alt="Schematic illustration of timing Information Extraction block diagram."/>
Figure 38.40 Timing Information Extraction block diagram (Shamaei et al. [64, 65]).
Source: Reproduced with permission of Institute of Navigation, IEEE.
38.6.3 Code Phase Error Analysis
Section 38.6.2 presented a recipe for designing an FLL‐assisted PLL with a rate‐aided DLL receiver that can extract a pseudorange estimate from cellular LTE signals. This section analyzes the statistics of the error of the SSS code phase estimate. Recall from Section 38.6.1 that the SSS is zero‐padded to length Nc and an IFT is taken according to
where SSSS(f) is the SSS sequence in the frequency domain, Tsymb = 1/Δf is the duration of one symbol, and Δf is the subcarrier spacing.
The received signal is processed in blocks, each of which spans the duration of a frame, which can be modeled as
for kTsub ≤ t ≤ (k + 1)Tsub, where
Instead of the non‐coherent DLL discriminator used in the design in Section 38.6.2, a coherent DLL discriminator can also be used [57, 75]. Coherent discriminators are used when carrier phase tracking is ideal, and the receiver’s residual carrier phase and Doppler frequency are negligible (Δϕ ≈ 0 and ΔfD ≈ 0), while non‐coherent discriminators are independent of carrier phase tracking. Sections 38.6.3.1 and 38.6.3.2 analyze the statistics of the code phase error statistics with coherent and non‐coherent DLL tracking, respectively.
38.6.3.1 Coherent DLL Tracking
Assume that the residual carrier phase and Doppler frequency are negligible, that is, Δϕ ≈ 0 and ΔfD ≈ 0. Therefore, a coherent baseband discriminator may be used in the DLL. Figure 38.41 represents the structure of a coherent DLL that is used for tracking the code phase [55]. In what follows, the ranging precision of the DLL shown in Figure 38.41 is evaluated.
In the DLL, the received signal is first correlated with the early and late locally generated replicas of the SSS. The resulting early and late correlations are given respectively by
where Tc is the chip interval, teml is the correlator spacing (early‐minus‐late), and
where
It can be shown that the noise components of the early and late correlations,
Figure 38.41 Structure of a DLL employing a coherent baseband discriminator to track the code phase (Shamaei et al. [73]).
Source: Reproduced with permission of IEEE, European Signal Processing Conference.
Figure 38.42 Output of the coherent baseband discriminator function for the SSS with different correlator spacing (Shamaei et al. [73]).
Source: Reproduced with permission of IEEE, European Signal Processing Conference.
Open‐Loop
