## 2 Software-Defined GNSS Receiver
### BeiDou Signal Acquisition
#### 2.1.2 BeiDou GEO Satellites Acquisition  
In case of BeiDou GEO satellites which transmit D2 navigation signal, there is no NH code modulation on top of the data bits. But, D2 signal has a data bit rate of 500 bps, meaning that each data bit will last for 2 ms. Therefore, the bit transition in case of BeiDou D2 signal may occur after every 2 ms unlike the GPS L1 C/A signal, where the bit transition may occur only after 20 ms. In view of this much frequent sign transition occurrences, a similar strategy like D1 signal acquisition technique is implemented for BeiDou D2 signal. The implementation strategy for D2 signal acquisition is described in the following.  
* The chosen number of coherent integration summation should be even (_i.e.,_ multiple of 2 due to the bit interval duration of D2 signal).
* For a coherent integration period of \(T_{coh}\) ms (which is chosen as even), a (((\(T_{coh}\))/2) \(\times\) 1000 \(=)\)\(X_{bit}\) number of data bits is selected first. For example, for a coherent integration period of 4 ms, the number of data bits, \(X_{bit}\) = 2. In case of \(X_{bit}\) = 2, all possible combinations for incoming data bits will be \(2^{Xbit}\) = 4. Therefore, there will be four possibilities for incoming received data bits, which are: [+1 +1], [+1 -1], [-1 +1], and [+1 +1].
* The frequency resolution is chosen such that the frequency bin size is less than \((2/3)\times T_{coh}\), where \(T_{coh}\) is the coherent integration time. In case of a 4 ms integration time, the frequency bin size should be less than or equal to 166.67 Hz.
* Each of the \(2^{X_{bit}}\) data-bit set is then multiplied with the locally generated BeiDou PRN codes in order to form a \(T_{coh}\) ms long data-modulated-PRN-code-cycles. It is important to note here that while forming the data-modulated-PRN-code-cycles, the data bits are hold such that they match the locally generated PRN code chip rate. In other words, the data bits are hold such that 1 data bit lasts for 2 ms, as is the case for BeiDou D2 signal.
* An FFT-based correlation is then performed on each of the possible \(2^{X_{bit}}\) data-bit combinations of the incoming BeiDou signal with the locally generated \(T_{coh}\) ms long data-modulated-PRN-code-cycles (_i.e.,_ the output of Step 4).  
Figure 3: Acquisition correlation peaks for different NH indices.  
* As the data-bit set length is \(2^{X_{bit}}\), there will be altogether \(2^{X_{bit}}\) chunks of correlation matrices with all possible code delay and carrier Doppler combinations for a specific BeiDou GEO satellite. The winning index is the one which has the maximum correlation peak, and therefore, it can then be used for detecting the presence of the satellite, along with the estimation of the carrier Doppler and the code phase via a pre-detection threshold computed against a certain probability of false alarm.  
The resultant acquisition metric after utilizing the above two acquisition strategies for BeiDou IGSO/MEO and GEO satellites is shown in Figure 4. BeiDou PRNs 05 (GEO); 07, 09, 10 (IGSO); 11, 13, 14 (MEO) were acquired successfully, which were in view with \(10^{0}\) or more elevation angle at the time of data collection in Finnish Geodetic Institute, Finland.