) SOANADT, with PCA |
Conclusion
This paper examined the performance of a WDM FSO communication system in a turbulent atmosphere by applying MC simulation techniques. Results obtained in this paper showed that even when the crosstalk power is very small compared to the signal power, the fluctuations in the crosstalk due to atmospheric turbulence may have an adverse effect on system performance. Results obtained also show that amplification is needed for the PCA to have a beneficial impact on system performance. In fact, the PCA limits system performance in non-amplified systems. Also, the SOANADT performed better than the NOAADT. This is because the OA in the SOANADT is well driven into the saturation regime (due to the combination of the signal and crosstalk powers at the OA input) thereby elaborating the advantage of using a non-adaptive decision threshold. Lastly, even though the use of an adaptive decision threshold with optical amplification has once again proved to give the best results in FSO communication systems, the use of a saturated gain OA with a non-adaptive decision threshold has the capacity to provide acceptable performances for short distance communication (i.e.,<2 km) when the OA input power is high enough. However, care has to be taken not to overload the receiver.