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In order to achieve the desired loop noise‐equivalent bandwidth, K in Eq. (38.11) must be normalized according to

Figure 38.18 Output of the coherent baseband discriminator function for the CDMA short code with different correlator spacings (Khalife et al. [12]).

Source: Reproduced with permission of IEEE.

(38.15)

In cellular CDMA systems, for a t_eml of 1.2, the loop filter gain becomes K ≈ 4B_{n, DLL}; hence, the choice of K in Section 38.5.2.3. Assuming a zero‐mean tracking error, that is, , the variance of the code start time error is given by

At steady state, var{Δt_{k + 1}} becomes

(38.16)

where Δt is the steady‐state code start time error. Combining Eqs. (38.15)–(38.16) yields

(38.17)

The pseudorange can hence be expressed as

where v(k) is a zero‐mean random variable with variance σ² = c² · var {Δt}. Figure 38.19 shows a plot of the standard deviation of Δt, denoted by σ, as a function of the carrier‐to‐noise ratio C/N₀ for t_eml = 1.25 chips.