Nonlinear mean-square multiuser detection and set-theoretic estimation for digital communications

This dissertation addresses two different but related problems. First is that of optimal joint detection of signals in a multiple access digital communication system. The problem is formulated in an alternative framework based on nonlinear mean-square estimation. It is shown that for a large class of signaling schemes that are commonly in use, nonlinear MMSE multiuser detection is equivalent to minimum probability of error multiuser detection.; Additionally, it is shown that nonlinear MMSE multiuser detection—and hence minimum probability of error detection—can be approximated by a simple iterative solution. The desired solution is shown to be a fixed point of the proposed iterations. Approximate realizations of the iterative solution are derived for CDMA systems with various modulation schemes and channel characteristics. The proposed solution, when applied to systems with forward error correction (FEC) coding or multiple receive antennas is shown to yield Turbo multiuser detectors. In all cases, simulation studies show that substantial improvements in cell capacity, coverage areas and battery-life of transmitters are obtained over conventional techniques, with an insignificant increase in computational complexity.; The second problem addressed by this dissertation is that of parameter estimation for linear-in-parameters systems in a deterministic framework. The proposed approach, called Set-Membership Filtering (SMF), is based on computing sets of filter parameters that satisfy a specified filter error bound. Algorithms are derived to adaptively implement SMF for static and dynamic systems. They feature performance close to that of least-squares methods at a fraction of their average complexity.; Continuous and discrete $\ell \infty$ minimax filtering problems are formulated to design filters that minimize worst-case filter error magnitudes. In contrast to existing minimax algorithms that solve minimax problems over only a finite data set, an adaptive algorithm is derived to solve finite, discrete-infinite, and continuous minimax problems. The proposed algorithm has numerous applications in communications, signal processing, control and applied mathematics.; SMF theory is applied to the problem of channel equalization, and an adaptive set-membership algorithm is developed for blind equalization. The proposed algorithm is shown to offer unique advantages over the celebrated CM algorithm in terms of performance and complexity.