**R.Ibragimov, V.Konyshev, O.Naniy, V.Treshchikov, R.Ubaydullayev**

Dependence of the bandwidth of DWDM lines with coherent 100g DP-QPSK channels on bandwidth and transmission range

Increasing the capacity of optical communication lines continues to remain a relevant task by maintaining the rapid growth of market demand in the volume of transmitted information [1, 2]. Recent studies indicate the need for exponential growth in the capacity of telecommunications systems to meet the needs of the IT market [3].

The current generation of fiber-optic communication links is characterized by various methods of data transmission, which allows to significantly increase the overall performance of such lines without changing the cable infrastructure. Among the methods of increasing the bandwidth,an increase in the bandwidth used to transmit information while maintaining the existing cable infrastructure seems to be the most economical, and therefore the most attractive solution. Alternative methods such as spatial multiplexing and the use of complex multi-level formats are more expensive in long-distance communication links. When using spatial multiplexing, all existing cable infrastructure needs to be replaced. And in case of using multi-level formats, it may be necessary to install intermediate regenerators or additional amplifiers.

PHENOMENOLOGICAL MODEL OF COHERENT NONLINEAR DWDMCHANNEL IN THE LONG-DISTANCE LINES WITHOUT DISPERSION COMPENSATION

There are different approaches to assessing the performance of DWDM lines in the nonlinear mode. We have proposed a phenomenological model of a coherent optical DWDMline, which accounts for the influence of the three major factors leading to degradation of the optical signal: noise of amplified spontaneous emission of optical amplifiers, the nonlinear self-interaction and cross-coupling of channels, as well as the noise of linear cross-coupling of adjacent channels. It was previously established that nonlinear effects and cross-coupling can be described approximately as two additional types of noise additive to the noise of amplified spontaneous emission.

Numerical modelling and experiments conducted previously set basic properties of three kinds of noise and a model convenient for practical calculations phenomenological that describes the evolution of optical signal characteristics in an extended DWDM line isproposed [4, 5].

The model is based on of the following assumptions. Firstly, the nonlinear distortions are considered quantitatively as Gaussian noise, allowing the addition of spontaneous emission noise. Secondly, the cross-coupling due to overlapping spectra of adjacent channels in their strong convergence can also be represented as excessive additive noise. In this case, the total noise power is simply equal to the sum of the powers of the three noise components (noise of amplified spontaneous emission, nonlinear noise channel and cross-coupling noise):

PN.Summ = PASE + PNL + PX. (1)

Here PASE = hνBAFN is ASE noise fromNspans (it does not depend on signal strength),PNL = η (K,Δf) · P3N1+ε is nonlinear noise from N spans, PX = kX (Δf) · P is the noise of channel cross-coupling, manifests itself once in a photodetector, where

h is the Planck’s constant, h = 6.626 •10–31 mW •c2;

v is the reference carrier frequency of the optical signal,v = 193.1 THz;

B is the normalized bandwidth,B = 12.5 GHz;

A is the attenuation in the optical span;

F is the noise factor of the optical amplifier;

η is the coefficient of nonlinearity, mW-2;

kxis the coefficient of channel cross-coupling, dimensionless;

N is the number of optical spans;

P is the power of the channel signal at the entrance to the span, mW;

s is the parameter of superlinear noise addition of multi-span DWDM line (in DWDMlines without compensations = 0.2) [4].

If we introduce partial OSNR values equal to the ratio of the signal power to the powers of the corresponding partial noise components:

is the linear OSNR;

is the nonlinear OSNR;

is the cross-channel OSNR, caused by the convergence of adjacent channels and the overlapping of their spectra [5],

is the ratio of the signal to the total noise, which determines the error rate;

then the relation (1) can be rewritten in the following form

. (2)

It has been experimentally shown that the coefficient of nonlinearity ηdepends on the number of optical channels Kin the DWDM system, as well as on the distance between neighboring channelsΔf[5], [6]. It is convenient to represent this dependence in the following form:

η (К, Δf) = η∞ · F (К, Δf), (3)

where η∞ is the coefficient of proportionality (for SMF fiber η∞ = 1.15 • 10–4 mW-2).

Based on the processing of the experimental results for F(K, Δf ), the following model dependencewas received:

. (4)

Figure 1 shows the dependencies η from the number of channels for typical values of Δf.

It can be seen from Fig.1 that the coefficient of nonlinearity increases more rapidly from an increase in the number of channels at lower values of the interchannel interval.

ESTIMATING THE EFFECT OF THE DISTANCE BETWEEN CHANNELS ON OSNR BER

Experimental study of the effect of coherent adjacent channels on the 100G DP-QPSK channel with a strong convergence is described in [5]. By approximating the data presented in this article, a model dependence of the channel cross-coupling coefficient was obtained:

КX (Δf) = 0,069 · (Δf – 30,7)–0.74. (5)

The dependence graph (5) is shown in Fig.2.

In the experiment, the central channel was surrounded by two channels on both sides symmetrically at a distance of 33, 37.5, 50 GHz.

DEPENDENCE OF THE OPERATING RANGE OF POWER AND THE OPTIMAL POWER OF THE COMMUNICATION SYSTEM ON THE NUMBER OF SPANS

When calculating fiber-optic communication systems it is necessary to know the operating range of the powersintroduced to the optical spans (Pmax, Pmin), within whichthe communication system remains operational (OSNRBTB < OSNRBER).

When designing such a system usually tougher requirements are specified. The concept of OSNR margin is used (OSNRM). This parameter is defined as follows:

, (6)

whereOSNRL is the linear OSNR, defined above, obtained on the basis of measurements by an optical spectral analyzer,OSNRRis the required OSNR, the minimal linear value of OSNR, obtained by adding a noise line to a value at which the communication system stops being operational.

The measured required OSNR in the back-to-back configuration is customarily designated asOSNRR. In our case OSNRBTB = 11.92 dB [4].

Based on this, the expression (6) for the OSNR margin taking into account(2) takes the following form

. (7)

When designing DWDM line with a margin of OSNRM= mthe following inequality must be observed:

. (8)

Thus, the range of capacities (Pmax2, Pmin2) corresponds to the case m = 2 (the margin is 3 dB), see Fig.3.

It was found that the dependences of OSNRBTB and OSNRMon the signal power P have maxima that are reached for different values of P. For this reason, the optimization is made through the calculations of the optimal powers at the input of each span in two ways:

• by the criterion of maximization of OSNRBTB (corresponding to the minimum of BER), optimal power PB;

• by the criterion of maximization of OSNRM (corresponding to the maximum OSRN margin), optimal power PM.

When optimizing according to the second method, DWDM lines can be constructed more resistant to the introduction of additional ASE noise. The power introduced into the spans is larger in this case more. Thus, by P minimizing according to expression (2) we find PB, and by maximizing(7) we find PM [4, 7, 10]:

(9)

. (10)

A range of permitted powers allows the maximum number of spans that can be achieved in the coherent system with a given input power, Fig.3.

The width of the operating range of input powers Pmax – Pmin decreases as the number of spans increases [7].

RANGE OF OPERATION OF A BROADBAND DWDM SYSTEM WITH A BANDWIDTH OF 40 AND 200 NM

Using the empirical expressions (2), (9), (10), it is possible to estimate the range of the projected communication system for arbitrary values of the interchannel intervalΔf and the number of channelsK:

, (11)

where m is the previously defined energy margin in the line (m = 1 – no margin, m = 2, margin is 3 dB).

The expression allows to calculate the maximum distance of the N-channel DWDM system. In this case, the reference value of OSNRBTB = 11.9 dB is obtained from previous measurements. The dependences of the number of channels on the amplification band for various values of limiting distance are given in Table 1. For reference, the values of spectral efficiency are given. Spectral efficiency is determined as the ratio of the velocity (in bps) of data transmitted per 1 Hz of the frequency band used. For the studied transmission system (100 Gbps channels), the spectral efficiency is calculated as follows:

, bps/Hz, (12)

where W is the used transmission band, expressed in nm,K is the number of spectral channels.

With an inter-channel interval exceeding 150 GHz, the channel cross-coupling nonlinear effect is negligible and does not change the value of η, according to (4).

When adding new optical channels, the maximum range which can be provided in the given amplification band is determined. If at a given distance between the channels there is no OSNR margin, the distance increases, and the system range is recalculated. Fig. 4 shows the dependences for the optical bands of 40 and 200 nm. The calculations also took into account the OSNR margin.

The calculation shows that when the amplification band of the group signal increases, the capacity of the system increases by a factor of five. The maximum range of the system is 7900 km for the 200 nm band. Thus, the transition from the 40 nm amplification band to the 200 nm band dramatically increases the capacity of the whole system; this is especially strongly reflected when working on short communication lines.

In the experiments conducted earlier, the maximum range of the system was 4000 km for the SMF fiber without dispersion compensators on the line.This value is limited to a maximal chromatic dispersion (70,000 ps/nm), which allows to compensate for the transponder’s available in the product line of "T8 " [8, 9].

CONCLUSIONS

The principle possibility of the DWDM system operating using amplifiers with a band of 200 nm is considered.

A phenomenological model consistent with the experimental data is described and justified, which is convenient for calculating the structure and parameters of communication lines, performed during design work. This model is used to estimate the possibility of increasing the capacity of DWDMlines with 100 Gbps DP-QPSK channels by increasing the operating range of the spectrum (up to 200 nm). It is shown that, taking into account the energy margin of up to 3 dB used in the design, the throughput of DWDM lines up to 2000 km in length can be increased to 75 Tbps. As the range increases, the throughput of DWDM lines decreases, but remains at the level of 15 Tbps at a range of 5000 km.

Thus, the expansion of the working spectral range of fiber-optic communication lines allows to significantly increase their throughput without replacing the existing cable infrastructure. Such an expansion of the operating band of optical amplifiers from the current 40 nm to 200 nm provides a fivefold increase in the bandwidth of fiber-optic links, which prolongs the period of their operation.

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