**3.1 Evaluation of bit error ratio (BER)**

The bit error ratio (BER) evaluation is a straightforward and relatively simple method for performance evaluation based on counting the errors in the received bit streams. The error counting in a practical system with a transmission speed greater than 1 Gbit/s can be a long process, especially for realistically low BER values (< 10–9). For investigation of performance of an optical transmission system by simulation, several effective statistical methods have been developed [Binh, 2009].

Conventional methods of Q-factor and hence BER calculation are based on the assumption of Gaussian noise distribution. However, new methods relying upon statistical processes with account for the distortion dynamics of optical fibers are necessary in order to include the common patterning effects.

The former statistical technique employs the expected maximization theory in which the *pdf* of the detected electrical signal is approximated as a mixture of multiple Gaussian distributions.

The latter technique is based on the generalized extreme values (GEV) theorem [Bierlaire et al., 2007, Markose & Alentorn, 2007]. Although this theorem is well-known in other fields (financial forecasting, meteorology, material engineering, see e.g. [Kotz & Nadarajah, 2000] to predict the probability of occurrence of extreme values, it has not yet been applied in optical communications.

Exactly as the BER set used in experimental transmission, the BER in the simulation of a particular HDWDM system configuration is calculated. In this case the BER is the ratio of the occurrence of errors (Nerror) to the total number of transmitted bits (Ntotal) and given as:

$$BER = \frac{\aleph\_{error}}{\aleph\_{total}} \tag{1}$$

The Monte-Carlo method offers a precise picture via the BER metric for all modulation formats and receiver types. The optical system configuration under a simulation test must include all the sources of impairments imposing on signal waveforms, including fiber impairments and amplified spontaneous emission (ASE) [Binh, 2009].

## **3.2 Optical signal-to-noise ration (OSNR)**

The optical signal-to-noise ratio (OSNR) is a widely used evaluation criterion for characterizing the system performance in already deployed transmission lines. The optical noise created by transmission media and devices around an optical signal reduces

Realization of HDWDM Transmission System with the Minimum Allowable Channel Interval 199

Fig. 5. The setup used for investigation of HDWDM transmission [Bobrovs et al., 2010].

2010].

filter at different FWHM values.





**Attenuation, dB**


0

At the fibre end each channel is optically filtered with an Anritsu Xtract tunable optical filter (see Fig. 6). An essential parameter of such a filter is its centering on the signal to be extracted. Its position has to be adjusted regarding the signal harmonics [Ivanovs et al.,

The Anritsu Xtract tunable optical band-pass filter covers all transmission bands of a standard single mode optical fiber. The filter operates in the range of 1450-1650 nm, covering the E, S, C and L bands and, partially, the U band. The main drawback of this BPF is 6 dB insertion losses, which is a limiting factor in realization of high-speed HDWDM

> 0.15 nm 0.4 nm 0.8 nm

Fig. 6. The measured amplitude responses of the Anritsu Xtract tunable optical band-pass

1549.5 1549.7 1549.9 1550.1 1550.3 1550.5

**Wavelength, nm**

transmission systems for moderate distances without optical amplifiers.

the receiver's ability to correctly detect the signal. This effect can be suppressed by an optical filter placed before the optical receiver. Depending on the amplifier infrastructure used in a transmission system, the OSNR is proportional to the number of optical amplifiers and to the gain flatness of a single amplifier. This latter can be an especially critical issue in HDWDM systems, because of the gain non-uniformity in multi-span transmissions.

In practice, the OSNR can be found by measuring the signal power as the difference between the total power of the signal peak and the background noise; this latter, in turn, is determined by measuring the noise contributions on either side of the signal peak. However, it is difficult to separate measurements of the signal and noise power, because the latter in an optical channel is included in the signal power. The determination of this parameter in a HDWDM system can be made by interpolating it between the adjacent channels [Binh, 2009].

For a single EDFA with output power, *Pout*, the OSNR is given by [Jacobsen, 1994]:

$$OSNR = \frac{P\_{out}}{N\_{ASE}} = \frac{P\_{out}}{(NFG\_{op} - 1)h\nu B\_o} \tag{2}$$

where *NF* is the amplifier noise figure, *Gop* is the optical amplifier gain, *hv* is the photon energy, and *Bo* is the optical bandwidth found by measurement. However, OSNR does not provide good estimation to the system performance when the main degrading sources involve the dynamic propagation effects such as dispersion and Kerr nonlinearity effects.

When addressing the value of an OSNR, it is important to define the optical measurement bandwidth over which the OSNR is calculated. To obtain this value, the signal power and noise power are derived by integrating all the frequency components over the bandwidth [Rongqing & O'Sullivan, 2009].

In practice, the signal and noise power values are usually measured directly, using the optical spectrum analyzer (OSA), which does the mathematics for the users and displays the resultant OSNR versus wavelength or frequency over a fixed resolution bandwidth. The value of *Δλ* = 0.1 nm at 1550 nm, is widely used as a typical value for calculation of the OSNR.
