# Physical Layer Definition for a Long-Haul HF Antarctica to Spain Radio Link
## 4 Physical Layer Tests Analysis
### Modulation Tests
#### 4.4.2 Multi-Carrier and Single-Carrier Modulations  
Multi-Carrier modulation schemes have been tested to increase the spectral efficiency in comparison to spread spectrum techniques, and so, to increase the bitrate at a reasonable BER. A first comparison between the DS-SS and OFDM modulation schemes performance was presented in [9] based on real data transmitted from Antarctica to Spain through the HF ionospheric channel. These results encouraged us to do a step forward and propose a single carrier scheme. A modulation scheme based on a single carrier is proposed in [18] to mitigate the drawbacks of PAPR (Peak-to-Average Power Ratio) [32] and ICI (Inter-Channel Interference) presented on the previous works using OFDM [9]. This modulation scheme is known as Single-Carrier Frequency Domain Equalization (SC-FDE) and has a modulator similar to the OFDM, as detailed in [18]. Several parameters have been modified to study the best configuration for the SC-FDE. These parameters are (i) bandwidths of 400, 800, 1250 and 2500 Hz; (ii) block lengths of 10, 30, 50, 70 and 90 ms and (iii) PSK and Quadrature Phase-Shift Keying (QPSK) constellation. An intensive test of this modulation scheme was done in [10] due to the good results obtained in [18], with real analyzed data transmitted from Antarctica to Spain. The best results in terms of CDF of BER of this experiment are shown in Table 6.  
From this test, we can conclude that the modulation scheme that offers a better performance in terms of a trade-off between BER and bitrate is a PSK of 50 ms and a bandwidth of 400 Hz. OFDM used in the initial tests [9] can be replaced by a promising technique known as Single-Carrier Frequency-Division Multiple Access (SC-FDMA), because it is less sensitive to ICI \begin{table}
\begin{tabular}{c c c c c c} \hline \hline \multirow{2}{*}{**Constel.**} & **BW** & **T\({}_{b}\)** & **Bitrate** & **Spec. Eff.** & **CDF (BER)** \\  & **(Hz)** & **(ms)** & **(bps)** & **(bps/Hz)** & **(\textless{}0.05)** \\ \hline PSK & 400 & 10 & 296.3 & 0.74 & 0.54 \\
**PSK** & **400** & **30** & **358.2** & **0.90** & **0.56** \\
**PSK** & **400** & **50** & **373.8** & **0.93** & **0.57** \\ PSK & 400 & 70 & 381.0 & 0.95 & 0.39 \\ PSK & 800 & 10 & 592.6 & 0.74 & 0.40 \\ PSK & 800 & 30 & 716.4 & 0.90 & 0.32 \\ Q-PSK & 400 & 10 & 592.6 & 1.48 & 0.41 \\ Q-PSK & 400 & 30 & 716.4 & 1.79 & 0.42 \\ Q-PSK & 400 & 50 & 747.7 & 1.87 & 0.45 \\ Q-PSK & 400 & 70 & 761.9 & 1.90 & 0.37 \\ \hline \hline \end{tabular}
\end{table} 
Table 6: Selected test results for SC-FDE. More results can be found in [10]. \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline \multirow{2}{*}{**PN Length**} & **T\({}_{s}\)** & **BW** & **Bitrate** & **Modulation** & **BER** & **BER** \\  & **(ms)** & **(kHz)** & **(bps)** & **Scheme** & **(5\%)** & **(10\%)** \\ \hline
**2047** & **123** & **16.6** & **89** & **S** & **0.73** & **0.81** \\
1023 & 123 & 8.3 & 81 & S & 0.66 & 0.79 \\
511 & 127 & 4 & 73 & S & 0.64 & 0.78 \\
2047 & 123 & 16.6 & 162.83 & QQ & 0.56 & 0.66 \\
255 & 127 & 2 & 65 & S & 0.53 & 0.67 \\
511 & 127 & 4 & 125.24 & QQ & 0.49 & 0.57 \\
1023 & 123 & 8.3 & 146.62 & QQ & 0.47 & 0.58 \\ \hline \hline \end{tabular}
\end{table} 
Table 5: CDF (Cumulative Density Function) of the BER results for 5% and 10%, sorted from the best (_i.e._, maximum probability) to the worst results (_i.e._, minimum probability), for Signaling (S) and Quasi-Quadriphase (QQ) modulations in the bandwidth test. The bold results show the best probabilities of reception. and has lower values of PAPR. This technology is based on the OFDM modulator/demodulator, and modified versions of both OFDM and SC-FDMA are compared in [10]. The tests conducted in [10] found a trade-off between the increment of SNR and the Error Vector Magnitude (EVM) to reduce the BER. They took into account several parameter variation for both OFDM and SC-FDMA with IBOs of 1, 4 and 7 dB and 8, 16 and 32 sub-carriers.