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In order to demonstrate the presence of the discrepancy between sectors’ clock biases, a cellular CDMA receiver was placed at the border of two sectors of the i‐th BTS cell corresponding to the US cellular provider Verizon Wireless and was drawing pseudorange measurements from both sector antennas. The receiver had full knowledge of its state and of the BTS’s position. Subsequently, the receiver solved for the BTS clock biases and observed in sectors p_i and q_i, respectively. A realization of and is depicted in Figure 38.54.

Figure 38.54 suggests that the clock biases and can be related through

where ɛ_i is a random sequence that models the discrepancy between the sectors’ clock biases and

is the indicator function.

Note that the cdma2000 protocol requires all PN offsets to be synchronized to within 10 μs from GPS time; however, synchronization to within 3 μs is recommended [80]. Since each sector of a BTS uses a different PN offset, then the clock biases and will be bounded according to −10μs and −10μs . Therefore, ɛ_i will be within 20 μs from GPS time, namely

The discrepancy between the clock biases observed in two different sectors of some BTS cell over a 24 hour period is shown in Figures 38.55(a)–(b) for two different BTSs. Both BTSs pertained to the US cellular provider Verizon Wireless and are located near the University of California–Riverside campus. The cellular signals were recorded between September 23 and 24, 2016. It can be seen from Figure 38.55 that ∣ɛ_i∣ is bounded by approximately 2.02 μs and 0.65 μs, respectively, which is well below 20 μs. In the following subsection, a stochastic dynamic model for ɛ_i is identified.