 Section 2.1 (with a prime superscript) where appropriate. Again assuming an input as in (2.1) and (2.2), and making similar assump- tions to those leading up to (2.7), the input to the loop filter of the MCTL can be shown [11] to be given by9 e(t) = = + Kmne(t, e1) (2.7') where E, = 1 =128,-287; D(8))=D(8,+ np); n = =1, 12, 43, (2.8') is the loop discriminator characteristic and Ne(t, Et) is the equivalent addi- For simplicity of presentation, we shall pursue only the "one-delta" loop where N = 2. n;(1) yo(+) TO DATA DEMODULATOR c(t-) VOLTAGE- PN CODE CONTROLLED FILTER GENERATOR CLOCK (VCC) c(t-4-8) Figure 2.25. The modified code tracking loop (MCTL). The Modified Code Tracking Loop tive noise defined by (t, e1) = + VSm(t-T,) X (RPN(8))N.A(t)+ [RPN_(E1) - RPN.(8,)].Noo(t)} (2.9') Nco(t) = s(t) = (t) = H(p)[{c(t-T,+8)-ct-t - = - - - (2.6') Figure 2.26 is a comparative illustration of the discriminator characteristics of the DLL and the MCTL. We immediately observe that the non-zero region of the MCTL characteristic is only 2/3 that of the DLL and thus the modified loop has a 1/3 less pull-in capability. Furthermore, although the two discriminator characteristics have identical slopes at E = 0, the DLL always creates a larger error voltage for any value of timing error. Despite these disadvantages, when compared with the DLL, the MCTL does have an improved noise performance as previously mentioned. Figure 2.26. One-delta loop discriminator characteristics for the DLL and MCTL (reprinted from [11]). Pseudonoise Code Tracking in Direct-Sequence Receivers Specifically, the equivalent noise spectral density Ne(e1) of Ne(t, Et) is given by [11]: (2.22') with KL and M4 defined in (2.23) and PH in (2.25). Following steps similar to those leading up to (2.29), we find that the normalized mean-squared tim- ing error for the MCTL is given by (2.29') where the squaring loss SL is now (2.30') Comparing (2.30') with (2.30) for N = 2, = we observe that the NXN power of the MCTL is one-half that of the DLL, thus producing an ass