This paper uses MAP estimation techniques to obtain carrier reconstruction circuits for unbalanced QPSK signals. In addition, the performance analysis of these circuits is carried out to the extent that a loop design can proceed. Optimal weighting coefficients in the receiving system are identified as functions of the

power and data rate splits. Finally, numerical results are presented in order to demonstrate the utility of the theory developed. This signal design will be used in the development of the Tracking and Data Relay Satellite System (TDRSS) and the Navigation Satellite Timing and Ranging Global Positioning System (NAVSTAR GPS).