function of GPS C/A code and cellular CDMA PN sequence according to the cdma2000 standard (Khalife et al. [12]).
Source: Reproduced with permission of IEEE.
In a GPS receiver, the pseudorange is calculated based on the time a navigation message subframe begins, which eliminates ambiguities due to the relative distance between GPS SVs [55]. This necessitates decoding the navigation message in order to detect the start of a subframe. These ambiguities do not exist in a cellular CDMA system. This follows from the fact that a PN offset of one translates to a distance greater than 15 km between BTSs, which is beyond the size of a typical cell [56].
Finally, the pseudorange estimate ρ can be deduced by multiplying the code start time by the speed of light c; that is,
Figure 38.14 shows the intermediate signals produced within the tracking loops of the cellular CDMA navigation receiver: code error; phase error; Doppler frequency; early, prompt, and late correlations; pseudorange; and in‐phase and quadrature components of the correlation.
38.5.2.4 Message Decoding
Demodulating the sync and paging channel signals is performed similarly to the pilot signal but with two major differences: (i) the locally generated PN sequence is furthermore spread by the corresponding Walsh code and (ii) the subaccumulation period is bounded by the data symbol interval. In contrast to GPS signals, in which a data bit stretches over 20 C/A codes, a sync data symbol comprises only 256 PN chips, and a paging channel data symbol comprises 128 chips. After carrier wipe‐off, the sync and paging signals are processed in the reverse order of the steps illustrated in Figures 38.5 and 38.7, respectively. It is worth noting that the start of the sync message always coincides with the start of the PN code, and the corresponding paging channel message starts after 320 ms minus the PN offset (expressed in seconds), as shown in Figure 38.15. Recall that the long code is also used to spread the paging message in the downlink (see Figure 38.7). The long code state decoded from a sync message is valid at the beginning of the corresponding paging channel message.
The long code is generated by masking the outputs of the 42 registers and computing the modulo‐two sum of the resulting bits. In contrast to the short code generator in cellular CDMA and the C/A code generator in GPS, the 42 long code generator registers are configured to satisfy a linear recursion given by
The long code mask is obtained by combining the PN offset and the paging channel number p as shown in Figure 38.16.
Figure 38.14 Cellular CDMA signal tracking: (a) code phase error (chips), (b) carrier phase error (degrees), (c) Doppler frequency estimate (hertz), (d) prompt (black), early (red), and late (green) correlation, (e) measured pseudorange (m), and (f) correlation function (Khalife et al. [18]).
Source: Reproduced with permission of IEEE.
Figure 38.15 Sync and paging channel timing (Khalife et al. [18]; 3GPP2 [50]).
Source: Reproduced with permission of IEEE.
Subsequently, the sync message is decoded first, and the PN offset, the paging channel number, and the long code state are then used to descramble and decode the paging message. It is important to note that the long code is first decimated at a rate of 1/64 to match the paging channel symbol rate. More details are specified in [47]. Figure 38.17 shows the demodulated sync signal as well as the final information decoded from the sync and paging channels. Note that the shown signal corresponds to the US cellular provider Verizon, which does not broadcast its BTS position information (latitude and longitude). Moreover, note that the last digit in the BTS ID corresponds to the sector number of the BTS cell. This is important for data association purposes, since different sectors of the same BTS cell are not perfectly synchronized. This is discussed in more detail in Section 38.7.
Figure 38.16 Long code mask structure (Khalife et al. [18]; 3GPP2 [50]).
Source: Reproduced with permission of IEEE.
Figure 38.17 Message decoding: demodulated sync channel signal (left) and BTS and system information decoded from sync and paging channels (right) (Khalife et al. [18]).
Source: Reproduced with permission of IEEE.
38.5.3 Code Phase Error Analysis
Section 38.5.2 presented a recipe for designing a receiver that can extract a pseudorange estimate from cellular CDMA signals. This section analyzes the statistics of the error of the code phase estimate for a coherent DLL. It is worth noting that when the receiver is closely tracking the carrier phase, the non‐coherent dot‐product discriminator and a coherent DLL discriminator will perform similarly. Hence, for simplicity, the analysis is carried out for a coherent baseband discriminator. To this end, it is assumed that ts is constant. Therefore, the carrier aiding term will be negligible, and the code start time error Δtk will be affected only by the channel noise. As mentioned in Section 38.5.2.3, it is enough to use a first‐order loop for the DLL, yielding the following closed‐loop time‐update error equation [57]:
where
