## 5 Results and Discussion
### PRIME: Equalizer  
Table 4 collects the results with the alternative spline curve model for the channel estimation of the equalizer. Table 5 represents the incremental results compared to the initial configuration with a polynomial curve published in [10].  
\begin{table}
\begin{tabular}{c c c} \hline \hline  & **Tonemap Used** & **Power Reallocation** \\ \hline Original [10] & ’111111’ & No \\ \hline Tonemap calculation & ’111111’ & No \\ \hline Standard Tonemap & Calculated & No \\ \hline Power reallocation & Calculated & Yes \\ \hline \hline \end{tabular}
\end{table}
Table 3: Simulation parameters and steps for G3-PLC.  
\begin{table}
\begin{tabular}{l c c c c c c c c c c c c c c c c c} \multicolumn{11}{c}{**Header Type B \({}^{*}\)**} & \multicolumn{11}{c}{**Header Type B \({}^{*}\)**} & \multicolumn{11}{c}{**Header Type B \({}^{*}\)**} & \multicolumn{11}{c}{**Header Type B \({}^{*}\)**} \\ \hline Parameter & Robot DPSK & Robot DPSK & DPSK,CC  
As this proposal for PRIME equalization is an implementation option of the receiver, it does not affect the data rate of the transmitted signal. By contrast, the link budget experiences a 1.2 dB improvement.  
As shown in Table 5, schemes without a convolutional encoder do not improve with the proposed new equalizer. The reason is that, despite the improvement of the equalizer, any disturbance affecting the pilot subcarriers introduces errors in the payload, and with no error correction, the reception of the frames fails.  
With respect to the different types of disturbance, for the noise sources with the highest tonal component (ETSI tonal noises and der04, der06), modulations with a convolutional encoder show 6.6 dB improvement in their in-band metrics. This confirms the expectations about the Spline stability described in Section 3.1. By contrast, the average increase in their in-band metrics for these modulations is 0.1 dB in the case of non-tonal noises. Therefore, the subsequent analysis of the equalizer improvement is focused on modulation schemes with convolutional encoder and for the noises with high tonal components, where the performance enhancement is noticeable.  
DBPSK and DQPSK PRIME 1.4 robust modes increment 7.3 dB their link budget for high tonal noises. Similarly, the equivalent non-robust modes with convolutional encoder show a 7.2 dB increase with respect to the implementation of a polynomial equalizer. Therefore, the equalizer performance is independent from the by-4 repetition mechanism. This is because the by-4 repetition is limited to the payload, so that pilot subcarriers used as data input for the equalizer remain untouched between robust and non-robust modes.  
With the spline model, the link budgets of header type B modulations improve 6.9 dB for high tonal noises with convolutional encoder, while header type A modulations improve 6.1 dB. Header type A occupies two OFDM symbols, so it has 26 IQ points for the equalization, while header type B occupies four OFDM symbols, meaning 52 IQ points for the equalizer. The higher the number of the pilot subcarriers, the better the improvement of the spline-based equalizer, although it is non-proportional to the number of pilot subcarriers available.  
Some situations, like the most robust modulations with ETSI periodic impulse, have a link budget decrease of 0.4 dB. This worsening is due to the higher degree of freedom of the spline. This also happens when AWGN is used as a reference, where the required SNR also increases slightly. This is the only drawback identified for this improvement proposal.