ociated reduction in mean-squared tracking jitter. To demonstrate the magnitude of Es/No,dB Figure 2.27. Minimum squaring loss comparison for NRZ data modulation (reprinted from [11]). The Modified Code Tracking Loop Es/No,dB Figure 2.28. Minimum squaring loss comparison for Manchester data modulation (reprinted from [11]). this reduction, it is sufficient to numerically compare the minimum squar- ing loss of (2.30) with that of (2.30') as is done in Figures 2.27 and 2.28 for the case of NRZ or Manchester data and two-pole Butterworth band-pass filters. The appropriate expressions for KL, M, and M4 are obtained from Tables 2.1 and 2.2. With regard to the acquisition behavior of the MCTL, it has been shown [11] that for equal rms tracking jitters, i.e., MCTL = D'DLL, the maximum nor- malized search rate is given by (2.91) as compared with the previously found y=1 for the "one-delta" DLL. Figure 2.29 illustrates y as a function of ENo for NRZ and Manchester data types, and two-pole Butterworth band-pass filters. Also shown is the curve Pseudonoise Code Tracking in Direct-Sequence Receivers MANCHESTER DATA NO FILTERING EFFECTS NRZ DATA Es/No,dB Figure 2.29. Normalized search rate comparison (reprinted from [11]). corresponding to ignoring the arm filter band-limiting effects, i.e., M2 = M4 = KL = 1 and Bh = Rs. We observe that for small values of E/N the MCTL indeed has a higher search rate capability than the DLL, whereas for large values of E/No, it asymptotically approaches a maximum decrease of 40% in search rate capability. Finally, when compared with the DLL, the MCTL has the advantage of being significantly less sensitive go gain imbalances at alow values of pre- detectio signal-to-noise ratio PH resulting in lower tracking bias errors. At high PH'S, the gain imbalance sensitivities of the two configurations are nearly equivalent, both being of course much less sensitive than the addi- tional DLL. 2.8 THE COMPLEX SUMS LOOP (A PHASE-SENSING DLL) The complex sums loop [12] is by far the least conventional of al