Performance Analysis of Crosstalk Subcarrier Multiplexing and Wave Division Multiplexing in Optical Communication System

In traditional optical communication, duplexity is achieved by using two fibers, each having a transmitter and a receiver. Economically, bidirectional wavelength division multiplexing (WDM) transmission systems utilizing a single fiber will be more attractive not only reducing the use of the fiber by a factor of two , but also the number of components. Duplex transmissions over a single fiber can double the capacity of an installed unidirectional link. The idea of this paper is to study another approach using the subcarrier multiplexing (SCM)-based optical network and evaluate the physical transmission quality of analog and digital signal using SCM approach and the characteristic of fiber nonlinear crosstalk such as stimulated Raman scattering, Cross phase modulation and four-wave mixing in the SCM externally modulation optical link. A suitable bandwidth of 890 – 950 MHz is selected for subcarriers and channel bandwidth of 200 KHz and carrier. By measuring the optical bit interference (OBI) performance limitations of the subcarrier multiplexing WDM optical transmission system is investigated. The OBI for 10 channels for input power 1 dB is -40 dB whereas for 110 channels the OBI is -20 dB separation of 250 KHz are considered.

width and high optical power that is used to carry data over long distance. The light is then coupled into the transmission channel, the optical fiber cable, where most of the dispersion and attenuation takes place [5]. The receiver block which is the last part of the system converts the optical signal back into the replica of the electrical signal using the Avalanche photodiode (APD) or PIN-type photodiode then to the amplification stage before reaching the end user [9][10][11][12].

3) Wavelength Division Multiplexing (WDM) System
WDM as shown in Figure 2, [1,[13][14][15][16] combines multiple optical TDM data streams onto one fiber through the use of multiple wavelengths of light. Each individual TDM data stream is sent over an individual laser transmitting a unique wavelength of light. Wavelength division multiplexing was used with only two wavelengths 1310 nm and 1550 nm. However, this was suitable only for limited applications for example; applications in which analog optical cable television signals co-existed with digital optical telecommunication signals. WDM takes advantage of the fact that different wavelengths of light can be transmitted over a single fiber simultaneously [17,18].

5) Fiber Nonlinear Crosstalk
In addition to transmitter and receiver noises in optical systems, fiber nonlinear crosstalk can significantly degrade the transmission system performance. There are two basic fiber nonlinear mechanisms [1, 4, and 15]. The first mechanism that causes fiber nonlinearities is the scattering phenomena, which produces Stimulated Raman Scattering. The second mechanism arises from the refractive index of glass being dependent on the optical power going through the material. This results in producing Cross Phase Modulation (XPM) and FWM crosstalk [13][14][15][16].
As for the crosstalk interaction between pump channel and signal channel in the SCM/WDM system, assuming pump channel has a shorter wavelength than probe channel, the most significant crosstalk term is due to the SRS interaction between pump channel optical carrier and probe channel subcarriers [18][19][20][26][27][28][29][30].
A formal approach to determining SRS crosstalk levels is to solve the coupled propagation equations for the optical intensity I at wavelengths λ1 and λ2 [10,15].

( ) ( )
Where z is the distance along the fiber, g is the Raman gain (loss) coefficient and ν is the group velocity of each channel in the fiber. Assuming λ2 < λ1 (channel 2 is designated as pump channel and channel 1 as probe channel).
By neglecting the SRS term, on the right hand side Eq. 1 of and solving for ; then substituting into Eq.2 and solving for are gets [10,15]: | is the group velocity mismatch between the pump and signal channels and A similar approach can be used to solve for by neglecting the SRS term, on the right hand side of Eq.2 and solving for , then substituting into Eq.1 to get [10,15] (

6) Analysis of SCM in Presence of OBI
There are M numbers of subcarrier multiplexing (SCM) in a given optical channel, having the same average power. Each of these fields can be represented by [11,12]: Where the intensity modulation by an RF is signal of center frequency and can be represented by [11][12][13][14][15]: Where m(t) is NRZ data signal with bit period .
The total field in an optical channel is the sum of M fields and can be represented as [11,20]: The electric field at the output of the fiber is given by: Where α is the fiber attenuation coefficient, L is the fiber length and ( ) represents the fiber impulse response.
The photodetector (PD) converts this field into an electrical signal proportional to the field intensity.
Here ( ) contributes nonzero beat interference terms. The output of the PD is passed through a pre-amplifier followed by a band pass filter. If any of the spectral components of ( ) falls within the bandwidth of any of the M users BPF, it will cause OBI.
Where represents the required subcarrier frequency.
The power spectrum of the i-th subscriber's signal component can be expressed as: Using band pass filter, output signal power of the required sub-carrier can be calculated as [11][12][13][14][15]: Where B is the specified bandwidth of the subcarrier or bandwidth of the BPF.
This (cross) is the source of the OBI.

7) Four-Wave Mixing Crosstalk in SCM Externally Modulated Optical Link
Four-wave mixing crosstalk is one of the major limiting factors in SCM/WDM optical fiber communications systems that use narrow channel spacing, low chromatic dispersion and high optical channel power. The time-averaged optical power ( ) through the FWM process for the frequency component fijk is Written in as [22].
where is the third-order nonlinear susceptibility, (which is related to nonlinear refractive ( ) The generated wave efficiency η, with respect to phase mismatch ∆βL [10,22]  The time-average optical power generated through the FWM process can be modified in terms of generated wave efficiency as [10,22] ( ) ( ) ( ) Using D = 6 (none of frequencies are the same).

8) Dual Parallel Linearized External Modulators
The basic configuration of optical dual parallel linearization technique is shown below in figure [5]. Figure 5: Dual parallel MZ modulator in [6].
By providing less optical power and higher RF drive power to the secondary modulator, the secondary modulator has higher OMI and greater distortion. By providing more optical power to the primary MZ modulator, the third-order distortion products created in the secondary modulator can be made to cancel the distortion products from the primary modulator with a small cancellation of the fundamental signal, result with MATLAB in fig [14][15][16].
where A is the splitting ratio of the input power divider and B is the ratio of RF drive power. Assuming V (t) is a multi-sinusoidal signal, using trigonometric identities and Bessel functions, the amplitude of the fundamental carrier with frequency can be expressed as [10]:

10) Discussion
The number of channels can be increased without significant penalty if the input power is kept low. The number of channels can also be increased if the bandwidth is taken more for more carrier separation.
Line Coding: NRZ input data.
Interchannel Spacing and number of Channels: 250 KHz.