## 4 Data Transmission
### OFDM proposal
To do so, the transmitter inserts known pilot symbols in the time-frequency lattice and the receiver estimates the channel at the scattered pilot positions and then interpolates the channel on the data symbol positions. To properly estimate the channel at the data symbol positions, the pilot spacing has to fulfill the Nyquist sampling theorem. This means that the pilot separation in time, \(N_{T}\), and frequency, \(N_{F}\), must fulfill  
\[N_{T}\leq\left\lfloor\frac{1}{2\cdot f_{d}\cdot T_{S}}\right\rfloor\quad\text{ and}\quad N_{F}\leq\left\lfloor\frac{1}{2\cdot\tau_{max}\cdot\Delta_{F}}\right\rfloor \tag{4}\]  
respectively. Where \(f_{d}\) is the Doppler frequency, \(\tau_{max}\) is the maximum delay spread of the channel and \(T_{S}\left(T_{S}=T_{U}+T_{CP}\right)\) is the OFDM symbol time. According to [26], the maximum Doppler frequency expected for this channel is always lower than 1.5 Hz and the maximum delay spread expected is always lower than 2.1 ms. Note that, \(N_{T}\) and \(N_{F}\) can not be arbitrarily low because both power efficiency and throughput are reduced as the pilot density increases. During the 2005-2006 Antarctic survey, the performance of OFDM systems employing different pilot densities (\(N_{T}=5;\ N_{F}=\{2,4,8\}\)) and pilot distributions (rectangular and hexagonal) was evaluated. Table 2 shows the performance in terms of BER for the different experiments, the throughput for each experiment is also stated. As previously discussed, one can observe that BER can be reduced by increasing the pilot density at expenses of reducing the data throughput. Also one can observe that as stated in [39], hexagonal pilot distribution always outperforms rectangular pilot distribution. Figure 6: CDF of the EVM of received symbols gathered from the SAS-OE HF link. OFDM signals were transmitted at frequencies between 4.4 MHz and 17.6 MHz from 21 UTC to 09 UTC, during the 2006–2007 Antarctic survey. **Envelope fluctuations and nonlinear amplification. ** One of the major drawbacks of OFDM is the sensitivity to nonlinear amplification. The OFDM signal is characterized by suffering from large envelope fluctuations, thus, when the time domain signal is fed through a non-linear device (such as the transmitter's power amplifier) a distortion term is introduced that results in out-of-band radiation and increased error probability. The spectral outgrowth is a limiting factor for regulated transmissions where the signal spectrum has to be located below a power spectral mask. However, our communication system is not restricted by any spectral mask and, therefore, only the BER degradation is of importance. To reduce the nonlinear distortion introduced by the transmitter's power amplifier one can set its operating point far from saturation. In that sense the BER degradation caused by the amplifier is reduced as it is operating in a more linear region. However, one should note that, for a given amplifier, setting \begin{table}
\begin{tabular}{c c c c} \hline Pilot distribution & Pilot density & BER without coding & Bit rate (bps) \\ \hline \multirow{3}{*}{Rectangular} & \(N_{F}\) = 8 & 2.9e–2 & 222.6 \\  & \(N_{F}\) = 4 & 1.5e–2 & 193.6 \\  & \(N_{F}\) = 2 & 1.2e–2 & 129.3 \\ \hline \multirow{3}{*}{Hexagonal} & \(N_{F}\) = 8 & 1.6e–2 & 225.6 \\  & \(N_{F}\) = 4 & 1.1e–2 & 194.6 \\ \cline{1-1}  & \(N_{F}\) = 2 & 1.0e–2 & 126.3 \\ \hline \end{tabular}
\end{table} 
Table 2: BER and data throughput with different distribution and pilot spacing in the frequency domain. In time domain, pilot spacing was constant, \(N_{T}=5\). Data was gathered from the SAS-OE skywave link during the 2005-2006 Antarctic survey. Figure 7: CDF of the BER of received symbols gathered from the SAS-OE HF link. OFDM signals were transmitted at frequencies between 4.4 MHz and 17.6 MHz from 21 UTC to 09 UTC, during the 2006–2007 Antarctic survey. the operating point far from saturation means reducing the power of the transmitted signal and, as a result, reducing the SNR at the receiver.