To help meet the demand for ubiquitous wireless data services, national regulatory agencies worldwide have recently made available several gigahertz of contiguous spectrum for unlicensed indoor use, notably the ultra-wideband and 60 GHz bands. This is causing a paradigm shift in the design of wireless networks, as energy efficiency supplants spectral efficiency as the primary design concern. Energy efficient modulations have existed for decades, but have only recently been considered for use in high-speed wireless networks where dispersive channels hinder performance through multipath and intersymbol interference.
This dissertation presents the first investigation of equalization for a class of energy efficient modulations that comprises orthogonal, biorthogonal, and transorthogonal modulation. We consider the use of a (possibly fractionally-spaced1) finite-length decision-feedback equalizer (DFE), and begin by presenting a generalized multirate system model that encapsulates all of these energy efficient modulations, as well as some classical modulations such as pulse amplitude modulation. The DFE structures we propose assume two forms: a chip-rate DFE very similar to the classical DFE, and a block DFE implemented as a multirate filter bank that operates symbol-by-symbol. We derive the minimum mean-squared error DFE tap values for these two structures, which follow from straightforward application of Wiener filter theory. However, we show that several modifications to the equalizer enable us to exploit inherent signal properties of some of the modulation schemes; these changes have the effect of permitting perfect equalization with a finite-length equalizer in situations where perfect equalization would otherwise not have been possible, and also permit a reduction in equalizer complexity.
Adaptive equalization of these modulations is the focus of the second half of the dissertation. We briefly discuss the trained least mean square algorithm, and demonstrate that its decision-directed counterpart is unsuitable for cold startup of equalizers for these modulations. This leads us to consider the use of the two most popular classical blind equalization algorithms – the Constant Modulus Algorithm (CMA) and the Shalvi-Weinstein Algorithm (SWA) – both of which we show to be similarly unsuitable in their pure form largely due to their reliance on i.i.d. source statistics. With the lack of a suitable blind algorithm, we proceed with a general discussion of blind algorithm development, including the desired properties of blind algorithm cost functions, a methodology for algorithm assessment, and guidelines for selecting cost functions. Finally, we present the first two blind algorithms beyond decision direction for biorthogonal modulation, including a discussion of their characteristics and convergence. The first algorithm, called LTBOMB, is CMA-like in spirit, and we show that the zero-forcing solutions are locally stable under ideal conditions. The second algorithm, called TROMBONE, was designed with a SWA-like philosophy in mind, and thus relies on a spectral prewhitener before equalization. We show that the ZF solutions are stationary points of TROMBONE, and include simulations demonstrating the performance of the two blind algorithms. We conclude with a summary of results and a listing of some immediate open issues revealed by this dissertation.