Position, Navigation, and Timing Technologies in the 21st Century. Группа авторов

eNodeB cell ID are determined. Then, the MIB is decoded, and the bandwidth of the system as well as the frame number are extracted. This will allow the UE to demodulate the OFDM signal across the entire bandwidth and locate the SIB1 REs. The UE moves on to decode the SIB1 message, from which the scheduling for SIB4 is deduced and is subsequently decoded. SIB4 contains the cell ID of intra‐frequency neighboring cells as well as other information pertaining to these cells. Decoding this information gives the UE the ability to simultaneously track signals from different eNodeBs and produce TOA estimates from each of these eNodeBs. Signal tracking and TOA estimation will be thoroughly discussed in the next two subsections. Figure 38.37 summarizes all the aforementioned system information extraction steps.

      38.6.2.3 Tracking

      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