Joint channel power and amplifier gain optimization in coherent DWDM systems
Graphical abstract
Introduction
Optical networks have formed the backbone of the internet. Enormous growth in the demand for high data rate has led to the capacity crunch [1]. To tackle this capacity shortage, power optimization subject to maximizing the achievable rate [2], [3], space-division multiplexing [4], [5], [6], and elastic optical networks can be considered as the most promising solutions. Elastic optical networks bring some obvious benefits such as spectral- and energy-efficient traffic grooming [7]. Spectral efficiency is also improved by using advanced modulation formats, e.g., polarization multiplexed M-ary quadrature amplitude modulation (PM-M-QAM), for M=4, 8, 16, 32, 64, 128, and 256. Recently, the de-aggregation of 16-QAM to 4-level pulse amplitude modulation was experimentally performed in [8], which can be used to optimize spectral usage. The most overriding factor that restricts the capacity of the optical networks is Kerr nonlinearity [9].
Finding efficient ways to predict the performance degradation due to the Kerr nonlinearity is then of key importance for modern design of dense wavelength division multiplexing (DWDM) optical networks. Brute-force numerical approaches such as the split-step Fourier method to solve the nonlinear Schrödinger equation are not a viable option due to the high computational complexity caused by the wide transmission bandwidth considered. On the other hand, many approximated analytical models for nonlinear fiber propagation in the time and frequency domain are currently available in the literature [10], [11], [12], [13], [14], [15]. Such analytical models are key enablers of physical layer network optimization [16], [17], [18], [19], [20], [21], [22]. The authors of [17] proposed joint power allocation, routing, and wavelength assignment using the enhanced Gaussian noise model [14]. Among the others, the Gaussian noise (GN) model [12], [23] have risen to popularity due to their broad applications and relative simplicity.
Exploiting the GN models has opened up a new horizon in optimizing routing, wavelength assignment, modulation level, channel coding, and power allocation in the planning of coherent polarization-multiplexed optical networks [18], [24], [25], [26], to maximize the minimum received SNR or the network’s total achievable rate. It has been shown that the remarkable saving in capital expenditure can be obtained by power optimization for different modulation formats [27] and matching transmission equipment to network demand [28]. Using the GN model, resource allocation is optimized in elastic optical networks with the objective of minimizing the maximum bandwidth usage [29]. The same authors jointly optimize the routing, spectrum, modulation format, and power spectral density per connection in elastic optical networks [30]. Power optimization is also performed considering either a single flat (equal) launch power over all channels or individual different power values for different channels in [18], where maximizing the achievable rate and minimum margin of SNR is the objective function of the optimization. In [31], the limitation of electrical power available to the undersea optical amplifiers has been modeled in the channel powers optimization in long-haul coherent DWDM systems. The authors of [31] not only imposed the undersea power constraint and allowed gains to vary, but also accurately modeled amplifier physics including power saturation
In all the aforementioned studies (except [31]) the amplifier gains are fixed and set based on the loss of fiber spans. In addition, the power saturation of optical amplifier has not been modeled. In this paper, we propose to jointly optimize channel powers and amplifier gains, and also include the power saturation, gain tilt and ripple, and noise figure non-flatness of optical amplifiers in the optimization problem. Furthermore, in our system model a fiber link with multiple different spans (i.e., spans with different lengths or fiber types) is considered, which is more practical. We will show that the joint optimization of channel powers and amplifier gains results in higher SNR, compared with the conventional channel power optimization methods.
The rest of the paper is organized as follows. In Section 2, the system model is described. The SNR estimation based on the GN model is presented in Section 3. The proposed optimization problem is formulated in Section 4. Numerical results are presented in Section 5, and the paper is concluded in Section 6.
Section snippets
System model
We consider a long-haul fiber-optic communication system based on coherent DWDM technology, in which Nyquist rectangular spectral shape channels with bandwidth are transmitted over fiber spans. The lengths of spans can be different, where (km) indicates the length of span , and the total length (L) of fiber link is . Let , , and denote the power at the input of th span, symbol rate, and central frequency of th channel, respectively, and indicates the total
Estimating the power of NLI noise
We utilize incoherent approximation of the GN model, referred to as incoherent GN (IGN) [32], to estimate NLI noise imposed by Kerr effect. In the GN model, four-wave mixing (FWM) among all DWDM channels are categorized into three types [33]: (i) self-channel interference (SCI), (ii) cross-channel interference (XCI), and (iii) multi-channel interference (MCI), where SCI is intra-channel NLI, and XCI and MCI are inter-channel NLIs. The total power of NLI noise () is obtained by adding the
Problem formulation
In this section, we formulate the power and gain optimization problem with objective of maximizing minimum SNR margin, where SNR margin indicates the difference of SNR and required SNR () in logarithmic representation.
In the former section, we showed that is a function of input power of all channels and gains of amplifiers, and is a function of gains of amplifiers. Accordingly, is a function of input powers and gains of amplifiers. Let indicate a matrix which its
Numerical results
We solve the proposed optimization problem, referred to as joint power and gain optimization (JPGO), and compare it with its conventional alternative [3], referred to as optimized power and fixed gain (OP-FG). In OP-FG, amplifier gains are set based on the span loss, , and channel powers are obtained by solving the optimization problem proposed in [3].
In all numerical results, unless specified, we assume that , , =80 km, =50 GHz, dBm, =30 dB, =20
Conclusion
In this paper, we formulated the problem of joint channel powers and amplifier gains optimization in coherent DWDM systems as a convex optimization. Furthermore, we optimized a fiber link with multiple different spans and modeled the practical limitations of optical amplifiers such as output power saturation, maximum gain limitation, gain tilt and ripple, and noise figure non-flatness. We showed that in a 5-span fiber link with span length of 80 km (100 km) the proposed method leads to 1 dB
CRediT authorship contribution statement
R. Hashemi: Conceptualization, Methodology, Software, Writing - some part of original draft. H. Beyranvand: Conceptualization, Methodology, Writing - some part of original draft. H. Rabbani: Data curation, Methodology, Writing - some part of original draft.
Declaration of Competing Interest
The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.
Acknowledgment
This work was supported in part by Iran National Science Foundation (INSF) .
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