Position, Navigation, and Timing Technologies in the 21st Century

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 38.17shows 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.

Section 38.5.2presented 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 t sis constant. Therefore, the carrier aiding term will be negligible, and the code start time error Δ t kwill 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]:

(38.11)

where e DLL, kis the output of the code phase discriminator. The discriminator statistics are discussed next.

In order to study the discriminator statistics, the received signal noise statistics must first be determined. In what follows, the received signal noise is characterized for an additive white Gaussian noise channel.

Received Signal Noise Statistics:To make the analysis tractable, the continuous‐time received signal and correlation are considered. The transmitted signal is assumed to propagate in an additive white Gaussian noise channel with a power spectral density . The continuous‐time received signal after down‐mixing and bandpass sampling is given by

and the continuous‐time matched‐filtered baseband signal x ( t ) is given by

The resulting early and late correlations in the DLL are given by

where and . Assuming the receiver is closely tracking the carrier phase [55], the early and late correlations may be approximated with

where and are zero‐mean Gaussian random variables with the following variances and covariances:

Coherent Discriminator Statistics:The coherent baseband discriminator function is defined as