DESIGN AND PERFORMANCE ANALYSIS OF COHERENT RECEIVERS FOR CONTINUOUS PHASE MODULATIONS

Abstract

The aim here is to contribute to the theory of receiver design for coherent digital communications, with an emphasis on developing structures which are suitable for digital implementation. Attention is focused on continuous phase modulations (CPM). The prime motivation is to achieve a performance as close as possible to that of the perfectly coherent receiver. The effects of carrier phase noise on the error performance of these receivers is also considered. Our investigation starts with binary orthogonal signaling, which is memoryless, albeit continuous phase. The orthogonal signal structure has been shown to be the superposition of an antipodal signal set and an unmodulated component which can be used for channel measurement. The generalised quadratic receiver developed here exploits the estimator-detector structure of the quadratic receiver, and generalises it to a receiver in which the estimator makes an estimate of the channel gain in each signaling interval based on the totality of the unmodulated components of the signal received over all or a subset of the signaling intervals. It is shown to be capable of achieving substantial performance gain over the conventional quadratic receiver. Both the random phase and fading channels are considered. The generalised quadratic receiver cannot be immediately extended to CPM, in which there is memory in the signal. Therefore, we first concentrate on one of the approaches to designing coherent sequence estimation receivers, namely, the two-stage receiver. The first stage, being the carrier phase estimator, extracts the carrier phase information and feeds this to the second stage. The second stage is a Viterbi decoder which treats the carrier phase estimate as if it were the true value of the carrier phase and uses it in sequence estimation. The carrier phase estimator is decision aided by a quadratic receiver and the Viterbi decoder. Minimum-shift keying (MSK) over the random phase channel is examined in detail. Another approach to designing coherent receivers for CPM over the random phase channel, is to view sequence estimation as searching for the true path through the phase trellis. This leads to the development of the Viterbi-type receiver. It can easily be implemented using a Viterbi decoder and its metric is the metric of the simultaneous maximum likelihood estimation receiver in block detection. A measure of its error performance is the quadratic detection distance defined here and it converges to the normalised Euclidean distance. The bit error probability of MSK is computed for the constant unknown phase channel. Next, we develop an approach by which the performance of coherent receivers in the presence of carrier phase noise can be analysed. The time-varying carrier phase process is modelled as a discrete Gaussian random walk. We first start off with analysis of the performance degradation on M’ary phase-shift keying. Both symbol-by-symbol detection and sequence estimation are considered. It is shown for the first time that under the assumption of small phase noise variance, the fluctuating carrier phase leads to additional Gaussian noise. Bit error probabilities are obtained for binary phase-shift keying (BPSK) and quadriphase-shift keying (QPSK). This provides a theoretical foundation to further extend the analysis to MSK with detection by the Viterbi-type receiver.