## 3 Simulation System and Results Discussion  
### The Establishment of the Simulation System  
To verify the performance of the K-means cluster algorithm applied for the IPM modulation format scheme, the simulation system of a single carrier system for the data center interconnection network was established, as shown in Figure 3. Additionally, the parameters of the system are listed in Table 1. At the transmitter, the iterative polar quantization procedure was run to generate the transmitted initially constellations. We  
Figure 2: The cluster classification result after employing K-means algorithm to 64 QAM; black intersections: ideal constellation points under impacting by NLPN (associated centroids); colored dots: the signals in the cluster associated with the nearest black intersections.  
generate three constellations here, and the order of these constellations \(M\) is equal to 16, 64, 256, respectively. Random pseudo-random binary sequences (PRBS) are generated in MATLAB and sent to the modulator to realize IPM modulation. The modulated signals are shaped by root raised cosine filter, which roll-off factor is equal to 0.25. After pulse shaping, signals are split up into two streams, amplified by electrical amplifiers (EA), and sent to one of the branches of Mach-Zehnder Modulator (MZM). Another branch is driven by External Cavity Laser (ECL), which operates at 1550 nm and its linewidth is 0.1 MHz. Polarization beam splitter (PBS) divide the optical source into two orthogonal polarization beams. Those two orthogonal polarization beams and two streams of data signals interact on MZMs to produce the modulated optical signals combined as optical wave by polarization beam combiner (PBC). Multi-span fiber link consists of recirculation loop, single-mode (SMF) fiber with a length of 100 km, and erbium-doped fiber amplifier (EDFA) with the gain of 20 dB. The main parameters of SMF are chromatic dispersion (CD), attenuation, and nonlinear coefficient, which is equal to 20 ps\(/\)(nm\(\cdot\)km), 0.2 dB/km, and 1.3 \(\left(\mathrm{W}\cdot\mathrm{km}\right)^{-1}\), respectively. At the receiving end, an optical source generated by another ECL drives the balanced photodetector (PD) after 90\({}^{\circ}\) hybrid to complete the process of coherent receiving.  
\begin{table}
\begin{tabular}{c c c} \hline \hline
**Symbol** & **Description** & **Normal Value** \\ \hline \(N\) & Number of symbols & \(10^{5}\) \\ \(R\) & Transmission bit rate & 60 Gbit/s \\ \(r\) & Roll-off factor & 0.25 \\ \(\lambda\) & Wavelength & 1550 nm \\ \(\Delta v\) & Laser linewidth & 0.1 Mhz \\ \(\gamma\) & Nonlinear coefficient & 1.3 \(\left(\mathrm{W}\cdot\mathrm{km}\right)^{-1}\) \\ \(D\) & Chromatic dispersion & 20 ps\(/\)(nm\(\cdot\)km) \\ \(\alpha\) & Attenuation & 0.2 dB/km \\ \(G\) & EDFA gain & 20 dB \\ _Loop_ & Number of spans & 1–10 \\ \(L\) & Span length & 100 km \\ \(M\) & Order of constellation & 16, 64, 256 \\ \hline \hline \end{tabular}
\end{table}
Table 1: The parameters of simulation system.  
Figure 3: Simulation setup of a single carrier system for the data center interconnection network.  
The primary affection influence by SMF in a single carrier system is chromatic dispersion and self-phase modulation. Therefore, we need the offline DSP module to recover signals and calculate the BER. The process of DSP is shown in the block diagram at the bottom of Figure 3, which consists of normalization using Gram-Schmidt orthogonalizing process (GSOP), clock recovery using Gardner algorithm, CD compensation, adaptive equalization using constant modulus algorithm (CMA), and phase recovery using BPS or K-means. The recovery signals are demodulated, and then the MI and BER of the transmission are acquired.