Optimal Wireless Equalizers

Wireless channels bring in new challenges unforeseen in wireline environments, e.g., ISI becomes time varying. Traditionally the equalizers (which nullify the ISI) were designed to optimize their performance (e.g., MSE) as a standalone component (equalizers were designed using sufficient amount of training that is transmitted prior to the actual data transmission). This approach was well suited for time invariant wireline channels. However with time varying nature of the wireless channels, training sequence needs to be sent frequently and the optimality of the above approach is questionable. Information theoretic measures are better suited to design an equalizer in such an environment. The first goal of the thesis is to obtain the best wireless equalizer (blind/semi-blind or training), using novel information-theoretic arguments (which study the trade-off between the BW lost and accuracy gained) for a given wireless scenario. Any practical communication system uses training algorithms and they are still optimal, as long as one optimizes their performance as a standalone component (i.e., when the loss in BW due to the training sequence is not considered). A training algorithm commonly uses MMSE criterion to obtain the solutions (e.g., MMSE channel estimate, MMSE equalizer etc). The LMS, an iterative and computationally efficient algorithm, is often used to converge to the MMSE solution. With the advent of (time varying) wireless communications it becomes important to understand the tracking behavior of a wireless component (e.g., channel estimator, equalizer etc). Until now, the theoretical tracking behavior (of a channel estimator) is obtained by modeling the wireless channel either as a first order AR process (e.g., Random Walk model) or as a deterministic periodic process. Block fading model is also used to study a slow fading channel. However, an