**4. Mixed WDM transmission system models**

As a start model for our mixed WDM transmission system, 10 Gbit/s three – channel system was chosen. In this system optical signal modulation formats applied in each system's channel are different. Per channel transmission bit rate is chosen equal to 10 Gbit/s, because our research is focused on ultra – long haul mixed HDWDM transmission system development, which expecting existing 10 Gbit/s system's infrastructure use and further it's development.

### **4.1. Simplest model of mixed WDM**

In the mentioned system's first channel optical signal is transmitted for which modulation differential phase shift keying with non – return – to – zero encoding technique is used (NRZ – DPSK). For the system's second channel on – off keying method and NRZ encoding is used, despite the fact, that NRZ – OOK modulation format is not well situated for high density WDM systems with a large number of transmission channels and high transmission rate and, as consequence of that, a high total transmission capacity. This modulation format can be used as a good foundation and reference point for comparison of different modulation formats, because it's traditionally used modulation format in optical transmission systems, due to its relatively simple realization and historical domination "in [2]". As modulation format for the system's third channel binary polarization shift keying (2 – POLSK) was chosen. It's the newest modulation format and in the same times the most promising "in [16]".

Then all three differently modulated optical signals are combined and transmitted through 50 km long standard single mode fibre (SSMF), without using optical amplifiers. On the other fibre end optical signals are filtered with optical Gaussian filters, converted to electrical signals and then electrically filtered using Bessel electrical filters (see Fig. 2).

240 Optical Communication

confidence intervals for 10-12 nominal.

**4.1. Simplest model of mixed WDM** 

development.

promising "in [16]".

**4. Mixed WDM transmission system models** 

As one can see, when simulating 1,024 bits at BER = 10-12, the confidence interval magnitude is less than ±1 order. It points to the conclusion that OptSim simulation software allows obtaining sufficiently accurate preliminary results and there is no point to increase the total number of simulated bits, because obtained results accuracy does not improve sufficiently.

**Figure 1.** Q-factor uncertainty as a function form total number of simulated bits, and BER value 95%

As a start model for our mixed WDM transmission system, 10 Gbit/s three – channel system was chosen. In this system optical signal modulation formats applied in each system's channel are different. Per channel transmission bit rate is chosen equal to 10 Gbit/s, because our research is focused on ultra – long haul mixed HDWDM transmission system development, which expecting existing 10 Gbit/s system's infrastructure use and further it's

In the mentioned system's first channel optical signal is transmitted for which modulation differential phase shift keying with non – return – to – zero encoding technique is used (NRZ – DPSK). For the system's second channel on – off keying method and NRZ encoding is used, despite the fact, that NRZ – OOK modulation format is not well situated for high density WDM systems with a large number of transmission channels and high transmission rate and, as consequence of that, a high total transmission capacity. This modulation format can be used as a good foundation and reference point for comparison of different modulation formats, because it's traditionally used modulation format in optical transmission systems, due to its relatively simple realization and historical domination "in [2]". As modulation format for the system's third channel binary polarization shift keying (2 – POLSK) was chosen. It's the newest modulation format and in the same times the most SSMF length was chosen equal to 50 km, because it's better permissible length between two EDFA in an ultra – long haul transmission system, if fibre attenuation coefficient is 0.2 dB/km "in [4]". Large amplifier spacing in such system would result in a prohibitive increase in amplified spontaneous emission (ASE) noise and in order to achieve the greater range and information capacity, the amplifiers must be located close together with gain no greater than about 10 dB and preferably less "in [17]". Amplifier spacing further increment will lead to increase of ASE noise influence and as a result BER grow for each system channel. As well as, we must take into account system's accumulated dispersion level, because 10 Gbit/s network, where for optical signal modulation NRZ format is used, operates error free only if residual system dispersion is below 1000 ps/nm. SSMF has 17 ps/nm\*km dispersion and this mean that mentioned above dispersion level threshold won't be exceeded if length of the used fibre is below 58 km. In our case, we start studied optical signal transmission over only one span of ultra – long haul transmission system and that's why fibre length was taken from its possible optimal configuration.

In the first previously mentioned system for optical signal modulation in all three channels differential binary phase shift keying (DPSK) was used, in the second – the intensity modulation (IM) and in the third – polarization shift keying were used, while the fourth is a mixed transmission system, where for the first channels optical signal modulation NRZ – DPSK was used, for the second channel – NRZ – OOK and third – 2 – POLSK.

**Figure 2.** Simulation model of 3 – channel mixed WDM system


**Table 1.** Simulation results

The configuration type of this system was chosen precisely in order to clarify interchannel crosstalk influence effect to transmission in adjacent channels, if modulation formats applied for each channel are different. Number of channels in systems, where just one modulation format is used for the optical signal modulations, was chosen equal to the number of channels of mixed system under study. It was specially done, in order to provide, that a total amount of input optical power coupled into the fibre would be approximately equal. This condition was specially held, in order to provide, that fibre nonlinearities could become apparent to the same extent and transmission would take place under same conditions, to make a comparison of these four different transmission systems for a range of channel spacing values. Each system simulation was performed for five different channels spacing, whose values were chosen based on the establishment principle of ITU – T Recommendation G.694.1. As the result, systems were simulated at following values of channel intervals: 25, 37.5, 50, 75, 100 GHz. Systems channels were grouped around 193.1 THz central frequency value and were located in C – Band (1530 – 1565 nm). The simulation results are summarized (see Table 1.).

Let's also note, that optical bandpass Gaussian filters with -3 dB bandwidth equal to 0.11 nm were used for signal filtering at 25 GHz channel spacing, rather than in the other cases, where -3 dB bandwidth is equal to 0.3 nm. For electrical signal filtering Bessel filters with number of poles equal to 5 and -3 dB bandwidth equal to 10 GHz were used.

NRZ -

NRZ -

2POLSK

Mixed

**Table 1.** Simulation results

DPSK

OOK

**10 Gbit/s WDM System** 

1st

results are summarized (see Table 1.).

1,00˟10-40

3rd 7,12˟10-30

**Channel Spacing, GHz 25 37,5 50 75 100 BER**

1st 5,11˟10-12 6,49˟10-13 1,78˟10-16 5,90˟10-17 6,27˟10-17 2nd 3,25˟10-9 6,12˟10-10 1,00˟10-15 1,98˟10-17 4,00˟10-17 3rd 3,18˟10-12 2,64˟10-13 3,07˟10-16 1,23˟10-16 1,30˟10-16

1st 4,19˟10-29 9,00˟10-18 4,56˟10-22 4,54˟10-26 3,03˟10-26 2nd 1,06˟10-21 2,53˟10-13 1,04˟10-21 4,85˟10-26 1,84˟10-26 3rd 6,79˟10-31 2,60˟10-16 1,00˟10-22 1,62˟10-25 6,82˟10-26

1,00˟10-40 1,00˟10-40 1,00˟10-40 2nd 4,57˟10-18

1st (DPSK) 1,88˟10-25 9,95˟10-17 7,70˟10-17 3,49˟10-17 2,55˟10-17 2nd (NRZ) 3,23˟10-12 2,63˟10-10 3,68˟10-24 3,54˟10-25 2,18˟10-26 3rd (2POLSK) 1,00˟10-40 5,12˟10-27 1,00˟10-40 1,00˟10-40 1,00˟10-40

1,71˟10-29

The configuration type of this system was chosen precisely in order to clarify interchannel crosstalk influence effect to transmission in adjacent channels, if modulation formats applied for each channel are different. Number of channels in systems, where just one modulation format is used for the optical signal modulations, was chosen equal to the number of channels of mixed system under study. It was specially done, in order to provide, that a total amount of input optical power coupled into the fibre would be approximately equal. This condition was specially held, in order to provide, that fibre nonlinearities could become apparent to the same extent and transmission would take place under same conditions, to make a comparison of these four different transmission systems for a range of channel spacing values. Each system simulation was performed for five different channels spacing, whose values were chosen based on the establishment principle of ITU – T Recommendation G.694.1. As the result, systems were simulated at following values of channel intervals: 25, 37.5, 50, 75, 100 GHz. Systems channels were grouped around 193.1 THz central frequency value and were located in C – Band (1530 – 1565 nm). The simulation

Let's also note, that optical bandpass Gaussian filters with -3 dB bandwidth equal to 0.11 nm were used for signal filtering at 25 GHz channel spacing, rather than in the other cases, where -3 dB bandwidth is equal to 0.3 nm. For electrical signal filtering Bessel filters with

number of poles equal to 5 and -3 dB bandwidth equal to 10 GHz were used.

**Figure 3.** 3 – Channel NRZ – OOK system's output spectrum, signal eye diagrams and BER value in case of 25 GHz channel spacing, and 3 – channel NRZ – DPSK system's output spectrum, signal eye diagrams and BER value in case of 25 GHz channel spacing

At the beginning of the results analysis we will focus on traditionally used NRZ – OOK modulation format. As one can conclude form the simulation results, in the case of small channel spacing values the worst systems bit – error – ratio is for the second system channel. This is explained by the fact, that in this case interchannel crosstalk effects are more quintessential and signal spectrum compaction is maximal affordable (see Fig. 3). As one can see from this figure, further compaction leads to different signal spectrum overlapping and as a consequence imminent grow of BER values. If we increase the value of channel spacing, this difference between BER values of each channel disappears. But if we increase channel spacing up to 37.5 GHz, the worst channel BER is already less than desired 10–12 at the same filter characteristics. In the data transmission networks with 10 Gbit/s bitrates and higher, if forward error correction techniques (FEC) are not used, BER value must be <10–12.

If we increase channel spacing value form 37.5 GHz up to 50 GHz, the worst channel BER improves till 1.04. 10–21. Further increment of spacing form 50 to 75 GHz or even up to 100 GHz at the given modulation and coding format, as well as bit rate, is not needed, because the BER improvement is not significant (see Fig. 4 – 5).

**Figure 4.** Eye diagram of the worst (2nd) NRZ – OOK system's channel, 50 GHz channel spacing and BER=1.04. 10–21

**Figure 5.** Eye diagram of the best (2nd) NRZ – OOK system's channel, 100 GHz channel spacing and BER=1.84. 10–26

If we use for optical signal modulation NRZ – DPSK format, the resulting BER values for each simulated channel at certain channel spacing values is several orders worse than it is in the NRZ – OOK format cases (see Fig. 6 – 7). Channel spacing reduction form 100 GHz to 50 GHz, leads to reduction of the worst channel bit – error – rate by one order. This lets make a conclusion about NRZ – DPSK modulation formats suitability to high spectral density transmission conditions. It's non-susceptible to channel spacing decreases or increases, if it happens to specified threshold values, above which a sudden channel degradation process is unavoidable.

BER=1.04.

BER=1.84.

10–26

is unavoidable.

10–21

**Figure 4.** Eye diagram of the worst (2nd) NRZ – OOK system's channel, 50 GHz channel spacing and

**Figure 5.** Eye diagram of the best (2nd) NRZ – OOK system's channel, 100 GHz channel spacing and

If we use for optical signal modulation NRZ – DPSK format, the resulting BER values for each simulated channel at certain channel spacing values is several orders worse than it is in the NRZ – OOK format cases (see Fig. 6 – 7). Channel spacing reduction form 100 GHz to 50 GHz, leads to reduction of the worst channel bit – error – rate by one order. This lets make a conclusion about NRZ – DPSK modulation formats suitability to high spectral density transmission conditions. It's non-susceptible to channel spacing decreases or increases, if it happens to specified threshold values, above which a sudden channel degradation process

**Figure 6.** Eye diagram of the best (2nd) NRZ – DPSK systems channel, Δf=100 GHz and BER=4.00. 10–17

**Figure 7.** Eye diagram of the worst (3rd) NRZ – OOK systems channel, Δf=100 GHz and BER=6.82. 10–26

However, if the channel spacing is reduced to 25 GHz, then all three channels BER values are greater than required 10-12 but middle channels BER is even greater than ITU – T defined 10-9. If the modulation format, applied for optical signal in each WDM system transmission channel, is polarization shift keying (2 – POLSK), it is possible to achieve the best possible of channel BER values, irrespective to the channel spacing values as compared to other modulation formats. This is possible due to 2 – POLSK modulated signal spectrum (see Fig. 8). As can been seen, 2 –POLSK modulated optical signal spectrum is narrower than NRZ – DPSK and NRZ – OOK modulated signal spectrum. This property provides to a data signals greater error protection, when it is spread through the optical fibre transmission systems, and WDM signal spectrum lines at the beginning and at the end differ only by the level, spectrum extension and nonlinear effect influence are minimal.

If in multi-channel communication system for optical signal modulations different modulation formats are used, then obtained BER values for each channel will depend not only on the individual modulation format capability to resist from interchannel distortion, but also form that, which modulation format is used in the channel, which is the source of this disorders. This feature gets stronger on small (<50 GHz) channel spacing values, and the obtained simulation results for mixed system allow us to conclude this.

If in a mixed system 50, 75 or 100 GHz channel spacing are used for channel separation, then the channel BER values corresponding to BER values obtained for systems, where only one modulation format is used for the optical signal modulation. It is approximately 10-17 in NRZ – DPSK case, about 10-25 in NRZ – OOK and 10-40 in 2 – POLSK. Reducing channel spacing to 37.5 GHz, become evident special features of combined transmission and they stand out even more against the background, if 25 GHz interval is used for channel separation. As it can be seen from the obtained results, the first channel, where is used phase modulation, BER level is several orders lower (10-25) than it is for the first channel of 3 – channel NRZ – DPSK system (10-12) (see Fig. 8), the same can be applied to the second channel of the mixed system (10-12) and 2nd channel (10-21) of 3 – channel NRZ – OOK system (see Fig. 8).

**Figure 8.** NRZ – DPSK, NRZ – OOK, 2 – POLSK optical signal spectrums at the transmitter end after electrical conversion, and 3 – Channel mixed system's output spectrum, signal eye diagrams and BER value in case of 25 GHz channel spacing

As one can see from these figures, eye opening in both cases are materially different, eye opening for mixed system is narrower than for traditional NRZ – OOK system's 2nd channel signal, if 25 GHz interval is used for channel separation.

The next step for mixed WDM system performance evaluation is to increase the channel quantity, bitrate and also transmission line length. Upgraded mixed WDM scheme contains nine channels, which are grouped in three groups with an identical transmitter and receiver block configuration but with different channel central wavelengths. It was specially done in order to take into account linear and nonlinear crosstalk influence, which experience central's group channels from adjacent channels. The central group consists from channels number 1 to 3, left group consists from channels number 4 to 6 and right group – from 7 to 9. For further system's analysis we will use only channels number 1 – 3, but 4 – 6 and 7 – 9 is used as sources of transmission impairments.

246 Optical Communication

If in multi-channel communication system for optical signal modulations different modulation formats are used, then obtained BER values for each channel will depend not only on the individual modulation format capability to resist from interchannel distortion, but also form that, which modulation format is used in the channel, which is the source of this disorders. This feature gets stronger on small (<50 GHz) channel spacing values, and the

If in a mixed system 50, 75 or 100 GHz channel spacing are used for channel separation, then the channel BER values corresponding to BER values obtained for systems, where only one modulation format is used for the optical signal modulation. It is approximately 10-17 in NRZ – DPSK case, about 10-25 in NRZ – OOK and 10-40 in 2 – POLSK. Reducing channel spacing to 37.5 GHz, become evident special features of combined transmission and they stand out even more against the background, if 25 GHz interval is used for channel separation. As it can be seen from the obtained results, the first channel, where is used phase modulation, BER level is several orders lower (10-25) than it is for the first channel of 3 – channel NRZ – DPSK system (10-12) (see Fig. 8), the same can be applied to the second channel of the mixed

system (10-12) and 2nd channel (10-21) of 3 – channel NRZ – OOK system (see Fig. 8).

**Figure 8.** NRZ – DPSK, NRZ – OOK, 2 – POLSK optical signal spectrums at the transmitter end after electrical conversion, and 3 – Channel mixed system's output spectrum, signal eye diagrams and BER

As one can see from these figures, eye opening in both cases are materially different, eye opening for mixed system is narrower than for traditional NRZ – OOK system's 2nd channel

value in case of 25 GHz channel spacing

signal, if 25 GHz interval is used for channel separation.

obtained simulation results for mixed system allow us to conclude this.

In the first channel as in previous model the NRZ – OOK signal optical modulation format is used. This modulation format can be used as a reference point for comparison of different modulation formats. It is traditionally used modulation format in optical transmission systems due to its relatively simple realization and historical domination "in references [8, 12]". Data transmission rate for this channel is chosen equal to 40 Gbit/s. For the system's second channel 2 – POLSK modulation format was chosen, because it's the newest and in the same time the most promising modulation formats for optical transmission systems "in [2]". In this case per channel bit rate was chosen equal to 40 Gbit/s. And finally, as modulation format for the system's third channel NRZ – DPSK was chosen. Per channel bit rate was chosen equal to 10 Gbit/s.

Modulation format allocations to each system's channels was performed on the basis of the fact that such modulation formats distribution among channels provides the lowest possible average BER value for system channels at 10 Gbit/s per channel bit rate and 25 GHz channel spacing, comparing to other five possible formats distribution variants. As for per channel bit rate assignment, then such variant provides SE = 0.4 bit/s/Hz and an average BER value not greater than 10-40, if for CD compensation ideal FBG is used (see Fig. 9). Comparing with two other mixed data rates mixed system variants, which can provide SE = 0.4 bit/s/Hz, then their can secure BER < 10-12 or even < 10-14, but their average channel BER >10-40 "in [3]". Thus, as a simulation model of mixed system was chosen a transmission system with a following configuration: [NRZ – OOK (40 Gbit/s, 193.025 THz)] – [2 – POLSK (40 Gbit/s, 193.100 THz)] – [NRZ – DPSK (10 Gbit/s, 193.175 THz)].

As one can see (see Fig. 9), then SE equal to 0.4 bit/s/Hz was obtained in case, if 75 GHz interval is used for channel separation. That channel spacing value was selected based on the establishment principle of ITU – T Recommendation G.694.1, which provides a frequency grid for dense wavelength division multiplexing applications. The frequency grid, anchored to 193.1 THz, supports a variety of channel spacing's ranging from 12.5 GHz to 100 GHz and wider. Afterwards all optical signals from nine channels are combined and transmitted through 50 km SSMF using 4dBm fixed output power optical amplifier, which operates on basis of EDFA. This amplifier is necessary, because we simulate optical signal transmission through one span of ultra-long haul system.

The output power level is chosen equal to 4 dBm due to the fact that this level can ensure the lowest average BER values for transmission channels of that configuration mixed transmission systems but with bit rate of 10 Gbit/s per channel and 25 GHz channel spacing comparing to other fixed output power levels "in [3]". On the other fiber end optical signals are filtered with optical Super Gaussian filters, converted to electrical signals and then electrically filtered using Bessel electrical filters.

**Figure 9.** Mixed HDWDM system 1st/2nd/3rd channel's BER correlation diagram, detected signals eye diagrams and BER values at 75 GHz channel spacing

In order to achieve the greater range and information capacity, the amplifiers must be located close together with gain no greater than 10 dB and preferably less "in [2]". Amplifier spacing further increment will lead to increase of ASE noise influence and as a result BER growth for each system channel. As well as, we must take into account system's accumulated chromatic dispersion management strategy, which will be the next sections main goal.

### **4.2. Chromatic dispersion management strategies**

Chromatic dispersion divides into material and waveguide dispersion.Waveguide dispersion is caused by physical structure of optical fiber core and cladding (refractive index profile), and as a result different wavelengths propagate at different velocities in the core and cladding. Material dispersion is dominant part of chromatic dispersion, and it is caused by change of optical fiber core and cladding refractive index with wavelength "in [4]".

Dispersion compensating fiber (DCF), fiber Bragg grating (FBG) and optical phase conjugator (OPC) can be used for chromatic dispersion compensation.

DCF has large negative dispersion (D = -80 ps/(nm\*km), that helps to compensate chromatic dispersion. Such an optical fiber with negative dispersion is achieved by developing a complex refractive index profile. The effective core area (*Aeff*) of a DCF is much smaller than standard ITU – T G.652 single mode fiber, thereby dispersion compensating fiber experience much higher optical signal distortions caused by nonlinear optical effects (NOE). Typical dispersion compensating fiber has small effective core area Aeff = 12 μm2 whereas standard single mode optical fiber has Aeff = 80 μm2, and DCF has attenuation coefficient up to α = 0.6 dB/km, whereas standard single mode optical fiber has α = 0.2 dB/km. Impact of nonlinear optical effects can be reduced by lowering optical power "in [4]".

Chirped fiber Bragg grating (FBG) is effective technology for chromatic dispersion compensation, because it is more suitable for large transmission capacity WDM systems. It has grating period which is not constant, but changes linearly over the length of the grating with the shorter grating period located at the beginning of the grating. FBG grating period is distance between two adjacent maximum values of the refractive index.

The fiber grating reflects a narrow spectrum of wavelengths, that are centred at reflected wavelength (*λB*) and passes all the other wavelengths. Dispersion affected input pulse with width τ is passing Chirped fiber Bragg grating and at output its width is decreased by *Δτ* and shape is restored. Chirped fiber Bragg grating has shorter grating periods at beginning, but over the length of the grating these periods linearly increase. Therefore shorter signal wavelengths are reflected sooner and have less propagation delay through the FBG, but longer signal wavelengths travel further into the fiber grating before they are reflected back and have more propagation delay through the FBG. Typically the length of the fiber grating is from 10 to 100 cm "in [4]".

A significant advantage of using fiber Bragg grating over DCF fiber is its relatively small insertion loss. For comparison, commercial DCF specified to compensate accumulated chromatic dispersion of 100 to 120 km standard single mode fiber span have about 10 dB of insertion loss, whereas a FBG based dispersion compensation unit, capable to compensate the same fiber span length, insertion loss is only up to 4 dB. In contrast to DCF fiber Bragg grating can be used at higher optical powers without inducing nonlinear optical effects. These CD compensation methods described above will be practically implemented in our investigated mixed system model.
