An examination of several P25 Frame Sync sequences in the complex plane shows distinct patterns in the antipodal symbols (term coined here to denote the samples which are taken from the receiver's Gardner clock-synchronization block at a point 1/2 way between the data symbols). We thus take symbols from the Gardner block at a 9600 rate.
In standard constant-envelope PSK the antipodal points would always have the same magnitude as the data symbols. In LSM however these points may be sent at partial (or zero) power. Likewise the phase is varied in controlled ways. In P25 the first five symbols of the FS are "plus" and the last five are "minus". In the detailed images follwing the correlations below, three images are shown (complete FS, first five data symbols and last five data symbols). One often-seen pattern is the antipodal symbols receive separate treatment for "plus" data symbols (center image) than for "minus" data symbols (right-hand image). This pattern is manifest on the previous page (antipodal symbols at full power and no phase offset for plus data symbols; whereas for minus data symbols the antipodal symbols are sent at zero power).
First we differentially decode the received symbols and perform a cross-correlation of the resulting real signal against the P25 FS, confirming a high-quality signal:
Next we try a complex cross-correlation, again using the P25 FS:
Note: phase of constellations consistent within rows, but effectively random otherwise.