# SC-FDE Layer for Sensor Networks in Remote Areas Using NVIS Communications
## 2 Background Study
### Sc-Fde  
SC-FDE has the particularity of having the IFFT function in the receiver, which solves the main multicarrier modulation problems (high PAPR and low signal-to-noise ratio). The IFFT is performed at the receiver side together with the FFT [35]. This avoids the need forprecise frequency synchronization and for a linear amplifier. In addition, it has advantages such as having almost constant envelope characteristics, being considered a single carrier, and using a simple equalization as it is performed in the frequency domain [26]. Furthermore, it also maintains some of the advantages such as the integration of Cyclic Prefix (CP), where the multipath effect produced by ionospheric transmissions can be avoided, thus making the transmission more robust. Considering the ionosphere channel results in [36], the CP can be variably designed to fit the channel, resulting in higher efficiency without the need for multiple symbols to avoid multipath. Figure 1 displays a block diagram of the OFDM modulation and the IFFT position change for the SC-FDE implementation. Serial bits are converted to symbols (Mapping), taking into account the modulation order after the parallel conversion. After that, the Cyclic Prefix is added to then convert all the symbols to serial again for transmission purposes. On the receiver side, the CP is removed and the FFT algorithm is applied. Then, the equalization is performed to compensate for the channel effects. Finally, the IFFT is applied along with the serial to parallel conversion in order to obtain the array of bits. In SC-FDE pilot schemes, values have a variation compared with other modulations. For example, OFDM can have a symbol full of pilots (all the subcarriers with the same value). In contrast, SC-FDE needs to have different pilot values due to the FFT, which converts these values to zero. Therefore, the root Zadoff-Chu sequence must be used, which is a sequence that presents different values but in-module are the same value [37]. SC-FDE modulation is noise-sensitive, so the equalization method can be improved by taking noise into account, as well as the effects of the channel. Additionally, the study in [26] showed that other equalization types are better than the ZF. MMSE and Maximum Likelihood (ML) had the best performance. Nevertheless, the research performed in [38] showed that, despite being the one with the best results, the ML method is much more complex in computational terms. Therefore, it is also possible to estimate noise and use (1), which outperforms the (2) method when noise cannot be  
Figure 1: OFDM and SC-FDE schemes. Note the change of IFFT position between OFDM and SC-FDE. considered negligible, although it is not as robust against Inter-symbol Interference (ISI) [39]. H\({}_{\text{est}}\) is the channel effect estimation and \(\sigma^{2}\) is the variance of the noise. \[\text{H}_{\text{mmse}}=\frac{\text{H}_{\text{est}}\text{*}}{(|\text{H}_{\text{ est}}|^{2}\text{+}\sigma^{2})} \tag{1}\]  
\[\text{H}_{\text{zf}}=\frac{1}{\text{H}_{\text{est}}} \tag{2}\]  
As noted above, multicarrier techniques produce peaks due to the division of the channel into subcarriers, which produces a high PAPR value. Many techniques, such as the Crest Factor Reduction (CFR) try to reduce this negative point. This commonly used technique uses different methods to reduce the peaks such as Clipping and Filtering, Peak Windowing, and Peak Cancellation, among others. Clipping is a very good option to reduce the PAPR due to its low computational cost and high effectiveness [40; 41]. It consists of saturating the signal above a fixed threshold called Clipping Ratio (CR). It helps to increase the average power; however, one of its main drawbacks is that it introduces higher nonlinearity, causing out-of-band emissions and interference to the target link. The clipping ratio is calculated in Equation (3) and illustrated in Figure 2. It shows an example of how the signal reacts to this technique. The signal x(n) maintains its value as long as it does not exceed a certain threshold.