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Section 38.5.2 presented a recipe for designing a receiver that can extract a pseudorange estimate from cellular CDMA signals. This section analyzes the statistics of the error of the code phase estimate for a coherent DLL. It is worth noting that when the receiver is closely tracking the carrier phase, the non‐coherent dot‐product discriminator and a coherent DLL discriminator will perform similarly. Hence, for simplicity, the analysis is carried out for a coherent baseband discriminator. To this end, it is assumed that t_s is constant. Therefore, the carrier aiding term will be negligible, and the code start time error Δt_k will be affected only by the channel noise. As mentioned in Section 38.5.2.3, it is enough to use a first‐order loop for the DLL, yielding the following closed‐loop time‐update error equation [57]:

(38.11)

where e_{DLL, k} is the output of the code phase discriminator. The discriminator statistics are discussed next.