Improved Performance QPSK Demodulator for Digital Satellite

Practical realizations of the optimum closed loop structure for coherent demodulation of QPSK signals demands the approximation of the hyperbolic tangent nonlinearity (Tanh) 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 theoretical loop. A practical implementation of this loop is proposed for the digital satellite radio system, and its practical performance is evaluated. The results 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. Introduction The introduction of high fidelity digital sound recording and reproduction techniques constitutes a challenge to the broadcasting systems and operators, because the high bandwidth necessary for transmission of high quality digital recordings is not compatible with the limitations of conventional terrestrial transmission methods. A solution for this problem consists in using Direct Broadcasting by Satellite (DBS), such as is done with the Kopernikus1 and TV-SAT2 satellites by the German DBS system. This system provides national coverage with 16 high quality digital stereophonic channels, establishing a complete digital link between broadcasting studios and home radio sets [1]. The signal transmitted from the satellite to earth, using a carrier around 12 GHz modulated in QPSK at 20.48 Mb/s, is down converted to the frequency of 40.15 MHz for cable distribution. However, to make this system feasible, it is necessary to develop receiving equipment for the consumer market using highly sophisticated techniques, similar to those used in ground stations for satellite communications. One of the critical subsystems in the domestic receivers is the QPSK demodulator because, as the QPSK signal has no discrete component in its power spectrum, the carrier can not be recovered by a conventional phase locked loop (PLL) and the receiver may present frequent losses of synchronism, resulting quality degradation of the regenerated sound. The development of a QPSK demodulator with a superior performance, to be integrated in the Digital Satellite Radio (DSR) receivers, will constitute an important technological advantage. Optimum quadriphase demodulator In a QPSK receiver, the error probability is minimized if the demodulator selects the signal with the larger a posteriori probability: the demodulator calculates the a posteriori probabilities of each of the possible transmitted signals, and decides towards the one with the larger probability. This constitutes the so called maximum a posteriori (MAP) probability criterion. Using as an error control signal the gradient of the likelihood function, whose solution when set to zero is the MAP estimator of carrier phase, a closed loop implementation can be developed which is commonly referred to as MAP estimation loop [2]. For the QPSK modulation format, this loop can be observed in Fig. 1. In general, this MAP estimation loop is impractical because of the difficulty of implementing the hyperbolic tangent (Tanh) nonlinearity. To arrive at practical realizations, one must first approximate this nonlinearity with simpler and more easily implementable functions. The two commonly accepted approximations for the quadriphase loop are [2] b(t) p(t) dt (k-1)T kT (k-1)T kT a(t) p(t) dt tanh ( ) tanh ( ) Symbol sync