# Performance Comparisons of Broadband Power Line Communication Technologies
## 3 Bit Rate and Power Spectrum Comparisons
For modulations, HPGP uses coherent QPSK in all three modes. Coherent QPSK is also used for Normal DF and Mini DF of IoT PLC. Normal DF also uses coherent 16 QAM and noncoherent \(\pi/4\)-DQPSK. HS PLC uses noncoherent modulation methods. In NORMAL mode, DBPSK, DQPSK, or D8 PSK is used depending on the channel conditions. Information about the used subcarrier modulations is transmitted in the form of TM. D8 PSK can transmit 3 bits per subcarrier, but it is more susceptible to noise than DBPSK and DQPSK. DV and EDV modes use DBPSK, which is the most robust against noise and distortions among the three differential modulations. For IoT PLC, the transmission rate is given as follows. \[R_{IoT}=\frac{1}{T_{s}}\times N^{\prime}_{tone}\times N_{bpt}\times R_{ FEC}\times\frac{1}{DV_{n}}\times\frac{4N}{4N+N_{pad}}(bps), \tag{2}\]  
where \(T_{s}\) and \(R_{ FEC}\) represent the symbol period and rate of the FEC, respectively. The results for the transmission rate are shown in Table 3. In IoT PLC, \(R_{ FEC}=1/2\). The values of \(N^{\prime}_{tone}\) and \(N_{pad}\) depend on \(N_{tone}\) and \(DV_{n}\). Although \(N^{\prime}_{tone}\) is not equal to \(N_{tone}\), the difference between the two values is small. In addition, the number of padding bits, \(N_{pad}\), is not large compared to \(4N\). Thus, Equation (2) can be approximated as follows. \[R=\frac{1}{T_{s}}\times N_{tone}\times N_{bpt}\times R_{ FEC}\times\frac{1}{DV_{n}}(bps). \tag{3}\]  
Note that the values of \(T_{s}\), \(N_{tone}\), \(N_{bpt}\), and \(DV_{n}\) are found in the specifications. Thus, with Equation (3), the transmission rate can be easily obtained. In addition, Equation (3) can also be applied to obtain the transmission rate for HPGP and HS PLC. The results for transmission rate obtained by Equation (2) at each \(DV_{n}\) are given Figure 9 when \(N_{tone}=800\) and \(N=1440\). In this figure, the results with Equation (3) are also provided for comparison. \(N_{bpt}\) can be 2 or 4 for IoT PLC. In Figure 9, the approximated results agree well with the results from Equation (2) except for the cases of small \(DV_{n}\). Specifically, when \(N_{bpt}=2\) and \(DV_{n}\geq 3\), the difference  
\begin{table}
\begin{tabular}{c c c c c c c c c} \hline \hline  & \multicolumn{2}{c}{**IoT PLC**} & \multicolumn{2}{c}{**HPGP**} & \multicolumn{2}{c}{**HS PLC**} \\ \hline
**Mode** & **Normal DF** & **Mini DF** & **STD** & **HS** & **MINI** & **NORMAL** & **EDV** & **DV** \\ \hline Freq. bands (MHz) & 2-28 & 2-28 & 2-28 & 2-28 & 2-28 & 4-23 & 4-23 & 4-23 \\ \hline IFFT size & 2560 & 2560 & 3072 & 3072 & 3072 & 512 & 512 & 512 \\ \hline Number of subcarriers in use & 800 & 800 & 916 & 916 & 915 & 152 & 152 & 124 \\ \hline \(f_{s}\) (MHz) & 62.5 & 62.5 & 75 & 75 & 75 & 50 & 50 & 50 \\ \hline Subcarrier spacing (kHz) & 24.41 & 24.41 & 12.21 & 12.21 & 12.21 & 97.66 & 97.66 & 97.66 \\ \hline Symbol period (\(\upmu\)s) &  
due to the approximation is almost negligible. When \(N_{bpt}=4\) and \(DV_{n}\geq 5\), the difference due to the approximation is also almost negligible. For HPGP, \(N_{bpt}=2\) and \(R_{FEC}=1/2\), regardless of the operating modes. The symbol period \(T_{s}\) and the number of subcarriers in use \(N_{tone}\) are shown in Table 2. The diversity number is shown in Table 1. Padding bits are also used in HPGP. Using Equation (2), the transmission rates are obtained and are shown in Table 4. The approximate transmission rates using Equation (3) are also obtained and shown in parentheses. The results of the transmission rates are shown in Figure 9 for comparison. In the NORMAL mode of HS PLC, the transmission rate varies according to the TM and the rate of the FEC, which can be set by the software or operator. We choose the maximum value of \(R_{FEC}\) for convenience, which is equal to \((239/255)\times(3/4)\). In addition, \(N_{bpt}\) changes with the modulation method determined by the TM. Likewise, we choose the maximum value of 3 for \(N_{bpt}\). Thus, the transmission rate obtained for the NORMAL mode is the maximum that the mode can achieve.