This IMA Volume in Mathematics and its Applications Wireless Communications contains papers based on invited lectures at the very successful IMA Sum mer Program on Wireless Communications, held on June 22 - July 1, 2005. We would like to thank Prathima Agrawal (Auburn University), Daniel Matthew Andrews (Lucent Technologies), Philip J. Fleming (Mo torola, Inc.), George Yin (Wayne State University), and Lisa Zhang (Lucent Technologies) for their superb role as workshop organizers and editors of the proceedings. We take this opportunity to thank the National Science Foundation for its support of the IMA. Series Editors Douglas N. Arnold, Director of the IMA Arnd Scheel, Deputy Director of the IMA v PREFACE This volume presents papers, based on invited talks given at the 2005 IMA Summer Workshop on Wireless Communications, held at the Institute for Mathematics and Its Applications, University of Minnesota, June 22 July 1, 2005. The conference provided a well blended program to facilitate the com munications between academia and the industry, and to bridge the mathe matical sciences, engineering, information theory, and communication com munities. The emphases were on design and analysis of computationally efficient algorithms to better understand the behavior and to control the wireless telecommunication networks. As an achieve, this volume presents some of the highlights of the conference, and collects papers covering a broad spectrum of topics. All papers have been reviewed.