Alejandro Ribeiro, University of Minnesota, USA and Georgios B. Giannakis, University of Minnesota, USA
The signal processing (SP) community has played a defining role in the field of wireless communications traditionally rooted around the so called physical layer. The emergence of cross-layer approaches and, more recently, the interest in network science calls for sound mathematical approaches to the design of wireless networks. Many SP tools can be applied to tackle these problems. The present tutorial targets researchers interested in working at the interface of signal processing and networking, in what we could call the emerging field of signal processing for networking. A by-product of this tutorial will be to enhance the interdisciplinary links between signal processing, communications and networking communities.
The theme of this tutorial is a unifying framework for optimal design of wireless networks. In particular, we show how to formulate a networking problem for wireless mobile ad-hoc networks (MANETS) to jointly optimize end-to-end user rates, routes, link capacities, transmitted power, frequency and power allocation across subcarriers and fading states. We show the rather surprising result that the resulting non-convex optimization problem has zero duality gap. This result is then exploited to establish that conventional layering can be optimal in wireless MANETS. Specifically, by selecting Lagrange multipliers appropriately, it is possible to decompose the original problem into smaller sub-problems associated with conventional networking layers. The solution of these per-layer optimization problems coincides with that of the originally formulated cross-layer optimization problem.
This layering result, uncovers the fact that the challenge in wireless networks is not as much in crosslayer optimization as in cross-terminal optimization of the physical layer. It is in solving this cross-terminal optimization problem where the most significant challenges are found and were research opportunities for SP researchers arise. This tutorial will cover the following topics.
The optimal wireless networking problem will be formulated, and the basic result establishing zero duality gap will be presented. It will then be explained how this result implies two fundamental properties of wireless networks in the presence of fading: i) the decomposition of the problem into the traditional networking layers can be optimal; and ii) the separability of the resource allocation problem into per-fading-state subproblems is possible. We will further discuss how of all the per-layer problems, it is the physical layer optimization that presents the biggest challenge.
Lagrangian decomposition techniques will then be discussed as a means of translating the solution of an optimization problem into a wireless networking protocol. This will be shown to lead to a decomposition of the networking problem in layers and layer interfaces. The layers are responsible for computing optimal networking variables whereas the interfaces update costs – mathematically corresponding to Lagrange multipliers – that the layers require in determining optimal network variables.
The last topic that will be discussed is the application of stochastic optimization tools to the wireless networking problem. This tools are widely known to our community as applied in adaptive filters. We will discuss how classical results in stochastic optimization lead to results in which optimal networking variables are computed without knowledge of the fading statistics but based only on observations of the current fading states. This results are reminiscent of adaptive filter’s results whereby the statistics of the input are learnt on the fly. In wireless networks not only the statistics of input variables, but of channel dynamics have to be acquired over time.
Alejandro Ribeiro received his B.Sc. degree in Electrical Engineering from Universidad de la Republica Oriental del Uruguay, Montevideo, Uruguay in 1998. He is currently a research associate in the Department of Electrical and Computer Engineering, University of Minnesota, Minneapolis, MN where he received his M.Sc. and Ph. D. degrees in Electrical Engineering in May 2005 and December 2006. From 1998 to 2003 he was a member of the Technical Staff at Bellsouth Montevideo. His research interests lie in the areas of communication theory, signal processing and networking. His current research focuses on wireless networking, cross-layer design, wireless sensor networks, and distributed signal processing. He received best student paper awards at the 2005 Int. Conf. Acoustics, Speech, Signal Process. (ICASSP) and 2006 ICASSP. Dr. Ribeiro is a Fulbright Scholar.
Georgios B. Giannakis (F’97) received his Diploma in Electrical Engineering from the National Technical University of Athens, Greece, 1981. From September 1982 to July 1986 he was with the University of Southern California (USC), where he received his MSc. in Electrical Engineering, 1983, MSc. in Mathematics, 1986, and Ph.D. in Electrical Engineering, 1986. After lecturing for one year at USC, he joined the University of Virginia in 1987, where he became a professor of Electrical Engineering in 1997. Since 1999 he has been a professor with the Department of Electrical and Computer Engineering at the University of Minnesota, where he now holds an ADC Chair in Wireless Telecommunications.
His general interests span the areas of communications, networking and signal processing – subjects on which he has published more than 250 journal papers, 450 conference papers, two research monographs and two edited books. Current research focuses on wireless networks, complex-field and space-time coding, ultra-wideband and cognitive radios, cross-layer designs and wireless sensor networks.
G. B. Giannakis is the (co-) recipient of six paper awards from the IEEE Signal Processing (SP) and Communications Societies. He also received Technical Achievement Awards from the SP Society in 2000 and from EURASIP in 2005. He served as Editor in Chief for the IEEE SP Letters, as Associate Editor for the IEEE Trans. on Signal Proc. and the IEEE SP Letters, as secretary of the SP Conference Board, as member of the SP Publications Board, as member and vice-chair of the Statistical Signal and Array Processing Technical Committee, as chair of the SP for Communications Technical Committee and as a member of the IEEE Fellows Election Committee. He has also served as a member of the IEEE-SP Society’s Board of Governors, the Editorial Board for the Proceedings of the IEEE and the steering committee of the IEEE Trans. on Wireless Communications. He is currently a Distinguished Lecturer of the IEEE-SP Society. He has delivered plenary and tutorial talks in many IEEE Conferences.