## 2 Data and Methods
As long as the linear and non-linear correlation of the propagating channels affect the medium; and only considering the response of the linear type and defining that the relation \(N_{0}\) does not depend on the change in the wavelength of the channel and maintaining the same output power for the \(\varepsilon\) multiplexed channels of type \(i\) and the \(\varphi\) multiplexed channels of type \(j\); the net capacity of the system will be given in terms of Equation (5) [9]:  
\[C_{tot[bits/s]}=(\sum_{i=1}^{\varepsilon}B_{chi}+\sum_{j=1}^{\varphi}B_{chj}) \ Log_{2}(1+\frac{P_{s-ch}}{N_{0}B}). \tag{5}\]  
The limit of spectral efficiency can be calculated, if the bandwidth of the occupied channels is less than the spacing of the adjacent channels, which means it is necessary that the lateral bandwidth of each of the spectra symmetrical propagating in the middle is contained within the spacing implemented in the DWDM system. Thus, the spectral efficiency would be given by Equation (6). \[\eta_{bps/Hz}=\frac{(C_{OCH1[\frac{bits}{s}]}+C_{OCH2[\frac{bits}{s}]})}{( \frac{B_{OCH1[Hz]}}{2}+\frac{B_{OC2[Hz]}}{2})+\Delta_{\varphi}[Hz]}. \tag{6}\]  
If it is desired to decrease the spacing of adjacent channels to a limit in which intersymbolic interference is not generated depending on the type of modulation and the propagation regime, the maximum total efficiency of a system that implements multiple channels would be represented by [9]:  
\[\eta_{max(\frac{bps}{Hz})}=\frac{\sum_{i=1}^{\varepsilon}B_{chi}Log_{2}\left( 1+\frac{P_{s-chi}}{N_{0}B}\right)+\sum_{j=1}^{\varphi}B_{chj}Log_{2}\left(1+ \frac{P_{s-chj}}{N_{0}B}\right)}{\left(\frac{B_{CH[Hz]}+B_{CH[Hz]}}{2}\right)+ (N-1)\Delta_{\varphi}}, \tag{7}\]  
Whose measurement and control variables correspond to:\(\mathrm{C_{N}}\) (Nominal capacity per wavelength): It is presented as the net binary capacity propagated at the access level. \(\mathrm{C_{Total}}\) (Total capacity of the co-propagating system): It is presented as the sum of the individual capacities of the propagated channels. \(\mathrm{C_{Pro}}\) (Information propagation capacity per kilometer): It is presented as the relationship between the amount of information and the propagated distance. \(\mathrm{\eta_{ded}}\) (Dedicated spectral efficiency per wavelength): It is presented as a net relationship between the nominal capacity and the occupied bandwidth. \((N-1)_{\Delta v}\) (Optical spacing of adjacent channels). \(\mathrm{\eta_{dist}}\) (Theoretical Distributed Spectral Efficiency of the system): It is presented as a ratio of the total capacity generated in the system vs. the optical spacing. \(\mathrm{\eta_{dis}}\) (Analytical distributed spectral efficiency throughout the system): it is presented as a relation of Equation (5) between the total capacity vs. the real occupied spectrum and the maximum allowable SNR relation [9]. Where, the total capacity of the system is divided over half the lower bandwidth occupied by the first optical channel of the spectral grid (lower frequency), plus half the upper bandwidth occupied by the last optical channel of the spectral grid (higher frequency), plus the channel spacing represented as \((N-1)\Delta_{v}\) (\(N\) frequency shifts) [9]. As can be seen in Figure 1, all of the parameters described in Equation (7) are related, so it is possible to manipulate these factors in order to improve spectral efficiency. Equation (7) was used to define the behavior of the spectral efficiency in a quasilinear system for a network with a heterogeneous architecture of NG-PON type. Table 1 shows the variables to be used in the proposed model. Future networks require high speeds, such as 100 Gbps. To transport a large amount of traffic, these networks are affected by degradations that alter the scope of the optical distance, require expensive equipment to offer long distances or, failing that, a greater number of regenerators, which translates into expenses.