# Physical Layer Definition for a Long-Haul HF Antarctica to Spain Radio Link
## 4 Physical Layer Tests Analysis
### Modulation Tests
#### 4.4.1 Spread Spectrum Modulations  
Spread spectrum tests were performed first using DS-SS modulation, in order to analyze the throughput and BER of the system versus the length of the PN sequence, the bandwidth and the Energy per Bit to Noise power spectral density ratio (Eb/No) [9]. The results in terms of BER for the several possible combinations are shown in Table 4, whose best results led us to a suitable symbol length which performed properly for all spread spectrum tests. These first results encouraged us to try to improve the bitrate available for that robust modulation, using values of symbol length around the best results obtained in the previous tests (see Table 4). This second study was published in [8] and it used the Signaling and Quasi-Quadriphase approximation for spread spectrum [26]. The Signaling, as described in Section 4.2 (see Figure 11a for a graphical description of the modulation structure), and consists in using a whole family of PN sequences as symbols. The information of the transmission will be contained in the proper sequence by means of a codebook. The receiver has the assigned dictionary available. The Quasi-Quadriphase performs the same way using both in-phase and quadrature components (from now, I and Q components) [26], assuming the IQ components orthogonality and the low cross-correlation of the Gold PN sequences associated to the information [28] (see Figure 11b for a graphical detail of the dictionary structure). Therefore, associating information to both I and Q components, we could almost double the throughput of the Signaling option (the throughput is \(2n-1\) instead of \(n\) bps). The results for these tests are detailed in Table 5. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**PN Length** & **BW** & **Norm Max/Mean (CAZAC)** & **Norm Max/Mean (M)** \\ (chips) & **(Hz)** & **(10\({}^{-3}\))** & **(10\({}^{-3}\))** \\ \hline
2047 & 10 k & 0.346 & 0.363 \\
1023 & 10 k & 0.306 & 0.285 \\
511 & 10 k & 0.747 & 0.677 \\
255 & 10 k & 1.034 & 0.962 \\
2047 & 12 k & 0.392 & 0.331 \\
1023 & 12 k & 0.593 & 0.457 \\
511 & 12 k & 0.830 & 0.678 \\
255 & 12 k & 1.150 & 0.995 \\
2047 & 16 k & 0.386 & 0.396 \\
1023 & 16 k & 0.559 & 0.574 \\
511 & 16 k & 0.831 & 0.842 \\
**255** & **16 k** & **1.200** & **1.244** \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Table with the results of the tests: CAZAC sequences vs m-sequences, bandwidth (BW) of 10 kHz, 12 kHz or 16 kHz, and PN sequence length of 255, 511, 1023 and 2047 chips. The bold results show the best Max/Mean ratios. Table 5 shows us bitrates around a hundred of bits per second with reasonable quality assuming we are working in a hostile channel. These results, with high robustness against the channel variations, fading and noise, will lead us to the design of the physical layer for the hours of the day with low availability: during the daytime. In this sense, the best possible combination for the day transmission found is the 2047 PN length, Gold Sequence, with a bandwidth of 16.6 kHz of bandwidth and 89 bps of bitrate [28], performing in Signaling modulation. \begin{table}
\begin{tabular}{c c c c c c c c c} \hline
**PN seq.** & **BW** & **T** & **Bitrate** & **Spc. Eff.** & **CDF** & **CDF** & **CDF** & **CDF** \\
**Length** & **(kHz)** & **(ms)** & **(bps)** & **(bps/Hz)** & **(10\%)** & **(30\%)** & **(50\%)** & **(70\%)** \\ \hline  
1240 & 0.2490 & 0.3330 & 0.3740 \\ \hline \end{tabular}
\end{table} 
Table 4: Summary of the results for the DS-SS receptions. The bold combinations show the best results in this group of tests. These measures were performed during campaign 2012 (for more details see the operative days in Table 1). Spc. Eff. stands for Spectral Efficiency and it refers to the information rate that can be transmitted over a given bandwidth in a specific communications system, and CDF stands for Cumulative Density Function. Figure 11: Spread spectrum high throughput proposals for a robust transmission [8].