## 2 Data and Methods  
The great challenge of optical networks is to satisfy traffic demand while maintaining or reducing network costs, so for this, not only is it enough to increase capacity, but it is also necessary to improve the general utilization of the width band. A combination of improved transport capacity through higher spectral efficiency and bit rate will be required along with better network utilization, by integrating electrical sub-channel preparation into the transmission system [5]. According to [PERSON], the capacity of a channel communication is the maximum bit rate that can be transmitted without error, taking into account the noise, the available bandwidth and the limit power. This implies using strong error correction codes and that the robustness of the encoding increases as we approach the limit capacity [6]. The capacity is given by the Shannon formula, as observed in the Equation (1). \[C=BLog_{2}(1+\frac{S}{N}), \tag{1}\]  
where:  
_C:_ Represents the maximum capacity of the channel in bps. _B_: Represents the channel bandwidth measured in Hz. _S/N_: Represents the signal to noise ratio [7]. Shannon's Law establishes that the capacity of a system depends on the channel bandwidth and the signal-to-noise ratio. Therefore, a more efficient system with a worse SNR can offer the same performance as a less efficient one, and vice versa [8]. In the case of a dense wavelength division multiplexing (DWDM) system, the performance can be improved by using a wider optical bandwidth, or by increasing the spectral efficiency. For the first option additional amplifiers are usually required so increasing the spectral efficiency is usually the most economical alternative [6]. Thus, spectral efficiency is defined as the maximum achievable bit rate per unit of bandwidth and which will depend on aspects, such as the type of modulation, the propagation regime, the bandwidth occupied by the channel, and the signal ratio to noise; it is measured in bps/Hz, and the higher its value, the better the use of the frequency band used to transmit the data [9; 10]. Equation (2) represents how spectral efficiency is calculated. \[\eta_{[bps/Hz]}=C_{[bps]}/B_{[Hz]}, \tag{2}\]  
where:  
\(\eta_{[bps/Hz]}\): Represents spectral efficiency. \(C_{[bps]}\): Represents capacity. \(B_{[Hz]}\): Represents the bandwidth. In the GNTT Research group of the University of Cauca, in 2019, the work entitled \"Improvement of Spectral Efficiency in DWDM networks at 40 Gbps through the Advanced Modulation Formats DPSK and DQPSK\" was presented, an equation that expresses the spectral efficiency in terms of the capacity that could be provided for the transport of a network. This equation is an adaptation of the theoretical information presented by [PERSON], however, it is important to note that it was presented only for links of a homogeneous type, constant behaviors, and a linear propagation regime, therefore, it presents certain limitations, as heterogeneous networks are the future of optical networks. This information was taken up again in order to address the measurement of spectral efficiency in heterogeneous quasilinear systems in NG-PON network architectures. For an optical system based on wavelength division multiplexing parameters, such as the number of co-propagating channels, the power in the input signal, the spacing per channel, and the propagation regime are handled. Thus, Equation (1) can be expressed as an adaptation to new generation networks, as follows [9]:  
\[C_{1[bits/s]}=B_{ch1}Log_{2}(1+\frac{P_{sct1}}{N_{0}B}), \tag{3}\]  
\[C_{2[bits/s]}=B_{ch2}Log_{2}(1+\frac{P_{sct2}}{N_{0}B}), \tag{4}\]  
where:  
\(P\): Represents the power of each input channel. \(N_{0}\): Represents the noise of the channel. \(B\): Represents the bandwidth  
In which the \(C_{1}\) and \(C_{2}\) channels for transmissions with simple modulations, with only linear-type effects generated by power penalties, differ in their transmission rate.