Optimization of QPSK demodulators for digital satellite radio

Closed loop structures which result from the application of the maximum a posteriori (MAP) estimation technique, constitute the basis for optimally estimating carrier phase of QPSK signals. To arrive at practical realizations, one must approximate the hyperbolic tangent nonlinearity which is a consequence of the MAP theory with simpler and more easily implementable functions. This paper compares the commonly considered approximations to this nonlinearity and the practical structures which result, with an alternative in which the hyperbolic tangent nonlinearity is approximated by a saturated amplifier characteristic. It is shown that the performance of this new loop is for all practical purposes identical to the optimum MAP loop. A practical implementation of this loop is proposed, and a prototype QPSK coherent demodulator for the digital satellite radio system is presented. Practical performance results of the prototype demodulator are presented which validate the theoretical study, as well as the practical solutions adopted, concluding for the feasibility of a QPSK demodulator with a performance very close to the theoretical limit