Polynomial phase modulated (PPM) signals have been shown to provide improved error rate performance with respect to conventional modulation formats under additive white Gaussian noise and fading channels in single-input single-output (SISO) communication systems. In this dissertation, systems with two and four transmit antennas using PPM signals were presented. In both cases we employed full-rate space-time block codes in order to take advantage of the multipath channel. For two transmit antennas, we used the orthogonal space-time block code (OSTBC) proposed by Alamouti and performed symbol-wise decoding by estimating the phase coefficients of the PPM signal using three different methods: maximum-likelihood (ML), sub-optimal ML (S-ML) and the high-order ambiguity function (HAF). In the case of four transmit antennas, we used the full-rate quasi-OSTBC (QOSTBC) proposed by Jafarkhani. However, in order to ensure the best error rate performance, PPM signals were selected such as to maximize the QOSTBC’s minimum coding gain distance (CGD). Since this method does not always provide a unique solution, an additional criterion known as maximum channel interference coefficient (CIC) was proposed. Through Monte Carlo simulations it was shown that by using QOSTBCs along with the properly selected PPM constellations based on the CGD and CIC criteria, full diversity in flat fading channels and thus, low BER at high signal-to-noise ratios (SNR) can be ensured. Lastly, the performance of symbol-wise decoding for QOSTBCs was evaluated. In this case a quasi zero-forcing method was used to decouple the received signal and it was shown that although this technique reduces the decoding complexity of the system, there is a penalty to be paid in terms of error rate performance at high SNRs.

The estimation and analysis of signals that have polynomial phase and constant or time-varying amplitudes with the addititve noise is considered in this dissertation.Much work has been undertaken on this problem over the last decade or so, and there are a number of estimation schemes available. The fundamental problem when trying to estimate the parameters of these type of signals is the nonlinear characterstics of the signal, which lead to computationally difficulties when applying standard techniques such as maximum likelihood and least squares. When considering only the phase data, we also encounter the well known problem of the unobservability of the true noise phase curve. The methods that are currently most popular involve differencing in phase followed by regression, or nonlinear transformations. Although these methods perform quite well at high signal to noise ratios, their performance worsens at low signal to noise, and there may be significant bias. One of the biggest problems to efficient estimation of these models is that the majority of methods rely on sequential estimation of the phase coefficients, in that the highest-order parameter is estimated first, its contribution removed via demodulation, and the same procedure applied to estimation of the next parameter and so on. This is clearly an issue in that errors in estimation of high order parameters affect the ability to estimate the lower order parameters correctly. As a result, stastical analysis of the parameters is also difficult. In thie dissertation, we aim to circumvent the issues of bias and sequential estiamtion by considering the issue of full parameter iterative refinement techniques. ie. given a possibly biased initial estimate of the phase coefficients, we aim to create computationally efficient iterative refinement techniques to produce stastically efficient estimators at low signal to noise ratios. Updating will be done in a multivariable manner to remove inaccuracies and biases due to sequential procedures. Stastical analysis and extensive simulations attest to the performance of the schemes that are presented, which include likelihood, least squares and bayesian estimation schemes. Other results of importance to the full estimatin problem, namely when there is error in the time variable, the amplitude is not constant, and when the model order is not known, are also condsidered.