# Performance Analysis of NR-DCSK Based Copper Cable Model for G.fast Communication
## 5 Discussion and Simulation Results  
To evaluate the performance of NR-DCSK system over copper channel in the presence of impulsive and AWGN noise, a simulation model was developed. Then, the derived analytical results are analyzed. Table 1 lists the parameters of the copper channel based on the Chen model. Figure 5 shows the flowchart of the NR-DCSK system over the copper channel. After entering the initial parameter including \(R\), \(P\), \(\mathcal{L}\), number of frames \(N_{f}\), SNR, and all channel parameters, the reference chaotic sequence is generated. Then, the random bits are generated and passed on the mapping function to obtain the bipolar sequence.The \(i\)th frame data \(b_{i}\) is applied to Equation (1) to produce the NR-DCSK modulated sequence. The received sequence is calculated in the next step according to Equation (8). At the receiver, the receiver sequence is placed on the averaging function and then the variable  
\begin{table}
\begin{tabular}{c c c c} \hline \hline \(\mathbf{K_{1}}\) & \(\mathbf{K_{2}}\) & \(\mathbf{K_{3}}\) & \(\mathbf{L}\) (m) \\ \hline \hline \(4.8\times 10^{-3}\) & \(-1.709\times 10^{-8}\) & \(4.907\times 10^{-5}\) & 1609.344 \\ \hline \hline \end{tabular}
\end{table}
Table 1: Multipath copper channel parameters.  
Figure 4: Channel characteristics for [PERSON] model [32].  
decision is calculated according to Equation (10). Finally, the estimated bits \(\hat{b}_{i}\) is founded using thresholding function.  
Figure 6a,b show the BER performance of a NR-DCSK system over copper channel with \(\beta=200\), \(P=1\), \(5\), \(10\) for \(\gamma=0.05\), \(0.1\), respectively. The plots show the confirmation between the analytical BER expression from Equation (17) and the simulation results. The improvement in the performance of the proposed system is achieved and increases with the \(P\) value, i.e., at \(BER=10^{-3}\), the SNR gain is \(3\) dB when \(P\) increased from \(1\) to \(10\). Note that the NR-DCSK with \(P=1\) represents the conventional DCSK. This improvement is due to the reduction in the power noise by a factor \(P\) according to the averaging process as mentioned in Equation (9). Figure 7a,b illustrate the BER performance of NR-DCSK system over copper channel with \(\beta=600\), \(P=1\), \(5\), \(10\) for \(\gamma=0.05\), \(0.1\), respectively. When comparing Figure 7a,b with Figure 6a,b, it can be noted that increasing \(\beta\) from \(200\) to \(600\) will degrade the performance of NR-DCSK over copper channel by almost \(2\)-\(3\) dB. On the other hand, the effect of increasing \(P\) becomes more evident, i.e., when \(P\) rises from \(1\) to \(10\), the gain was about \(5\) dB. In all the plots, rising \(\gamma\) will affect the performance of the system due to Equation (17) by increasing \(P_{b}^{I}\), and hence the impulsive noise effect appears clearly.  
In Table 2, the SNR gain in dB as a result of applying the NR-DCSK technique is compared to the traditional DCSK system and listed for \(P=5\) and \(10\) and for \(\gamma=0.05\) and \(0.1\). The gain has increased by almost \(3\)-\(4\) dB with respect to increasing \(P\) factor from \(1\) to \(5\). However, increasing \(P\) from \(5\) to \(10\) results in increasing the SNR gain by \(1\) dB.  
Figure 5: Flowchart of the NR-DCSK system over copper channel.  
To demonstrate the effectiveness of the proposed model, we have implemented Low-Density Parity-Check (LDPC) coded NR-DCSK (LDPC-NR-DCSK) to compare the performance with related work. Irregular LDPC code with \(\frac{1}{2}\) rate and DVB-S2 standard with data block of 32,400 bits is used with Sum-Product Algorithm (SPA). Figure 8 shows the performance of the system in [16] with \(\gamma=0.1\) and the performance of the LDPC-NR-DCSK system with \(\gamma=0.1\) for \(\beta=200\) and 600, respectively. The SNR gain was 3 dB and 0.7 dB at BER = \(10^{-4}\) for \(\beta=200\) and 600, respectively.