## 4 Data Transmission
### DS-SS proposal  
This section is divided in three parts: (i) an introduction where DS-SS theoretic features are revised, (ii) a second one called DS-SS signaling technique where the method of modulation and demodulation used in this part of the paper is explained and compared with other techniques and finally (iii) a third one called System description and results, where the emitter and the receiver used in this experiment are described as well as the results obtained with this technique. Introduction.On the basis of the sounding results described in [26], the most relevant characteristics of the long-haul ionospheric link between the SAS and Spain are: (i) negative SNR at the receiver site for a signal bandwidth of 3 kHz and the system architecture described in Section 4.1., (ii) dispersion both in time and frequency, (iii) interference. We note that spread spectrum (SS) techniques and more specifically DS-SS are a good alternative to deal with this impairments [30]. SS techniques were first developed in the military field in the middle XXth century. Nowadays it is a principal technology in wireless and mobile communications [31, 32, 33]. The application of SS techniques in ionospheric communications has also been proposed in many papers (see, for example, [35]). DS-SS [34] is a transmission system where the signal uses a bandwidth much larger than the minimum required to send the information. Spreading is achieved by means of a code. At the receiver, a synchronized replica of that code is used to recover the data. Bit rate can be increased by using several spreading codes to transmit different baseband symbols at the same time and frequency. This technique is known as direct sequence code division multiple access (DS-CDMA). In order to maintain the SNR per symbol constant, conventional DS-CDMA systems set the transmit power to be proportional to the number of codes that are multiplexed (assuming that no multiple access interference occurs). However, as previously described the transmission power in our system is fixed. Hence, the more symbols are code multiplexed the less their SNR will be. In general, in a fix-power point-to-point DS-SS based system, the SNR per symbol after despreading can be expressed as  
\[\text{SNR}_{\textbf{d}}=\text{SNR}_{\textbf{rx}}+10\log(\frac{G_{p}}{N_{s}}) \;[\text{dB}] \tag{1}\]  
where \(G_{p}\) is the process gain of the spreading code, \(N_{s}\) is the number of spreading codes that are transmitted within a symbol interval and \(\text{SNR}_{\textbf{rx}}\) is the SNR at the input of the receiver. Note that \(N_{s}=1\)in DS-SS and \(N_{s}>1\) in DS-CDMA, and that (1) is defined assuming that no multiple access interference occurs, that is, the cross-correlation between all spreading codes is zero. The spectral efficiency can be expressed as  
\[\eta=k\cdot\frac{N_{s}}{G_{p}}\ [\text{bits/sec/Hz}] \tag{2}\]  
where \(k\) is the number of bits per symbol and the transmission bandwidth is assumed to be equal to the chip rate, _i.e._, spectral outgrowth due to upsampling is not taken into account. It is interesting to notice that when the transmitted power is fixed both DS-SS and DS-CDMA have the same performance[10], that is, if a certain \(\text{SNR}_{\text{d}}\) is desired both systems achieve the same spectral efficiency. From Equations (1) and (2) it can be observed that an increase in the spectral efficiency can only be achieved at expenses of reducing the SNR per symbol after despreading. This is in fact a major drawback for employing DS-SS/DS-CDMA in low-power skywave communication systems. Note that in such systems the SNR at the input of the receiver is very low (typically negative), therefore to achieve low bit error rate (BER), the spectral efficiency must be low. DS-SS signaling technique.In the Antarctica to Spain HF link, when a transmission bandwidth of 3 kHz is used, the typical SNR at the receiver is \(\text{SNR}_{\text{TX}}=-5\) dB [26]. Preliminary transmissions in [36] suggested that BPSK and \(G_{p}\geq 127\) should be used.