## 2 Materials and Methods
### Universal GNSS Channel Validation
#### 2.2.5 GNSS Test Scenarios
Although BOC(1,1) provides a similar effect than the Manchester code, TMBOC requires further thoughts. In the specific case of GPS L1 Cp, BOC(1,1) and BOC(6,1) are alternatively enabled over a pre-determined 33-chip long sequence; 33 being an integer factor of the 10,230 chip long primary code length. Considering a dual-component channel (processing a total of four sub-carriers), at most 4096 chips can be saved in a 16 kbit RAM. This is insufficient to match the longest primary codes. Hence, a shorten pattern is repeatedly applied based on lower bits of the primary chip address bus, _i.e._, modulo the shorter length. This memory is thus written via a 32-bit data bus, but read four bits at a time. A minimal set is pre-computed prior being repeated to fill out the RAM for future compliance (with the modulo operator %):  
\[\frac{\text{33 chips }\times 4\text{ sub}-\text{carriers}\times 8\text{ repeats}}{\text{32 bits}}=\text{33 memory addresses of pre }-\text{computed pattern} \tag{14}\]  
\[\text{addr}_{\text{TMBOC}}=\text{addr}_{\text{primary code}}\%\text{33} \tag{15}\]  
The resulting enable bits are applied at step 3 of the acquisition process, defined in Section 2.1.2. Other signals are always enabled; the memory being filled with '1'. In terms of the navigation message, CNAV-2 [11] requires a different approach than for CNAV used in both GPS L2C and L5. In fact, synchronization can be achieved on the Bose, Chaudhuri, and Hocquenghem (BCH) encoded 52-symbol Time of Interval (TOI), provided the receiver knows what to expect for the next frame. This prerequisite knowledge can be extrapolated from other signals tracked from the same broadcasted satellite. This approach is preferred over looking for \"non-variable\" data from sub-frame 2 that is both encoded with Low Density Parity Check (LDPC), and interleaved with sub-frame 3 using a 38 rows and 46 columns matrix. Since GPS block III satellites (_i.e._, the first intended to broadcast the modernized GPS L1C signal) scheduled for 2014 [45] have not been launched yet, chronograms were used to show sub-carrier weights in time for the pilot component. GPS L2C  
In the case of GPS L2C, the 10,230 chip-long L2 CM code is to be generated in (nominally) 20 ms, _i.e._, 511.5 chips per ms. To avoid partial chip every other ms, a 2 ms coherent integration approach is used. During acquisition (solely based on L2 CM), 10 such 1023 chip long partial correlations are required to parse the full L2 CM code. This acquisition is performed with a correlator spacing of \(\pm 28\) samples (based on 60 Msample/s), avoiding any effect from the L2 CL spreading code. The resulting search span, involving 20 ms iterations being repeated over the 10,230 different chip alignments and the 31 Doppler bins (each separated by \(2/3\times Tc=333\) Hz), could reach up to 6342.6 s, _i.e._, almost 2 h. To avoid this unacceptable worst case unaided sequential acquisition time, the satellite L1 C/A signal information can be extrapolated, provided its prior acquisition ( the navigation bit transition being aligned with the L2 CM code start), leading to the following set of Equations:  
\[\mathrm{Doppler}_{\mathrm{L2C}}=\frac{\mathrm{L2}}{\mathrm{L1}}\cdot\mathrm{ Doppler}_{\mathrm{L1~{}C/A}} \tag{16}\]  
\[\left\lfloor\frac{c_{\mathrm{L1~{}C/A}}}{2}\right\rfloor=c_{\mathrm{L1 CM}} \%\mathrm{1~{}ms} \tag{17}\]  
\[c_{\mathrm{L2 CM}}=c_{\mathrm{L2 CL}}\%\ 20\ \mathrm{ms} \tag{18}\]  
\[c_{\mathrm{L1~{}C/A}}=c_{\mathrm{L2 CM}}=0 \tag{19}\]  
\[c_{\mathrm{L1~{}C/A}}=c_{\mathrm{L2 CM}}=c_{\mathrm{L2 CL}}=0 \tag{20}\]  
In fact, the universal channels are synchronized with a global 1 ms pulse, allowing for a triggering mechanism to initialize the code generation at any given chip, at a given time stamp. Equation (20) is a simplification as the 1.5 s L2 CL code period starts more often than at the 6 s NAV or 12 s CNAV frames. The CNAV navigation symbols being transmitted at 50 symbol/s, a full L2 CM period must be accumulated to obtain one symbol.