ωn, f is the undamped natural frequency of the frequency loop, which can be related to the FLL noise‐equivalent bandwidth DLL: The carrier‐aided DLL employs a non‐coherent dot‐product discriminator given by
where Γ is a normalization constant given by
where
The DLL loop filter is chosen to be similar to Eq. (38.23), with a noise‐equivalent bandwidth Bn, DLL (in hertz). The output of the DLL loop filter vDLL (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 ωc = 2πfc and fc 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
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
where
(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].
