Mutual Tracking in Phase and Delay of Randomly Modulated Signals

A two-parameter tracking loop that mutually locks the phases and delays of two noise-contaminated replicas of a randomly phase-modulated signal, received via different channels, is analyzed. It is shown that, at high SNR, i.e., small tracking errors, the twoparameter loop can be considered as two uncoupled single parameter loops, provided the signals are beaten down to zero center frequency. Special emphasis is put on the delay error variance; it is found that, in general, the broadening of the phase loop bandwidth (provided for more rapid acquisition) induces larger delay-tracking errors. Also, such broadening decreases the expected time to loss of delay lock; the influence of the location of the absorbing boundaries for this problem is investigated. Quantitative results for a typical configuration are presented in Figs. 1-9.