Position, Navigation, and Timing Technologies in the 21st Century

(38.8)

where R cis the autocorrelation function of the PN sequences c ′ I, and is the code phase error, is the carrier phase error, and with and being independent and identically distributed Gaussian random sequences with zero mean and variance .

The expression for Z kin Eq. (38.8)assumes that the locally generated c Iand c Qhave the same code phase. To ensure this, both sequences must begin with the first binary “1” that occurs after 15 consecutive zeros; otherwise, ∣ Z k∣ will be halved. Figure 38.9shows | Z k| 2for unsynchronized and synchronized c Iand c Qcode phases (i.e. shifted by 34 chips). The correlation peak of the synchronized codes is four times the peak of the unsynchronized case.

The carrier wipe‐off and correlation stages are illustrated in Figure 38.10.

The objective of this stage is to determine which BTSs are in the receiver’s proximity and to obtain a coarse estimate of their corresponding code start times and Doppler frequencies. For a particular PN offset, a search over the code start time and Doppler frequency is performed to detect the presence of a signal. To determine the range of Doppler frequencies to search over, one must consider the relative motion between the receiver and the BTS and the stability of the receiver’s oscillator. For instance, a Doppler shift of 122 Hz will be observed for a cellular CDMA carrier frequency of 882.75 MHz at a mobile receiver with a receiver‐to‐BTS line‐of‐sight velocity of 150 km/h. Therefore, to account for this Doppler (at a carrier frequency of 882.75 MHz) as well as oscillator‐induced Doppler, the Doppler frequency search window is chosen to lie between −500 and 500 Hz. The frequency spacing Δ f Dmust be a fraction of 1/ T sub, which implies that Δ f D≪ 37.5 Hz, if T subis assumed to be one PN code period (e.g. a Δ f Dbetween 8 and 12 Hz can be chosen). The code start time search window is naturally chosen to be one PN code interval with a delay spacing of one sample.

Figure 38.9 | Z k| 2for (a) unsynchronized and (b) synchronized c Iand c Qcodes (Khalife et al. [18]).

Source: Reproduced with permission of IEEE.

Figure 38.10 Carrier wipe‐off and correlator. Thick lines indicate a complex‐valued variable (Khalife et al. [18]).

Source: Reproduced with permission of IEEE.

Similar to GPS signal acquisition, the search could be implemented either serially or in parallel, which in turn could be performed over the code phase or the Doppler frequency. The receiver presented here performs a parallel code phase search by exploiting the optimized efficiency of the fast Fourier transform (FFT) [53]. If a signal is present, a plot of | Z k| 2will show a high peak at the corresponding code start time and Doppler frequency estimates. A hypothesis test could be performed to decide whether the peak corresponds to a desired signal or noise. Since there is only one PN sequence, the search needs to be performed once. Then, the resulting surface is subdivided in the time axis into intervals of 64 chips, each division corresponding to a particular PN offset. The PN sequences for the pilot, sync, and paging channels could be generated off‐line and stored in a binary file to speed up the processing. Figure 38.11depicts the acquisition stage of a cellular CDMA signal with a software‐defined receiver (SDR) developed in LabVIEW, showing | Z k| 2along with , the PN offset, and the carrier‐to‐noise ratio C / N 0for a particular BTS [18].

After obtaining an initial coarse estimate of the code start time and Doppler frequency , the receiver refines and maintains these estimates via tracking loops. A phase‐locked loop (PLL) or a frequency‐locked loop (FLL) can be employed to track the carrier phase, and a carrier‐aided delay‐locked loop (DLL) can be used to track the code phase. FLLs are generally more robust than PLLs, are useful when transitioning from acquisition to tracking, and can track in more challenging environments [54, 55]. Figure 38.12depicts a block diagram of a PLL‐aided DLL tracking loop [12, 18]. The PLL and DLL are discussed in detail next.

Figure 38.11 Cellular CDMA signal acquisition front panel showing | Z k| 2along with , PN offset, and C / N 0for a particular BTS (Khalife et al. [18]).

Source: Reproduced with permission of IEEE.

Figure 38.12 Tracking loops in a navigation cellular CDMA receiver. Thick lines represent complex quantities (Khalife et al. [18]).

Source: Reproduced with permission of IEEE.

PLL:The PLL consists of a phase discriminator, a loop filter, and a numerically controlled oscillator (NCO). Since the receiver is tracking the data‐less pilot channel, an atan2discriminator can be used, given by