# Simulation of a Narrowband Power Line Communications System over Medium Voltage
## 5 Simulation Results and Discussion
### Maximum Reach of NB-PLC Signals via the MV Grid  
As already mentioned, the primary motivation of this work is to determine the maximum distance between repeaters, say \(D_{max}\), of an NB-PLC system destined for transferring low rate data via non-branched MV power lines. If such a distance is sufficiently large, a smaller number of repeaters will be necessary to transfer low rate SG data from remote nodes on the MV grid--usually in rural and/or remote areas--making such a data transmission technically easier and economically affordable. Here, \(D_{max}\) is determined for various target BER levels at the receiver input employing either F-OFDM or W-OFDM. Figure 6a,b show the dependence of BER on \(D_{max}\) when 2-QAM or 4-QAM is employed, respectively. The use of 8-QAM yields BER levels that exceed \(10^{-1}\). As a result, the corresponding curves are not presented. The numerical procedure followed to obtain Figure 6 consists of generating a random bit stream at the transmitter, transforming it into an OFDM band-pass signal, and subsequently transmitting it via the simulated NB-PLC channel. After OFDM demodulation, the decoded bit stream is compared to the transmitted one to determine the BER at the receiver output as a function of the input SNR and end-to-end PLC distance. Figure 5: Spectrum of (**a**) F-OFDM and (**b**) W-OFDM signals at the transmitter and the receiver. Figure 6: \(D_{max}\) for various input SNR levels using (**a**) 2-QAM and (**b**) 4-QAM (F = F-OFDM, W = W-OFDM). Figure 6 can be used to determine \(D_{max}\), given the target BER at the receiver which is determined by the specifications of a particular SG service. As switching and monitoring are critical network operations that are not subjected to stringent requirements neither with regard to BER nor to latency, the results of Figure 6 reveal that NB-PLC can be employed to transfer the relevant SG data across remote MV grids. It is also evident that F-OFDM is capable of transmitting NB-PLC signals to significantly greater distances than W-OFDM. In fact, for target BER levels in the range \(10^{-5}\)-\(10^{-3}\), F-OFDM achieves \(D_{max}\) values ranging from 2350 m up to 2450 m using 2-QAM or in the range of 1150 m up to 1200 m using 4-QAM. The corresponding ranges when W-OFDM is employed are 1400 m (for input SNR = 7.5 dB, target BER = \(10^{-5}\)) up to 1850 m (for input SNR = 20 dB, target BER = \(10^{-3}\)) and 600 m (input SNR = 7.5 dB, target BER = \(10^{-5}\)) up to 1000 m (input SNR = 20 dB, target BER = \(10^{-3}\)), respectively. F-OFDM offers a clear transmission range advantage over W-OFDM of at least 500 m (using 2-QAM) or of at least 150 m (using 4-QAM). It should be noted that, to obtain the BER results plotted in Figure 6, no use of forward error correction (FEC) has been made. Enhancing NB-PLC transmission with FEC encoding will result in larger \(D_{max}\) values for both F-OFDM and W-OFDM. Furthermore, as shown by the very small dispersion of the BER curves plotted for various input SNR levels, Figure 6 reveals that the BER performance of F-OFDM when employed for NB-PLC transmission over MV power lines is primarily affected by the distance rather than the noise levels. This is not the case when W-OFDM is employed, as the relevant BER curves are significantly differentiated when the input SNR varies. The less adverse effect of noise on F-OFDM signals compared to W-OFDM ones is attributed to the enhanced spectral confinement of the former signals in the NB-PLC frequency range. In addition, due to the spectral confinement of F-OFDM signals, LPF operations at the receiver do not cause significant distortion to the signal. The results obtained imply that it would be beneficial to extend NB-PLC operation up to 450 kHz, as this could offer enhanced SG capabilities over remote MV grids. Therefore, European authorities should consider either licensing or open use of the 148.5-450 kHz spectrum for NB-PLC. In addition, the results obtained may prove very useful for the design of NB-PLC systems over the MV grid.