## 2 Software-Defined GNSS Receiver
### BeiDou Signal Acquisition
#### 2.1.1 BeiDou IGSO and MEO Satellites Acquisition  
The traditional coherent acquisition techniques used for GPS L1 C/A signal acquisition cannot directly be applied to acquire BeiDou D1 signal transmitted from IGSO and MEO satellites due to the presence of NH code modulation. The presence of NH code modulation on top of navigation data bits increases the final data bit rate from 50 bps to 1 kHz. Therefore, the sign changes for BeiDou D1 signal occur more frequently than that of a GPS L1 C/A signal due to the presence of NH code. This eventually means that an acquisition scheme for BeiDou D1 signal with more than 1 ms coherent integration period may appear dangerous, if sign information is not consistently preserved. In view of this sign transition problem, a novel acquisition technique is implemented for BeiDou D1 signal that preserves the total useful signal energy in the presence of a sign transition, and hence, makes a correct acquisition decision  
\begin{table}
\begin{tabular}{c c} \hline
**Parameter** & **Value** \\ \hline Intermediate Frequency & 6.5 MHz \\ Front-end Bandwidth & 4.2 MHz \\ Sampling Frequency & 26 MHz \\ Number of Quantization bits & 2 bits \\ \hline \end{tabular}
\end{table}
Table 1: NSL stereo v2 front-End configuration for BeiDou B1I signal reception.  
Figure 1: BeiDou signal spectrum (**Top**); time-domain plot (**Bottom-left**); and bin distribution (**Bottom-right**) of the digitized IF samples.  
on the presence of the satellite, and its carrier Doppler and the corresponding code phase. The working principle of the novel BeiDou D1 acquisition technique, first introduced in [9], is also depicted in the following.  
* For a coherent integration period of \(T_{coh}\) ms, a (\(T_{coh}\times 1000=\)) \(X_{bit}\) number of NH code bits is selected first. For example, for a coherent integration period of 5 ms, the first 5 bits of NH code, _i.e._, [\(-1\)\(-1\)\(-1\)\(-1\)\(-1\)] can be selected. Also, a long incoming BeiDou signal of (\(T_{coh}+19\)) ms is required to carry out the FFT-based acquisition. In case of \(T_{coh}=5\) ms, the acquisition metric will be consisted of 24 ms long incoming signal.
* 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 5 ms integration time, the frequency bin size should be less than or equal to 133.33 Hz.
* The chosen \(X_{bit}\) long NH code sequence is then multiplied with the locally generated BeiDou PRN codes in order to form an \(X_{bit}\) long NH-code-modulated-PRN-code-cycle.
* An FFT-based correlation is then performed on each \(T_{coh}\) ms blocks of incoming BeiDou signal with the locally generated \(X_{bit}\) long NH-code-modulated-PRN-code-cycles (_i.e._, the output of Step 3 with an incoming signal index increment of 1. An example on how the incoming BeiDou D1 signal is structured for acquisition is shown in Figure 2 below for a coherent integration period of \(T_{coh}=5\) ms.
* As the NH code length is 20 bits, there are altogether 20 chunks of correlation matrices with all possible code delay and carrier Doppler combinations for a specific BeiDou satellite. The winning index is the one which has the maximum correlation peak as shown in Figure 3. Therefore, this winning NH index can 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.
* 24 ms long incoming BeiDou signal is structured into 20 chunks of 5 ms long block with an index increment of 1.  
Figure 2: 24 ms long incoming BeiDou signal is structured into 20 chunks of 5 ms long block with an index increment of 1.