## 1 Introduction
### Survey of GNSS Signals and Receiver Architectures
#### 1.1.1 GNSS Signal Description  
GNSS signals have undergone a noticeable evolution, multiplying constellations and signal definitions using new frequency bands, modulations as well as primary/secondary spreading code types, rates and periods. Global satellite-based navigation signals, with both open and restricted access on all frequency bands, are summarized in Table 1, where modulation families (detailed below) can be described as Binary or Quadrature Phase Shift Keying BPSK (\(q\)) or QPSK (\(q\)), Binary Offset Carrier BOC (\(p,q\)), Composite BOC CBOC (\(r,\ p,\ P_{r},\pm\)) and Time-Multiplexed BOC TMBOC (\(r,\ p,\ w_{r}\)), where:  
\(f_{\text{ref}}\) is the reference chipping rate, _i.e._, 1.023 Mchip/s,  
\(f_{\text{c}}\) is the current chipping rate, defined as \(q\cdot f_{\text{ref}}\),  
\(f_{\text{s1}}\) is the first sub-carrier rate, defined as \(p\cdot f_{\text{ref}}\) and  
\(f_{\text{s2}}\) is the second sub-carrier rate, defined as \(r\cdot f_{\text{ref}}\),  
\(P_{r}\) is the second sub-carrier power ratio, _i.e._, 1/11,  
\(w_{r}\) is the second sub-carrier weight, in terms of an occurrence ratio, _i.e._, 4/33.  
The last parameter of CBOC refers to the sign of the second sub-carrier compared to that of the first; in CBOC, data and pilot components are in phase opposition. From Table 1, one notices that GLONASS current signals are based on Frequency Division Multiplexing Access (FDMA), while modern ones will rely on Code Division Multiplexing Access (CDMA). New GLONASS and BeiDou signals are yet to be fully publically disclosed to fill out missing details. Also, GPS L2C TMBPSK modulation is based on two alternating 511.5 kchip/s spreading codes, _i.e._, 20 ms long CM and 1.5 s long CL, resulting in a merged stream of 1.023 Mchip/s.  
Current signals and those to come have different colors; yellow cells identify memory codes.  
The Mean Time To Acquire (MTTA) in Table 1 is computed per the worst case scenario represented by Equation (1) [9]:  
\[MTTA=\frac{\left(2-P_{D}\right)\left(1+K\cdot P_{FA}\right)}{2P_{D}}b\cdot M \cdot T_{P} \tag{1}\]  
where:  
\(P_{D}\): is the detection probability (assumed at 0.995)  
\(P_{FA}\): is the false alarm probability, _i.e._, a false positive (assumed at 0.001)  
\(K\): is the false alarm weight (assumed at 2)  
\(b\): is the number of search cells (combining code with 0.5 chip resolution and \(\pm\)5 kHz Doppler span)  
\(M\): is the non-coherent integration count (assumed at 1)  
\(T_{P}\): is the pre-integration time (assumed to match primary code period)  
In the case of the GPS L1 C/A signal, there could be 2046 code bins and 15 frequency bins, each spaced by 667 Hz assuming 1 ms integration and covering a \(\pm\)5 kHz Doppler span. This sequential acquisition scheme would result in a total of \(b=30,690\) search cells. In Table 1, MTTA is applied to both primary and secondary spreading codes, although secondary code could be extrapolated from the message time stamp instead of being searched. To sum up the review of GNSS signals, there are 291 civil GNSS RF signal components (_i.e._, considering both data and pilot components) currently available worldwide: six signal components on 32 GPS satellites + 2 \(\times\) 24 for GLONASS + 6 \(\times\) 6 for Galileo + 3 \(\times\) 5 for BeiDou, as listed in Table 1, half of those could be visible to any ground user. Hence, in order to harvest this signal power to maximize global robustness and precision, reducing receivers' total complexity and reusing as many resources as possible becomes more than desirable. The number of signal components available will increase to more than 530 as the new satellite constellations are deployed, on top of the local and augmentation signals...