**2.2. Application of optical modulation formats**

Since the introduction of the first optical transmission systems, capacities have steadily increased and the cost per transmitted bit has gradually decreased. The core of the global telecommunication network consists today of wavelength division multiplexed optical transmission systems. WDM is for these systems the technology of choice as it allows for a high spectral efficiency, i.e. the transmitted capacity per unit bandwidth. Commercial WDM systems generally use up to 80 wavelength channels with 50 GHz channel spacing and a bit rate of 10 Gbit/s or sometimes 40 Gbit/s per wavelength channel. This translates into a spectral efficiency between 0.2 and 0.8 bit/s/Hz. However, to cope with the forecasted increase in data traffic it will be necessary to develop next – generation transmission systems with even higher capacities. These transmission systems are expected to have a 40 Gbit/s or more bit rate per wavelength channel, with a spectral efficiency of between 0.8 and 2.0 bit/s/Hz. At the same time, such systems should be robust, i.e. provide a tolerance towards transmission impairments similar to currently deployed systems "in [9]".

Traditionally, optical transmission systems have used amplitude modulation. However, for the next generation of transmission systems this is not a suitable choice. They normally require too large channel spacing, have a high optical – signal – to – noise ratio (OSNR) requirement and generate significant nonlinear impairments. Current state-of-the-art transmission systems therefore often use differential phase shift keying (DPSK). Compared to amplitude modulation, DPSK generates less nonlinear impairments and has a lower OSNR requirement. However, due to the high symbol rate (e.g. 40-Gbaud) the robustness against the most significant linear transmission impairments, i.e. chromatic dispersion and polarization – mode dispersion (PMD) is still small. Tunable optical dispersion compensators can be used to improve the chromatic dispersion tolerance and PMD impairments are generally avoided through fiber selection. But optical compensation and fiber selection are generally not suitable for cost-sensitive applications "in references [17,18]". Another potential candidate to reduce the symbol rate is polarization multiplexing (POLMUX). This doubles the number of bits per symbol by transmitting independent information in each of the two orthogonal polarizations of an optical fiber "in [5]".

Our issue in a mixed system solution is offered as a part of common transmission system development, during the transition from traditional use of NRZ – OOK modulation format to alternative modulation formats, such as NRZ – DPSK and 2 – POLSK. Such hybrid solution can be topical in the case of combination or even in the case of different transmission systems merger, which results in the necessity to make a different modulated optical signal transmission over a single optical bus. As well as, such a need may occur in the future, switching traffic from a variety of WDM systems with the help of reconfigurable optical add – drop multiplexers (ROADM) and transmitting it further over common fibre to its destination or to the next ROADM "in [9]". The shift towards alternative optical signal modulation formats is necessary, because one of the major problem need to be overcome, in order to increase the total transmission capacity of core networks and a single fibre, are the reduction of transmission impairments and signal modulation format capability to resist against such impairments.

In high density WDM (HDWDM) systems with a large fibre span length between two optical amplifiers, signal form distortion causes such effects as linear chromatic dispersion, polarization mode dispersion, fibre non – linear effects or thereof combinations. In WDM system channel spacing reduction limiting factor is interchannel crosstalk, which originate due to optical fibre nonlinearities, such as crossphase modulation (XPM), selfphase modulation (SPM) and four – wave mixing (FWM) "in [13]". In order to reduce the impact of those effects, various optical modulation formats are increasingly being studied and offered, which could serve as an alternative to currently used traditional on – off keying. In this way manipulated signals are significantly distorted at high speed and high spectral density transmission conditions "in [14]".

#### **3. Measurement technique and accuracy**

236 Optical Communication

and some external modulated lasers, but all transmitter and receiver electrical parts with bandpass filters must be changed to a new one. The second one, channels compaction by location them closer to each other using smaller channel spacing between them, in that way increasing the number of channel in available transmission frequency spectrum "in [2,15]". In this case, the total transmission capacity increment is achieved only because of increasing the number of channels, as the individual transmission rate in each channel remains unchanged. And the third way, total transmission capacity increment, using channel compaction with

It is clear, that none of the proposed fibre's transmission capacity increment solution can be realized immediately, but it requires a certain amount of time and work, as any solution

Since the introduction of the first optical transmission systems, capacities have steadily increased and the cost per transmitted bit has gradually decreased. The core of the global telecommunication network consists today of wavelength division multiplexed optical transmission systems. WDM is for these systems the technology of choice as it allows for a high spectral efficiency, i.e. the transmitted capacity per unit bandwidth. Commercial WDM systems generally use up to 80 wavelength channels with 50 GHz channel spacing and a bit rate of 10 Gbit/s or sometimes 40 Gbit/s per wavelength channel. This translates into a spectral efficiency between 0.2 and 0.8 bit/s/Hz. However, to cope with the forecasted increase in data traffic it will be necessary to develop next – generation transmission systems with even higher capacities. These transmission systems are expected to have a 40 Gbit/s or more bit rate per wavelength channel, with a spectral efficiency of between 0.8 and 2.0 bit/s/Hz. At the same time, such systems should be robust, i.e. provide a tolerance towards

Traditionally, optical transmission systems have used amplitude modulation. However, for the next generation of transmission systems this is not a suitable choice. They normally require too large channel spacing, have a high optical – signal – to – noise ratio (OSNR) requirement and generate significant nonlinear impairments. Current state-of-the-art transmission systems therefore often use differential phase shift keying (DPSK). Compared to amplitude modulation, DPSK generates less nonlinear impairments and has a lower OSNR requirement. However, due to the high symbol rate (e.g. 40-Gbaud) the robustness against the most significant linear transmission impairments, i.e. chromatic dispersion and polarization – mode dispersion (PMD) is still small. Tunable optical dispersion compensators can be used to improve the chromatic dispersion tolerance and PMD impairments are generally avoided through fiber selection. But optical compensation and fiber selection are generally not suitable for cost-sensitive applications "in references [17,18]". Another potential candidate to reduce the symbol rate is polarization multiplexing (POLMUX). This doubles the number of bits per symbol by transmitting independent

information in each of the two orthogonal polarizations of an optical fiber "in [5]".

should be implemented gradually in several stages to avoid unnecessary problems.

simultaneous increment of individual channel's transmission bit rate.

transmission impairments similar to currently deployed systems "in [9]".

**2.2. Application of optical modulation formats** 

This research is based on powerful and accepted mathematical simulation software OptSim. It solves complex differential nonlinear Schrödinger equation (NLSE) using split-step Fourier method (SSFM). This equation describes optical signal propagation over the fiber and can be written as Eq. (1) "in [19]":

$$\frac{\partial}{\partial z} \cdot A + \frac{a^l}{2} \cdot A + j \cdot \frac{\beta\_2}{2} \cdot \frac{\partial^2}{\partial t^2} \cdot A - \frac{\beta\_3}{6} \frac{\partial^3}{\partial t^3} \cdot A =$$

$$= j \cdot \chi \cdot |A|^2 \cdot A \tag{1}$$

where *A(t, z)* is complex optical field; *z* is fiber length, [km]; �� is linear attenuation coefficient of an optical fiber, [km-1]; �� is the second order parameter of chromatic dispersion, [ps2/nm]; �� is the third order parameter of chromatic dispersion, [ps3/nm]; � is nonlinear coefficient, [W-1.km-1]; *t* is time, [s]. NLSE takes into the account linear and nonlinear affects and they influence to optical signal distortions. The principle of split-step method is better illustrated by (1), which can be written as follows "in [19]":

$$\frac{\partial}{\partial z} \cdot A(t, z) = \left(\mathcal{D} + \mathcal{N}\right) \cdot A(t, z) \tag{2}$$

$$\widehat{D} = -\frac{\alpha^l}{2} - j \cdot \frac{\beta\_2}{2} \cdot \frac{\partial^2}{\partial t^2} + \frac{\beta\_3}{6} \cdot \frac{\partial^3}{\partial t^3} \tag{3}$$

$$
\widehat{N} = f \cdot \chi \cdot |A|^2 \cdot A \tag{4}
$$

$$A\_L[n] = A[n] \* h[n] = \sum\_{k=-\infty}^{\infty} A[k] \cdot h[n-k] \tag{5}$$

$$A\_L'[n] = A[n] \otimes h[n] = $$

$$= FFT^{-1}\{FFT(A[n])\} \times FFT(h[n])\}\tag{6}$$

$$A(\mathbf{t}, \mathbf{z} + \Delta \mathbf{z}) \equiv \exp\left[\frac{\Delta \mathbf{z}}{2} \cdot \hat{D}\right] \cdot \exp\left\{\Delta \mathbf{z} \cdot \hat{N} \left[A\left(\mathbf{t}, \mathbf{z} + \frac{\Delta \mathbf{z}}{2}\right)\right]\right\} \cdot \exp\left(\frac{\Delta \mathbf{z}}{2} \cdot \hat{D}\right) \cdot A(\mathbf{t}, \mathbf{z})\tag{7}$$

$$\text{dev}[Q^\*] \equiv \sigma\_Q \cong \frac{q}{\sqrt{2 \cdot N\_{\text{total}}}} \tag{8}$$

$$\mathbf{Q} = \frac{|\mu\_1 - \mu\_0|}{\sigma\_1 + \sigma\_0},\tag{9}$$

$$\text{BER} = \frac{1}{2} \cdot \text{erfc}\left(\frac{\mathcal{Q}}{\sqrt{2}}\right) \tag{10}$$

$$\text{range} = 20 \cdot \log\_{10} \left( \frac{1 + \sqrt{\frac{z}{N\_{total}}}}{1 - \sqrt{\frac{z}{N\_{total}}}} \right) \tag{11}$$

$$\mathbf{Q\_{for 16.94 dB}} \in [16.55; 17.31], \text{[dB]} \tag{12}$$

$$\log 10 \{ \text{BER}\_{\text{for } 10^{-12}} \} \in [-12.97; -11.04] \tag{13}$$

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% confidence intervals for 10-12 nominal.
