l the loops discussed thus far in that its operation requires a spread-spectrum signal for- mat wherein the PN code is phase modulated on the transmitted carrier rather than the usual amplitude modulation case. In this sense, the complex Quadriphase PN Tracking sums loop may be regarded as the phase modulation analog of the ampli- tude-sensing DLL discussed previously. Indeed, the input signal plus noise is correlated with the sum and difference of quadrature carriers, phase modulated respectively by the advanced and retarded versions of the locally generated PN code (see Figure 2.30). The resultant correlations are first band-pass filtered and then band-pass limited (BPL) to remove the ampli- tude modulation. The relative phase between the two BPL outputs then rep- resents a measure of the PN code delay error. Since in virtually all DS/SS systems in use today the PN code is amplitude modulated on the transmitted carrier, particularly when the data modula- tion is also amplitude modulated on the carrier, we shall discontinue any fur- ther discussion of this loop, having included its mention merely for the sake of completeness. This is no to say that the complex sums loop is not capable of performance comparable with the DLL; indeed, it has been theoretically shown [12] to offer a factor of 4 improvement in rms tracking error and a factor of 2.67 improvement in maximum search velocity when compared with amplitude sensing correlation receivers such as the DLL. Rather, its lack of widespread acceptance in the design of current DS/SS receivers precludes our giving it extensive coverage. 2.9 QUADRIPHASE PN TRACKING Until now we have assumed that the PN spreading code is superimposed on a suppressed carrier binary data modulation. It is our intent in this section to investigate the applicability of the previous PN tracking techniques to var- ious forms of quadriphase PN modulation (QPN). The simplest form of QPN is obtained by spreading a quadriphase-shift- keyed (QPSK) modulation with a single PN code. In this case, t