he trans- mission-delayed signal analogous to (2.1) becomes s(t) = - +m2(t-T1)cos[wot+(t)]} (2.92) where m1(t) and m2(t) are unit power statistically independent binary data modulations of the same data rate and the remaining nomenclature is as pre- viously provided. If one uses the DLL of Figure 2.1 to PN track the sum of s(t) of (2.92) and ni(t) of (2.2), then, without belaboring the details, it can be shown that, analogous to (2.7), the error signal e(t) becomes e(t) - T1) + (t - Tt)] + Kmne(t, e1) (2.93) where the equivalent noise ne(t,et is now given by = (t) BAND-PASS LIMITER (BPL) ni (1) PHASE DETECTOR BAND-PASS LIMITER (BPL) PHASE VOLTAGE- MODULATOR PN CODE CONTROLLED CLOCK FILTER GENERATOR (VCC) Trackling PHASE MODULATOR Figure 2.30. The complete sums PN tracking loop. Quadriphase PN Tracking Now, since (2.95) with M2 defined in (2.14) and, because m1 (t) and m2(t) are independent, the auto-correlation function of (2.94) is again given by (2.18). Thus, we observe that the equation of operation remains unchanged from (2.15). In conclu- sion, the tracking and acquisition performance of the DLL with a QPN input as in (2.92) is identical to that with the biphase PN input of (2.1). Another form of QPN is obtained by spreading inphase and quadrature biphase modulated carriers with independent PN codes. Such a situation is typical of applications where separate addressing of each channel is required, as for example, in a multiple-access type system. Here the received signal (in the absence of noise) has the form s(t) = (2.96) If the two codes have identical chip rates, they are often staggered relative to one another by half a chip, i.e., T^ = T/2. This form of QPN is referred to as staggered quadriphase PN (SQPN) and is particularly used on non-lin- ear satellite channels to reduce regeneration of sidelobes removed by trans- mitter filtering prior to transmission voer the channel. Furthermore, from a practical implementation standpoint, c2(t) is often generated as a time-shift version of c1(t) where the time s