Dispersion Compensation Algorithm for Single Mode Fiber

— Optical fibers enable the transmission of data through a long distance at very high speed and very low latency. However, this can be limited as a result of dispersion. This paper presents a dynamic MATLAB script that can mitigate against the dispersion in a single mode fiber (SMF)by calculating the length of dispersion compensation fiber (DCF) needed to offset the dispersion. It also calculates the number of amplifiers needed and the positions the amplifiers are to be placed. The results from the MATLAB script were also authenticated using Opti system. The average Bit error rate (BER) values gotten with simulation parameters of different scenarios shown in tables 1 and 2 are 7.6857e-17 and 5.8036e-10 respectively. The average Quality factor (Q-Factor) values of 10.046203 and 7.286533 were also gotten respectively. This showed that the effect of dispersion was compensated using the DCF thus proving the validity of the script.

I. INTRODUCTION 1 The last decade has seen a shift from the third generation (3G) network to the fifth-generation network (5G). This has resulted to very high-speed communication, machine to machine connectivity and ultra-low latency, internet of things and so on [1]. This has led to applications that use a lot of bandwidth thereby generating much traffic. Fiber optics cables act as an excellent backhaul for this generated traffic because of its huge bandwidth. Fiber optics are long thin strands of glass with an approximate diameter of the human hair. Other advantages of fiber optics include immunity to electromagnetic interference, low loss transmission, signal security and abundant availability of its raw material.
In fiber optics communication, Information (voice, data or video) are transmitted through the glass in the form of light. The light acts as an electromagnetic carrier which is modulated to carry information [2] . Transmission through fiber optics cables is affected by several limitations especially as the distance increases. As the communication networks evolved to longer distances and higher bit rates, the linear effect of fibers, which are attenuation and dispersion, became important limiting factors [3].
In general, dispersion refers to the spreading of the pulses that make up a signal as it travels along the fiber. It is as a result of the physical property of the optic fiber. Single mode fibers (SMF) are mostly used in high-speed optical networks are susceptible to chromatic dispersion which leads to pulse broadening [4]. This occurs because of variation in propagation velocity with wavelength. This means that some wavelengths will reach the end of the fiber before others causing a propagation delay.
A key technology for long-haul fiber links is therefore 'dispersion compensation'. The most common solution has been 'dispersion compensating fiber' (DCF), which is simply fiber in which the chromatic dispersion has been engineered to be the exact opposite of the dispersion in the fiber link. This work aims to write a program to calculate the exact length of DCF to be used, the number of amplifiers to be used and the positions the individual amplifiers are to be placed while designing a link budget for a fiber optic communication network. Tables I and II show different parameters inputted into MATLAB program. The program also takes care of the budget analysis. The formulas used for the program are given below:
where n = number of amplifiers.

III. OPTISYSTEM SIMULATION
To validate the results from the MATLAB scripts, the values gotten are used to run a simulation on Opti system. The system is divided into three sections; transmitter, channel and receiver section. The transmitter section is made up of a Pseudo-random bit sequence generator, NRZ generator, Continuous Wave (CW) laser, Mach-Zehnder modulator. The channel consists of the SMF, DCF and Amplifiers. The Receiver section is made up of the Bessel optical filter, optical receiver and BER analyzer.
The pseudo random bit sequence generator outputs a binary sequence of pseudo random bits (pulses of 0s and 1s). The generated bits are fed into the NRZ Pulse generator. The NRZ pulse generator produces a series of non-return to zero pulses that are coded by a digital signal input into an electrical signal. The CW Laser generates a steady light beam with a very stable output power. The light generated by the CW laser together with the output from the NRZ Pulse generator is fed into the Mach-Zender Modulator (MZM). The MZM converts the electrical input to optical signals.
The capacity of the optical link (100 Gbps) is divided into sections of 10 Gbps and multiplexed using a WDM Mux into a fiber optic cable. At the receiving side, the optical signal is demultiplexed using the WDM Demux and fed into a Bessel optical Filter which helps to prevent transmission of specific wavelengths and passed to the optical receiver.

IV. RESULTS
The results from the MATLAB scripts are first obtained. Inputting the parameters from Table I into the MATLAB script gives the following results below: The length of the DCF is 60.000 kilometers The number of Amplifiers needed is 5.00 The amplifiers will be placed on the SMF after every 80.00 km The amplifiers will be placed on the DCF after every 33. The results from the MATLAB scripts are then validated using Opti system software. The results obtained from the simulation show a very low level of BER. It also gives a good Q-Factor. The Q-Factor indicates how distorted a pulse is [5]. The higher the BER, the lower the Q-Factor (i.e., the higher the level of distortion). The eye diagrams showing the Q Factor and BER for the design links are given below. Table 3 shows the various BER and Q Factor values obtained from the design links. The average BER values obtained were 7.6857e-17 and 5.8036e-10 which satisfied our minimum BER  I AND II  BER from  Table 1 BER from Table 2 Q-Factor from Table 1 Q-Factor from           Fig. 12b. BER 8 of 420km Link (9.08e-013).

V. CONCLUSION
The aim of this paper is to write a dynamic code using MATLAB that helps compensates for the effect of dispersion in single mode fiber with the aid of dispersion compensating fiber. The code helps to calculate the length of DCF needed, the number of amplifiers and the positions where the amplifiers are to be placed. The MATLAB results were also verified using Opti system software. The minimum requirement of e-09 was met. The best BER met was 6.00128e-022 which had a Q-Factor of 9.55592. The average BER values gotten with simulation parameters of tables 1 and 2 were 7.6857e-17 and 5.8036e-10 respectively. The average Q-Factor values of 10.046203 and 7.286533 were also gotten respectively, thus proving that we designed efficient transmission links using the parameters from Tables I and II. APPENDIX

MATLAB Code
The MATLAB script for the simulation is given as follows.