Modeling and Performance Enhancement of Hybrid Fiber Network-PON/DPPM-DWDM-FSO Communications under Atmospheric Turbulence Conditions

A Wavelength Division Multiplexing (WDM) access network using high-speed free-space optical (FSO) communication based on the passive optical networks (PONs) for the distribution link is proposed. In such network architecture, the FSO link can extend the system to areas where an optical fiber link is not feasible, and or provide limited mobility for indoor coverage. The performance of Hybrid Fiber/FSO (HFFSO) network based on digital pulse position modulation (DPPM), for both the indoor and outdoor environments of the optical access network, are compared with the performance of such a network that is based on conventional On-Off Keying Non-Return-to-Zero (OOK-NRZ) modulation using results obtained through computational and analytical modeling. The WDM channels suffer from inter-channel crosstalk, while the HFFSO communication performance in a clear atmosphere is limited by atmospherically induced The impairments, plus the amplified spontaneous emission noise from optical amplification, combining in a potentially problematic way, particularly in the upstream direction, which is investigated here. The results obtained indicate that in a clear atmosphere with a sufficiently high signal to crosstalk ratio the proposed system can achieve a human-safe and high-capacity access network. Dense Wavelength Division Multiplexing (DWDM) has dramatically increased the capacity of optical transmission systems. Its inherent advantages have made it the current favorite multiplexing technology for an optical network, also used on fiber optic backbones and long-distance transmission. The crosstalk due to interband crosstalk for Ultra-Dense WDM systems causes higher noise and degrades the network performance and analyzed the performance of DWDM-PON link that is corrupted crosstalk for Optical Cross-Connect (OXC). Then the analysis of BER with crosstalk was done. Using the equation for crosstalk number of channels was plotted using Matlab. An analysis is carried out to find the amount of crosstalk considering a WDM-FSO over OOK-NRZ and DPPM based OXC. The bit error rate performance degradation due to crosstalk is evaluated for the OXC parameter and number of wavelength per fiber.


Introduction
Over the years, there has been an exponential rise in the demand for broadband applications and Services [1,2]. Optical carrier technologies can be a good solution for the access networks since they potentially offer huge bandwidth [2][3][4][5][6]. Passive Optical Networks (PONs) (i.e. the last mile connection between individual homes and businesses and the public network) and have gradually replaced the copper-based access network technologies. Optical fiber has many advantages (low cost, no electromagnetic interference problems, and less power loss) over the incumbent copper system [7,8]. At the moment, Time Division Multiplexing (TDM/TDMA) systems are the most popular architecture for PONs although they are only suitable for a limited number of optical network units (ONUs) (unless augmented by optical amplification [9] and they typically use power splitter. Wavelength Division Multiplexing (WDM) systems, on other hand, allow more ONUs to be connected at high data rates and assign a distinct pair of dedicated wavelengths to each ONU such that a point-to-point connection is established between the ONU and the Optical Line Terminator (OLT) [1]. The WDM-PON increases the bandwidth and the greater data security that can be offered to the ONUs compared to the (TDM / TDMA) system [1,2,[10][11][12]. One of the popular modulation schemes widely applied in the free-space optical (FSO) communications in Digital Pulse Position Modulation (DPPM). This scheme is well known to be attractive in different (FSO) environments including inter-satellite atmospheric and indoor wireless channels [12]. DPPM has been proposed and intensively investigated for optical fiber systems [2] with the availability of bandwidth-intensive services such as Video On Demand (VOD), Internet Protocol Television (IPTV), IP Telephony and interactive gaming/video conferencing, there has been a rapid rise in bandwidth demand from users [ 10,12]. In response to this increase in bandwidth demand, Wavelength Division Multiplexing (WDM) systems have been investigated and/or deployed for optical fiber, Optical Wireless Communications (OWC), and atmospheric indoor wireless optical network [2]. WDM could also be applied in multiple user access networks, for example, the WDM Passive Optical Network (PON) is generally considered as a good solution to the bandwidth requirements for future access networks, with potential for higher data rate, improved data security and longer reach [1,2]. Dense Wavelength Division Multiplexing (DWDM) operates in the 1528 nm to 1568 nm wavelength range and can combine up to 32 signals on one fiber, 4 channels -8 channels -16 channels or 32 channels DWDM with 200 GHz. Free Space Optical (FSO) communications simply entail transmission of the optical signal through the earth's atmosphere and its subsequent reception. FSO communications have been successfully applied for shortdistance link (up to 4 km) [5]. Relative to fiber systems, FSO communications has the advantages of ease of set-up and technology provision of access in difficult locations, and relatively lower cost (i.e. no purchasing and installing of fiber, especially if it otherwise had to go underground) [13][14][15][16]. FSO communication-based access networks have competitive advantages over RF (or millimeter-wave) systems such as improved security, no spectrum licensing, and faster speed over the short-haul-access [4,5]. Despite the advantages of FSO communications, is faced with considerable challenges such as the effects of atmospheric attenuation and turbulence-induced scintillation, which have severe effects on the propagation field [4,5,7,14,17,18]. A DWDM access network using FSO communications in the distribution link is a realistic proposition since both optical fiber and FSO systems operate using similar optical transmission wavelength and system components [7,10,17,19]. Therefore, the integration of both technologies may yield a cost-effective and reliable hybrid optical access network solution. For long propagation distances, the use of an optical amplifier becomes necessary. However, the optically amplified signal is accompanied by ASE noise which somewhat offsets the performance benefits of the amplifier and complicates performance calculations [20][21][22]. The presence of inter-channel crosstalk in WDM systems is well reported [8,23,24]. However, it will be seen that the turbulent nature of the atmospheric channel in the distribution link of the hybrid optical access network causes fluctuation inter-channel crosstalk effects that significantly exacerbates its negative impact on performance. The probability of crosstalk power exceeding the signal power (either by the turbulent increase of crosstalk or turbulent decrease of signal or both) provides an ultimate performance limit. Experimental work has demonstrated the feasibility of WDM-FSO networks [10,25,26]. Optical Wavelength Division Multiplexing (WDM) networks are very promising due to their large bandwidth, their large flexibility, and the possibility to upgrade the existing optical fiber networks to WDM networks [27]. WDM has already been introduced in commercial systems. All-Optical Cross-Connect, however, has not yet been used for the routing of the signal in any of these commercial systems [1].
One key advantage of DWDM is that the gain region of Erbium-Doped Fiber Amplifiers (EDFA) is also in C-band, which enables all the wavelengths to be amplified to overcome loss over long spans of fiber and high passive losses (e.g. From splitting, multiplexing, etc.). The OXC is an essential network element in a WDM optical network [27]. A number of OXC architectures have been proposed in each of which have its own unique features, strengths, and limitations.

Network (Down / Up) Stream Transmission
The network components as shown in Figs. 1, 2 include a transmitter module which comprises of a laser driver (LD) and laser for optical signal generation, the input message signal (data), PPM modulator (PPM Mod), and a receiver module made up of a photodetector (PD), electrical amplifier and filter (EA) and the integrate and compare circuitry (ICC) for system decision [27]. Thus the system is intensitymodulated and the signal is received by direct detection.

Downstream Transmission:
In the downstream, N separates OLT laser transmit signals belonging to each ONU on a particular wavelength in a point-to-point fashion. In the downstream performance calculations, the same assumption as in the upstream is made for the optical wavelengths, channel spacing, and use of optimal threshold in the OOK scheme.
However, maximum OLT transmits powers are lower (typically 10 dBm) [2,27] to fiber nonlinearity. The downstream architecture is similar to the upstream but the system operation is different. Each wavelength at the OLT has a separate laser source which transmits the signal for the group of ONUs on its wavelength. As shown in fig   1, the signal on each wavelength is split into the number of ONUs on the wavelength and separately encoded with the Optical Orthogonal Code (OOC) for each ONU before being recombined for wavelength multiplexing [27]. The multiplexed signals propagate through the feeder fiber to the remote node for optical amplification and demultiplexed before each wavelength's signal is split into each ONUs signal and further transmitted the FSO link for decoding and reception [27]. The downstream crosstalk arises for the imperfect performance of the demux at the remote node.
Compared to the upstream transmission, there is additional splitter loss in the downstream; this is an optional operational cost that reduces the number of optical sources required at the OLT to the number of wavelengths (N), instead of one per user (i.e. NK) as is obtained in the upstream [27].

Upstream Transmission:
In the upstream, each ONU has a dedicated independent point-to-point optical link to the OLT with a laser of its own specific fixed wavelength. The distribution network (atmospheric channel) conveys the signal from the ONUs to a mux, which combines and transmits them through a single optical feeder fiber to the OLT as shown in Fig 2. At the OLT the demux separates the multiplexed optical signals into constituent wavelengths. Several (WDM/mux-demux) technologies exist [27]. The arrayed waveguide grating (AWG) based devices are very popular, mainly because of their low chromatic dispersion loss, however, production complexity, cost, and temperature-dependent loss variation are drawbacks [1,8,27]. The optical wavelengths are assumed to be in the C band (i.e. around 1550 nm) with channel spacing of 100 GHz [2] on the (ITU-T grid) thus benefiting from the low signal attenuation and developed optical device technology in those range of wavelengths.
Each group of ONUs transmitting on a fixed wavelength uses the same laser transmitters operating at a set central wavelength. Optically encoded signals from the ONUs located at homes, buildings, or kerb are transmitting upstream through a turbulent FSO link to the remote node. The Average optical received power at the OLT photodiode from an ONU on the desired signal wavelength and an ONU on the crosstalk wavelength are respectively written as [18,27]. Each RCL, located at the remote, collects the corresponding incident optical signal and then couples it through a short length of fiber using a fiber collimator as per [20] to the mux. An optical preamplifier of gain G and noise figure NF can be placed either at the remote node output to effectively increase the transmit power of the feeder fiber or at the demux input to help the effective OLT receiver sensitivity. A PIN photodiode with quantum efficiency η is placed after the demux to convert the information-bearing light into an electric signal. An integrate-and-dump receiver is assumed at the decision circuit with electrical bandwidth = ⁄ , where = ⁄ and Rb is the data rate. For the OOK-NRZ assumed here, the Kalman filtering method [27] represents a realistic adaptive approach of achieving a near-optimal threshold for each instantaneous level [27].

Optical amplifier placement:
There are two Cases. Case A is when the optical amplifier is placed at the remote node [27]. Case B is when the optical amplifier is placed at the OLT. In upstream Case A, the ASE noise loss due to feeder fiber attenuation and OLT demux loss, while in upstream Case B, the ASE noise suffers from OLT demux loss only [27]. In the downstream Case A, the ASE noise suffers remote node demux loss, atmospheric attenuation, and beam spreading. Case A and Case B for 20 Km fiber, which is not particularly significant when OSNR is good [27].

Turbulence Channel Modeling
Atmospheric scintillation occurs due to thermally induced refractive index changes of the air along with the optical link, causing rapid fluctuation of signal irradiance at the receiver, reduction in the degree of coherence of the optical signal [27,28], and potentially poor Bit-Error Rate (BER) [2,27].The Gamma-Gamma (GG) distribution is widely used for characterizing the whole range of turbulence effects, i.e., weak, moderate, and strong, not only because closed-form expressions exist but also because of their direct dependence on turbulence parameters and the closeness to experimental results [14,16,18,27,28].
Where ℎ is the attenuation due to atmospheric turbulence for the signal (ℎ ) or interferer (ℎ ), is the effective number of large-scale eddies of the scattering process, is the effective number of small-scale eddies of the scattering process, (۰) is the gamma function. The signal and interferer travel over physically distinct paths in the upstream as written in [27,[28][29][30][31][32].
Where , (ℎ ) and , (ℎ ) are respectively, the signal and interferer GG pdfs ( each with different , 2 ) as written in [2,27,31] R(h si , h i )   In the weak turbulence cases; error floors occur at much lower BER, then range shown, using a signal-to-crosstalk ration of 30 dB. To understand turbulence accentuation of crosstalk considers firstly the (S, turb XT) CASE (interferer with turbulence) and note that turbulent crosstalk sometimes increases its 1 value so that {data 0, crosstalk 1} is greater than {data 1, crosstalk 0} (neglecting receiver noises) [27]. In the non-amplified case in Fig. 3, the (S, turb XT interferer with turbulence case) and the (turb S, XT interferer with no turbulence) can superficially seem at the same, as the instantaneous crosstalk ratio (not the same as CXT) which used the average or turbulence-free values in its definition will have the same statistics in both cases. The difference that is one (S, turbXT) the ratio between the signal power and the noise does not change, while in the other (turb, XT), the ratio between the signal power and noise variesgreatly [27]. In Fig. 4, the same effect is observed when an optical amplifier is placed in the signal path (on the assumption that the optical filtering) provided by WDM or an optical band pass-filter does not reduce the crosstalk power while still being inter-channel of the optical amplifier case is presented in Fig. 4 for a signal to crosstalk ratio of 30 dB.
It takes into account a specific crosstalk rejection by the optical filtering instead [27].

Upstream transmission:
The single crosstalk can be used in situations where a dominant interferer exists (e.g. in some sparsely populated DWDM grids or where particular interferer transmitters are higher powered). Now the average received optical power at the OLT photodiode for the desired signal and an interferer is given, respectively, as equation written in [2. 21, 27-31].
Where , is the crosstalk i.e. additional loss (above ) the interferer has when coupled onto the signal photodiode by the demux. Also can be calculated from [3,14,27].
[ ] 2 8 And can of course be stated separately for the signal and the interferer [27].
L C ‫ـــــ‬ is the coupling loss for the signal and interferer can be calculated from [2,27,29].
‫ـــــ‬ is the ratio of the RCL radius to the radius of the back-propagated fiber mode, X D 4 , Ac= 2 is the spatial coherence area of the incident plane wave .
( . ; 3 5 ⁄ c is the sp ti l coherence r ius, and < ( ) is the modified Bessel function of the first kind and zero-order. At the amplifier output, the ASE Power Spectral Density (PSD) is 0 < 0.5(NFG-1) E.

Downstream Transmission:
The inter-channel crosstalk present here is treated as non-turbulence-accentuated as (setting aside wavelength difference impact on 2 ) it travel on the same path of atmospheric of the signal.
The downstream BER is given by [21,27,31] The average received optical power at the ONU photodiodes for desired signal and interferer are given, respectively, as [21,27,31]: are the OLT transmitter power can used for the electric domain noises [27].

The Calculations Results
Results in terms of required optical power are presented to predict the performance for various scenarios of the hybrid WDM network.   Cn=10^-17m ^ -2/3 Fig. 7 The FSO link length Vs Signal-to-noise-ratio (SNR) at dB.

FSO Link Performance under the Effect of Atmospheric Turbulence.
Atmospheric turbulence is known to cause signal fading in the channel. There are many different types of modulation schemes that are suitable for optical wireless communication systems. The effect of atmospheric turbulence-induced fading on the following techniques: On-Off Keying (OOK), Pulse Position Modulation (PPM), and phase-shift keying pre-modulated subcarrier intensity modulation. The classical modulation technique used for FSO is OOK [28]. This is primarily because of the simplicity of its design and implementation. The PPM requires no adaptive threshold and is predominantly used for deep space free-space optical communication links because of its enhanced power efficiency compared to the OOK signaling.

DPSK-Modulated Subcarrier
The DPSK pre-modulated SIM-FSO is demodulated by comparing the phase of the received signal in any signaling interval (with the phase of the signal received in the preceding signaling interval [28] as shown in Fig. 8. The demodulation of DPSKbased SIM-FSO is feasible during atmospheric turbulence because the turbulence coherence time, which is of the order of milliseconds, is far greater than the typical duration of two consecutive data symbols. This implies that the properties of the channels are fixed during a minimum of two symbol durations are prerequisites for non-coherent demodulation of the DPSK subcarrier signal.
The conditional BER of the DPSK pre-modulated subcarrier is given by [28].

. (( . ( )) 14
In the presence of scintillation, the following unconditional BER is derived using the Gauss-Hermite quadrature integration approximation as written in [28].  Here in Fig. 9, the BER of SIM-FSO based on different modulation techniques on the subcarrier is compared at a scintillation level of . The performance in a turbulence-free channel is included in the figure for the estimation of turbulenceinduced fading penalty. The figure shows clearly the performance superiority of BPSK-modulated SIM in terms of the amount of SNR required to achieve a given BER Due to atmospheric turbulence-induced channel fading, a BPSK pre-modulated SIM-FSO system will incur a power penalty of ~ 5 dB at a BER of ; ; the penalty rises to ~ 10 dB when the error performance level is raised to a BER of ; . This penalty is higher for other modulation techniques as shown in Fig. 9.

On-Off Keying
OOK is the dominant modulation scheme employed in commercial terrestrial wireless optical communication systems. This is primarily due to its simplicity and resilience to the innate nonlinearities of the laser and the external modulator. OOK can use either non-return-to-zero (NRZ) or return-to-zero (RZ) pulse formats. In NRZ-OOK, an optical pulse of peak power represents igit l sym ol " "while the transmission of an optical pulse of peak power represents igit l sym ol " ".

Pulse Position Modulation Scheme
In line-of-sight for the OWC links where the requirement for the bandwidth is not of major concern, PPM with its significantly better power efficiency seems to be the most attractive option for a range of applications PPM is an orthogonal modulation technique and a member of the pulse modulation family (see Fig. 11). The PPM modulation technique improves the power efficiency of OOK but at the expense of an increased bandwidth requirement and greater complexity. To achieve the same throughput as OOK, PPM slot duration s, is shorter than the OOK bit duration b by a factor L/M that is [28].

18
The transmit pulse shape for L-PPM is given by [28]. Hence, the PPM symbol sequence is given by [28].   Here in Fig. 12, the average optical power requirements and bandwidth requirements of OOK (NRZ and RZ), PPM, DPIM, and DH-PIM generated using Matlab. Figure   12 shows the trade-off between the bandwidth requirements and average power requirements. For OOK-RZ, the power requirements decrease with the duty cycle but the bandwidth increases. For PPM, DPIM, DH-PIM, average optical power requirements decrease as (average symbol length (L)) increase, however, the bandwidth requirements increase with L.

Log-Normal Turbulence Model
In describing the pdf of the irradiance fluctuation in a turbulence atmosphere, the beam is first represented by ̅ lectric field as shown in Fig. 13  The log-normal pdf is plotted in Fig. 13 for different values of log-irradiance variance of 1 2 . As the value of 1 2 increases, the distribution becomes more skewed with tails in the infinity direction there is fluctuation of the irradiance.

Gamma-Gamma Turbulence Model
There is fluctuation of light radiation traversing a turbulent atmosphere is assumed to consist at small-scale (scattering) and large-scale (refraction) effects as shown in Fig. 14 as written in [27,31]
The plot shows that as the turbulence increases from the weak to the strong regime, the distribution spreads out more, with an increase in the range of possible values of the irradiance.

Analysis of the Atmospheric Turbulence
We analyze laser transfer turbulent atmosphere, spot scale, offset angle and light intensity fluctuation are related.

Fig. 15 FSO link length (L) vs Rad (beam divergence).
When the distance increases to 10 km, the beam divergence increase to ( rad. This system type would be required to have greater beam-widths to compensate for any motions due to buildings way. For systems with automatic pointing and tracking, the transmit divergence angle can be narrowed sufficiently with mr as shown in Fig. 15. Here in Fig. 16, the Cn = ( ;9 ;2 3 ), L =10 km. Attenuation is increased with longer distances. Here in Fig. 17, the Cn=8 Here in Fig. 18, the Cn is ( ;9 ;2 3 ), Attenuation is high when Cn is increase. Refractive Index Structure (Cn) increase, ur ulence Intensity incre se as shown in Fig. 20. In fiber-optic communications, wavelength-division multiplexing (WDM) is a technology which multiplexes multiple optical carrier signals on a single optical fiber by using different wavelengths (colors) of laser light to carry different signals [32][33][34][35][36][37][38][39][40][41][42]. This allows for a multiplication in capacity, in addition to enabling bidirectional communications over one strand of fiber. This is a form of frequency division multiplexing (FDM) but is commonly called wavelength division multiplexing [32].

Cn , Here Cn=
A WDM system uses a multiplexer at the transmitter to join the signals together, and a demultiplexer at the receiver to split them apart as shown in Fig. 21.

DWDM Systems:
Dense wavelength division multiplexing, or DWDM for short, refers originally to optical signals multiplexed within the 1550 nm band to leverage the capabilities (and cost) of erbium-doped fiber amplifiers (EDFAs) (see Fig. 22), which are effective for wavelengths between approximately 1525-1565 nm (C band), or 1570-1610 nm (L band) [33]. EDFAs were originally developed to replace SONET/SDH opticalelectrical-optical (OEO) regenerators, which they have made practically obsolete.
EDFAs can amplify any optical signal in their operating range, regardless of the modulated bit rate. In terms of multi-wavelength signals, so long as the EDFA has enough pump energy available to it, it can amplify as many optical signals as can be multiplexed into its amplification band (though signal densities are limited by choice of modulation format) [34][35][36][37][38][39]. EDFAs allow a single-channel optical link to be upgraded in bit rate by replacing only equipment at the ends of the link while retaining the existing EDFA or series of EDFAs through a long haul route.
Furthermore, single-wavelength links using EDFAs can similarly be upgraded to WDM links at a reasonable cost. The EDFAs cost is thus leveraged across as many channels as can be multiplexed into the 1550 nm band [40][41][42].

Limitations of WDM:
Crosstalk will be one of the major limitations for the introduction of OXC in alloptical networks as shown in Fig. 23. Crosstalk occurs in devices that filter and separate wavelengths [35,[39][40][41][42][43][44][45][46]. The crosstalk within the same wavelength slot is called intra-band crosstalk.
Moreover, In-band crosstalk can be divided into coherent crosstalk and incoherent crosstalk. Coherent crosstalk is that whose phase is correlated with the signal considered and incoherent crosstalk, whose phase is not correlated with the signal. On the other hand, Inter-band crosstalk is crosstalk situated in wavelengths outside the channel slot (wavelengths outside the optical bandwidth) and considered as a less severe phenomenon as shown in Fig. 24. However, in the DWDM technique this can be very predominant and degrades the network performance severely. The different cl sses of crosst lk re cl rifie in Fig. 25.

b) Analysis of Bit Error Rate without Crosstalk:
The BER can be calculated with and without Crosstalk using some equations. In this section, the ideal case is shown. So Crosstalk is taken to be zero. The equation for crosstalk is given in the next section. BER is the number of bit errors that occur within the space of one second. This measurement is one of the prime considerations in determining signal quality. The higher the data transmission rate the greater the standard.
BER can be calculated with and without Crosstalk using some equations.
Here Q is a function proportional to the receiver signal-to-noise ratio (SNR).
It is expressed as [37].  The resulting graph Fig. 26 of the BER vs. the input power has plotted above. We have plotted this graph for three different bandwidths. It is seen that the BER increases with an increase in the input power. It is also shown that to use more bandwidth we need more input power. Here in Fig. 27, we show that BER increase for increasing crosstalk. For using more input power we get more crosstalk. For example, when 1.8 dBm is used as input power, the crosstalk is and for 9.1dBm input power, crosstalk is. At the same time, the BER is also increasing.
For using more input power we get more crosstalk. Fig. 28 shows the crosstalk plotted against the number of channel in a WDM system. Here we calculated crosstalk from the equation [29,30] as written in [35][36][37][38][39].  Where, M= number of hop.
b= bit ratio of signal peak power.
Ps= input power. ε = effective adjacent and effective non-adjacent.
N= number of channels.
X= switch. It can be said that if we increase the number of hop then crosstalk also increases.
Values taken for Fig. 28 Fig. 29 The number of channels and hops for related crosstalk.
For this graph in Fig. 29, we can find out the number of channels and hops for related crosstalk. For example for power penalty 8.1dB we got the corresponding crosstalk to be -40dB which is -. From the above graph, we can find combinations of hops and channels. Here, the combinations are : Hoops Channels   For this topology in Fig. 31, we assumed -30 dB input power and increased it significantly. the graph shows us that when input power is getting greater, the crosstalk is increasing slightly.    This curve from Fig. 33 is calculated from the BER curve with crosstalk. The difference between BER with crosstalk and BER without crosstalk at the BER of ; . The result shows that the power penalty increases with decreasing channel spacing.  The power penalty can be defined as the increase in signal power required (in dB) to maintain the same BER in the presence of impairments.

Conclusion and Future works:
We analyzed a hybrid fiber and DWDM-FSO/PON network and the effects of turbulence-accentuated interchannel crosstalk, it could be seen that DPPM systems required lower optical power compared to the OOK systems. It can be deduced from this analysis the interchannel crosstalk,turbulence-induced scintillation, and ASE noises are dominant causes of system degradation, especially in the upstream transmission, causing the BER to increase by several orders of magnitude and also we have used some basic equations to optimize the relation between hoops and channels.
No new equation was derived or used to form this relationship. The figures were plotted manually using the graphs plotted with the basic equations of BER and Crosstalk in Matlab software. At the first, a graph for BER vs. the input power was plotted using the BER equation. Then a graph of crosstalk vs. number of channels was plotted for a different number of hops. From this graph, the power penalty was found out. This power penalty was used to plot a graph of the power penalty vs. the crosstalk. Work can be carried out to evaluate the performance of a WDM system with bi-directional OXC and find the limitations due to crosstalk and optimum system parameters.