## 4 Data Transmission
### OFDM proposal  
The principle of OFDM is to divide a high data rate stream onto several parallel streams with lower data rate such that each sub-stream is associated with a given subcarrier. The main advantage of this concept is that each of the data streams experiences a flat fading channel, even though the overall channel is frequency selective. This means that no complex equalization at the receiver is necessary. Another advantage is that intersymbol interference (ISI) can be easily avoided by just introducing a cyclic prefix before each OFDM symbol [38]. One of the major drawbacks of OFDM is that it suffers from large peak-to-average power ratio (PAPR), which might be a major inconvenience for low power communications in long-haul ionospheric links. In the reminder of this section we present some preliminary research outcomes that try to study the feasibility of using OFDM to implement the physical layer of this long-haul HF link. Table 1 summarizes the default OFDM parameters value used throughout the experiments. Figure 5: Experimental results using the following configuration: BW = 3125 Hz, 64-ary DS-SS, QPSK and rate 1/3 turbo coding. Every cross corresponds to a demodulated frame. A 3 dB loss of SNR is observed when comparing experimental and theoretical results. **OFDM symbol design. ** One of the first aspects to clarify when designing an OFDM system is the length of the OFDM symbol and the subcarrier spacing. Since the subcarrier spacing is the inverse of the useful part of the OFDM symbol, the shorter the symbol length is the wider each subcarrier will be. Consequently the probability that each subcarrier experiences a non-flat fading increases. On the other hand, making the subcarrier spacing small to assure flat fading results in long OFDM symbols. The multipath fading channel is not constant in time, thus having very large OFDM symbols is not desirable or otherwise the channel will not be constant within an OFDM symbol. To correctly design the OFDM symbol, one must take into account the coherence time of the channel, delay spread and thus coherence bandwidth of the channel. In the following, a study of the OFDM symbol design in the system performance is presented. System performance is determined by means of the error vector magnitude (EVM) of the received symbols. EVM is defined as  
\[EVM=\sqrt{\frac{P_{error}}{P_{reference}}} \tag{3}\]  
where \(P_{error}\) is the mean-squared error between the received constellation points and the ideally received constellation points, and \(P_{reference}\) is the power of the outermost ideal constellation point. Figure 6 shows the cumulative density function (CDF) of EVM of real OFDM transmissions in the skywave link between the SAS and the OE. Bursts of OFDM symbols of length ranging from 10 ms to 60 ms were consecutively transmitted during several nights. As already expected, OFDM systems with too large (50, 60 ms) and too low (10 ms) symbol lengths, result in poor performance, while OFDM systems designed according to the channel characteristics (symbol lengths of 20, 30 and 40 ms) result in better performance. \begin{table}
\begin{tabular}{|c|c|} \hline Useful symbol length & \(T_{U}=\,30\) ms \\ \hline Cyclic prefix length & \(T_{CP}=\,2.8\) ms \\ \hline Number of subcarriers & \(N_{C}=\,16\) \\ \hline Frequency pilot separation & \(N_{F}=\,8\) \\ \hline Time pilot separation & \(N_{T}=\,5\) \\ \hline Channel estimation method & Least squares \\ \hline Interpolation method & Cubic splines \\ \hline Input back off & 3 dB \\ \hline Modulation & Binary Phase Shift Keying (BPSK) \\ \hline Error correction code & Convolutional (code rate = \(\frac{1}{2}\), \\  & constraint length = 7) \\ \hline \end{tabular}
\end{table} 
Table 1: Default OFDM parameters value. **Channel estimation. ** The next aspect to determine is the pilot insertion pattern for channel estimation. A correct detection of coherent OFDM systems requires that the receiver knows the amplitude and phase distortions introduced by the channel at each subcarrier.