Читать книгу Position, Navigation, and Timing Technologies in the 21st Century - Группа авторов - Страница 103

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.