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

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.

      38.6.2.4 Timing Information Extraction

      In LTE systems, the PSS and SSS are transmitted with the lowest possible bandwidth. The ranging precision and accuracy of the SSS is analyzed in [73, 74], which shows that the SSS can provide very precise ranging resolution using conventional DLLs in an environment without multipath. However, because of its relatively low bandwidth, the SSS is extremely susceptible to multipath. To achieve more precise localization using LTE signals, the CRS can be exploited. The ranging precision of SSS and CRS in a semi‐urban environment with multipath was studied experimentally in [63], which showed that CRS is more robust to multipath.

In the timing information extraction stage of the receiver, the TOA can be estimated by detecting the first peak of the channel impulse response (CIR). The CIR can be computed from the received signal model in the i‐th symbol, given in Eq. (38.19). The subscript i will be dropped in the sequel for simplicity of notation. The estimated CFR of the u‐th eNodeB is given by

(38.24)

where . Equation 38.24 is obtained using the fact that . The CIR estimate is obtained by taking the IFFT of the estimated CFR, yielding

      (38.25)

      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 38.40 shows 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.

      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 N_c and an IFT is taken according to

      where S_SSS(f) is the SSS sequence in the frequency domain, T_symb = 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 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; Δϕ and Δf_D are 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 (Δϕ ≈ 0 and Δf_D ≈ 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