## 2 Principe of Proposed End-to-End Optical Fiber System with the Adaboost Algorithm Receiver Design
### The Design of Optical Fiber Simulation Channel  
Similar to Reference [17], we considered the optical unamplified IM/DD link, which is the preferred solution for many low-cost short-range applications. Fiber dispersion and the nonlinearity produced by square-law PD photoelectric conversion are the main limiting factors in this communication channel. Due to the dispersive linear fiber channel model, the influence of a nonlinearity effect on the optical fiber channel is ignored, which means that there will be only inter-symbol crosstalk from the front and back. Therefore, as shown in Figure 1, the communication system on such a channel requires processing the sequence. In this work, we assume that a channel model includes LPF at the transmitter and receiver to reflect current hardware limitations, such as digital-to-analog and analog-to-digitalconverters (DAC/ADC), Mach-Zehnder modulation (MZM), partial discharge, electrically amplified noise, and optical fiber transmission.  
In the simulation channel of Figure 1, the LPF before channel is designed as a 33 MHz low pass filter, which reflected the bandwidth of AWG. Similarly, the LPF after channel is designed as a 33 MHz low pass filter which reflected the bandwidth of the oscilloscope.  
The other simulation channel can be expressed as a formula:  
\[r(t)=\left|\hat{h}\{g\{x(t)+n_{DAC}(t)\}\}\right|^{2}+n_{REC}(t)+n_{ADC}(t). \tag{11}\]  
The \(x(t)\) in the formula means the waveform after the 33 MHz LPF, and we first considered the noise of DAC (detailed description in Section 2.3). All the noise we considered is modeled as a Gaussian noise model. \(\hat{g}(x)\) is modeled as MZM, which is \(\hat{g}(x)=\sin(x)\). MZM in the simulation is designed as a sine function which can express in the range of [\(-\pi/4\), \(\pi/4\)]. The influence of chromatic dispersion in the optical fiber channel on the signal is \(\hat{h}(x)\). The influence of chromatic dispersion is added only in the frequency field; therefore, the time domain signal is converted to the frequency domain and multiplied by a parameter \(H(\omega,z)=\exp\Bigl{(}-j\pi\hat{g}_{2}^{\beta}z\omega^{2}\Bigr{)}\) to represent the effect of dispersion (\(\beta\) means Fiber dispersion parameter, \(z\) means distance length, and \(\omega\) means the angular frequency). Modulo square calculation is expressed as a photoelectric square law conversion. Therefore, the optical fiber is modeled as an intermediate medium that only provides attenuation and dispersion.  
The noise from the DAC/ADC (\(n_{DAC}(t)\) and \(n_{ADC}(t)\)) is modeled as additive and uniformly distributed, which is determined by ENOB (define it as 4). According to the experimental results, we estimate the variance \(\sigma_{r}^{2}\) of the additive white Gaussian noise \(n_{REC}(t)\). As we refer to experiment result, in order to better fit the actual situation, we adjust the Gaussian white noise amplitude to fit different distances. Our channel model includes fiber attenuation; thus, \(\sigma_{r}^{2}\) is changeable as a function of the transmission distance. We apply the value of \(\sigma_{r}^{2}=1.564\times 10^{-3}\) for the examined systems of 25 km. Referring to Reference [17], we made some modifications to the formula as follows:  
\[\sigma_{r}^{2}=3P\cdot 10^{-\frac{602\cdot ENOB+126}{10}}. \tag{12}\]  
As the fiber model includes attenuation (0.17 dB/km), this will yield different effective SNRs at each transmission distance.  
At the same time, due to the influence of dispersion on the channel, the whole system, with the increase of transmission distance, dispersion will seriously affect the bit error rate, so this paper focuses on the long-distance fixed length channel characteristic learning.