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

where .

The TOA estimate τ is then fed back to the tracking loops. A low pass filter (e.g. a moving average filter) can be used to remove outliers in the estimated τ . Figure 38.40shows the block diagram of the timing information extraction stage.

The first peak detection approach was implemented in [17, 64]. While this method is computationally inexpensive, the first peak of the CIR cannot be detected when the multipath has a short range. An adaptive threshold approach was developed in [65] that yielded more robust performance in urban environments experiencing severe multipath. In contrast to peak detection algorithms, super resolution algorithms (SRAs) can be used [5, 11], which are computationally involved. A computationally efficient receiver that deals with the shortcomings of the SRA‐based and first peak detection‐based approaches was proposed in [15, 19].

Figure 38.40 Timing Information Extraction block diagram (Shamaei et al. [64, 65]).

Source: Reproduced with permission of Institute of Navigation, IEEE.

Section 38.6.2presented 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 38.6.1that the SSS is zero‐padded to length N cand an IFT is taken according to

where S SSS( f ) is the SSS sequence in the frequency domain, T symb= 1/Δ f is the duration of one symbol, and Δ f 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 kT sub≤ t ≤ ( k + 1) T sub, where ; W SSS= 930 kHz is the SSS bandwidth; C is the received signal power including antenna gains and implementation loss; is the true TOA of the SSS signal; Δ ϕ and Δ f Dare the residual carrier phase and Doppler frequency, respectively; n ( t ) is an additive white noise with a constant power spectral density W/Hz; and d ( t ) is some data transmitted by the eNodeB other than the SSS, 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 (Δ ϕ ≈ 0 and Δ f D≈ 0), while non‐coherent discriminators are independent of carrier phase tracking. Sections 38.6.3.1and 38.6.3.2analyze the statistics of the code phase error statistics with coherent and non‐coherent DLL tracking, respectively.

Assume that the residual carrier phase and Doppler frequency are negligible, that is, Δ ϕ ≈ 0 and Δ f D≈ 0. Therefore, a coherent baseband discriminator may be used in the DLL. Figure 38.41represents 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 38.41is 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 T cis the chip interval, t emlis the correlator spacing (early‐minus‐late), and is the estimated TOA. The signal components of the early and late correlations, and , respectively, are given by

where is the propagation time estimation error, and R (·) is the autocorrelation function of s code( t ), given by

It can be shown that the noise components of the early and late correlations, and , respectively, are zero mean with the following statistics: