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The first step in acquiring an LTE signal is to extract the transmitted frame timing and the eNodeB’s cell ID [66–68]. These two parameters are obtained by the PSS and SSS. To detect the PSS, the UE exploits the orthogonality of the Zadoff–Chu sequences and correlates the received signal with all the possible choices of the PSS according to

(38.20)

where is the received signal, is the receiver‐generated PSS in the time domain, N is the frame length, (·)^* denotes the complex conjugate, (·)_N denotes the circular shift operator, and ⊛_N represents the circular convolution operation. Taking the FFT and IFFT of Eq. (38.20) yields

Figure 38.30 Block diagram of the LTE navigation receiver architecture (Shamaei et al. [65]).

Source: Reproduced with permission of IEEE.

(38.21)

where and . The FFT‐based correlation in Eq. (38.21) is also used to detect the SSS signal. Once the PSS and SSS are detected, the UE can estimate the frame start time.

After obtaining the frame timing, the UE estimates the frequency shift (Doppler frequency) using the CP in the received signal r(n). The apparent Doppler frequency, including the carrier frequency offset due to clock drift and the Doppler shift, can be estimated by the CP as

where N_CP is the set of CP indices, and T_s is the sampling interval [69]. Upon estimating the Doppler frequency, the acquisition of the LTE signal is complete. Figure 38.31 summarizes the LTE signal acquisition process.

The normalized correlation of received LTE signals with locally generated PSS and SSS signals are presented in Figure 38.32. It can be seen that since the PSS is transmitted twice per frame, the correlation has two peaks in the duration of one frame, which is 10 ms. However, the SSS correlation has only one peak, since the SSS is transmitted only once per frame. The figure also shows that the highest PSS correlation peak was at , and the highest SSS correlation peak was at . Therefore, the cell ID was calculated to be .

Figure 38.31 Signal acquisition block diagram (Shamaei et al. [64, 65]).

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

Figure 38.32 PSS and SSS normalized correlation results with real LTE signals (Shamaei et al. [64, 65]).

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