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After acquiring the LTE frame timing, a UE needs to keep tracking the frame timing for two reasons: (i) to produce a pseudorange measurement and (ii) to continuously reconstruct the frame. The PSS and SSS are two possible sequences that a UE can exploit to track the frame timing. The PSS has only three different sequences, making it less desirable to use in tracking the frame timing because (i) the interference from neighboring eNodeBs with the same sector IDs is high and (ii) the number of eNodeBs that the UE can simultaneously track is limited. The SSS is expressible in 168 different sequences; hence, it does not suffer from the same problems as the PSS. Therefore, the SSS will be used to track the frame timing. In this section, the components of the tracking loops are discussed, namely, an FLL‐assisted PLL and a carrier‐aided DLL.

FLL‐Assisted PLL: The frequency reuse factor in LTE systems is set to be 1, which results in high interference from neighboring cells. Under interference and dynamic stress, FLLs have better performance than PLLs. However, PLLs have significantly higher measurement accuracy compared to FLLs. An FLL‐assisted PLL has both the dynamic and interference robustness of FLLs and the high accuracy of PLLs [72]. The main components of an FLL‐assisted PLL are a phase discriminator, a phase loop filter, a frequency discriminator, a frequency loop filter, and an NCO. The SSS is not modulated with other data. Therefore, an atan2 discriminator, which remains linear over the full input error range of ±π, could be used without the risk of introducing phase ambiguities, given by

Figure 38.37 System information extraction block diagram (Shamaei et al. [64, 65]).

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

where is the prompt correlation at time step k. A third‐order PLL can be used to track the carrier phase, with a loop filter transfer function given by

(38.22)

where ω_{n, p} is the undamped natural frequency of the phase loop, which can be related to the PLL noise‐equivalent bandwidth [54]. The output of the phase loop filter is the rate of change of the carrier phase error , expressed in rad/s, where is the Doppler frequency estimate. The phase loop filter transfer function in Eq. (38.22) is discretized and realized in state space. The PLL is assisted by a second‐order FLL with an atan2 discriminator for the frequency as well. The frequency error at time step k is expressed as

where T_sub = 10 ms is the subaccumulation period, which is chosen to be one frame length. The transfer function of the frequency loop filter is given by

(38.23)

where ω_{n, f} is the undamped natural frequency of the frequency loop, which can be related to the FLL noise‐equivalent bandwidth [54]. The output of the frequency loop filter is the rate of change of the angular frequency , expressed in rad/s². It is therefore integrated and added to the output of the phase loop filter. The frequency loop filter transfer function in Eq. (38.23) is discretized and realized in state space.

DLL: The carrier‐aided DLL employs a non‐coherent dot‐product discriminator given by

where Γ is a normalization constant given by

where and are the early and late correlations, respectively, is the chip interval, W_SSS = 63 × 15 = 945 kHz is the SSS bandwidth, is the expectation operator, and is the interference‐plus‐noise variance. The calculation of the overall noise level including interference and channel noise is discussed in [65].

The DLL loop filter is chosen to be similar to Eq. (38.23), with a noise‐equivalent bandwidth B_{n, DLL} (in hertz). The output of the DLL loop filter v_DLL (in s/s) is the rate of change of the SSS code phase. Assuming low‐side mixing, the code start time is updated according to

The SSS code start time estimate is used to reconstruct the transmitted frame. Figure 38.38 shows the block diagram of the tracking loops, where ω_c = 2πf_c and f_c is the carrier frequency (in hertz). Finally, the pseudorange estimate ρ can be deduced by multiplying the code start time by the speed of light c (cf. Eq. (38.10)).

Figure 38.38 LTE SSS signal tracking block diagram (Shamaei et al. [64, 65]).

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

Figure 38.39 LTE SSS tracking results with a stationary receiver (Shamaei et al. [64, 65]).

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

Figure 38.39 shows tracking results with real LTE signals. Here, the PLL, FLL, and DLL noise‐equivalent bandwidths were set to 4, 0.2, and 0.001 Hz, respectively. To calculate the interference‐plus‐noise variance, the received signal was correlated with an orthogonal sequence that is not transmitted by any of the eNodeBs in the environment. Then, the average of the squared‐magnitude of the correlation was assumed to be the interference‐plus‐noise variance. Since the receiver was stationary and its clock was driven by a GPS‐disciplined oscillator (GPSDO), the Doppler frequency was stable around zero. Note that the aiding term τ is computed in the Timing Information Extraction block to improve SSS tracking. The term τ gets added to in the SSS generator block. The calculation of τ is discussed next.