The research in this dissertation addresses reduced rank adaptive signal processing, with specific emphasis on the multistage Wiener filter (MWF). The MWF is a generalization of the classical Wiener filter that performs a stage-by-stage decomposition based on orthogonal projections. Truncation of this decomposition produces a reduced rank filter with many benefits, for example, improved performance. This dissertation extends knowledge of the MWF in four areas. The first area is rank and sample support compression. This dissertation examines, under a wide variety of conditions, the size of the adaptive subspace required by the MWF (i.e., the rank) as well as the required number of training samples. Comparisons are made with other algorithms such as the eigenvector-based principal components algorithm. The second area investigated in this dissertation concerns "soft stops", i.e., the insertion of diagonal loading into the MWF. Several methods for inserting loading into the MWF are described, as well as methods for choosing the amount of loading. The next area investigated is MWF rank selection. The MWF will outperform the classical Wiener filter when the rank is properly chosen. This dissertation presents six approaches for selecting MWF rank. The algorithms are compared to one another and an overall design space taxonomy is presented. Finally, as digital modelling capabilities become more sophisticated there is emerging interest in augmenting adaptive processing algorithms to incorporate prior knowledge. This dissertation presents two methods for augmenting the MWF, one based on linear constraints and a second based on non-zero weight vector initialization. Both approaches are evaluated under ideal and perturbed conditions. Together the research described in this dissertation increases the utility and robustness of the multistage Wiener filter. The analysis is presented in the context of adaptive array processing, both spatial array processing and space-time adaptive processing for airborne radar. The results, however, are applicable across the entire spectrum of adaptive signal processing applications. / Ph. D.

The research presented in this dissertation is on the development and application of advanced reduced rank adaptive signal processing techniques for high data rate wireless code division multiple access (CDMA) communications systems. This is an important area of research in the field of wireless communications. Current systems are moving towards the use of multiple simultaneous users in a given channel to increase system capacity as well as spatial and/or temporal diversity for improved performance in the presence of multipath and fading channels. Furthermore, to accommodate the demand for higher data rates, fast signal processing algorithms are required, which often translate into blind signal detection and estimation and the desire for optimal, low complexity detection techniques. The research presented here shows how minimum mean square error (MMSE) receivers implemented via the multistage Wiener filter (MWF) can be employed at the receiving end of a CDMA system to perform multiuser detection (MUD) or interference suppression (IS) with no loss in performance and significant signal subspace compression better than any previous reduced rank techniques have shown. This is important for optimizing performance because it implies a reduction in the number of required samples, so it lessens the requirement that the channel be stationary for a time duration long enough to obtain enough samples for an accurate MMSE estimate. The structure of these receivers is derived for synchronous and asynchronous systems for a multipath environment, and then it is shown that implementation of the receiver in a reduced rank subspace results in no loss in performance over full rank methods. It is also shown in some instances that reduced rank exceeds full rank performance. Multiuser detectors are also studied, and the optimal reduced rank detector is shown to be equivalent to a bank of parallel single user detectors performing interference suppression (IS). The performance as a function of rank for parallel and joint multiuser detectors are compared. The research is then extended to include joint space-code (i.e. a joint multiuser detector) and joint space-time processing algorithms which employ receiver diversity for low complexity diversity gain. Non-linear techniques, namely serial interference cancellation (SIC) and parallel interference cancellation (PIC), will also be studied. The conventional matched filter correlator will be replaced by the MWF, thereby incorporating IS at each stage of the interference canceller for improved performance. A closed form expression is derived for the probability of error, and performance gains are evaluated. It will be further shown how the receiver structure can be extended when space-time codes are employed at the transmitter for additional diversity gain with minimal impact on complexity. The MMSE solution is derived and implemented via the MWF with some examples. It is believed that these new techniques will have a significant impact on the design of fourth generation (4G) and beyond cellular CDMA systems. / Ph. D.

The research presented in this dissertation is on the development of advanced reduced rank adaptive signal processing for airborne radar space-time adaptive processing (STAP) and steering vector mismatch robustness. This is an important area of research in the field of airborne radar signal processing since practical STAP algorithms should be robust against various kinds of mismatch errors. The clutter return in an airborne radar has widely spread Doppler frequencies; therefore STAP, a two-dimensional adaptive filtering algorithm is required for effective clutter and jamming cancellation. Real-world effects in nonhomogeneous environments increase the number of adaptive degrees of freedom required to adequately suppress interference. The increasing computational complexity and the need to estimate the interference from a limited sample support make full rank STAP impractical. The research presented here shows that the reduced rank multistage Wiener filter (MWF) provides significant subspace compression better than any previous techniques in a nonhomogeneous environment. In addition, the impact of steering vector mismatch will also be examined on the MWF. In an airborne radar environment, it is well known that calibration errors and steering vector mismatch can seriously degrade adaptive array performance and result in signal cancellation. These errors can be caused by many non-ideal factors such as beam steering angle errors, multipath propagation, and phase errors due to array imperfections. Since the MWF centrally features the steering vector on its formulation, it is important to assess the impact of steering vector mismatch. In this dissertation, several novel techniques for increasing robustness are examined and applied to the MWF. These include derivative constraints, quiescent pattern control (QPC) techniques, and covariance matrix tapers (CMT). This research illustrates that a combination of CMT and QPC, denoted CMTQ, is very effective at mitigating the impact of steering vector mismatch. Use of CMTQ augmentation provides the steering vector mismatch robustness that we desire while improving the reduced-rank and reduced sample characteristics of the MWF. Results using Monte Carlo simulations and experimental Multichannel Airborne Radar Measurements (MCARM) data confirm that the use of CMTQ gives superior performance to steering vector errors at a much reduced rank and sample support as compared to conventional techniques. / Ph. D.