Schur-Convex Structures in Wireless Communications
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Title: Schur-Convex Structures in Wireless Communications: Power and Feedback Control

This talk consists of two parts focusing on two different design problems in wireless communications,
but having the same unifying mathematical machinery connecting both.

In the first part, we will focus on the optimum single cell power control maximizing the aggregate (uplink)
communication rate of the cell when there are peak power constraints at mobile users, and a low-complexity
data decoder (without successive decoding) at the base station. It will be shown that the optimum power
allocation is binary, which means that links are either on or off. Further, the users transmitting at full power
correspond to the ones having better channel states. Sufficient conditions under which channel-state aware
time division multiple access (TDMA) maximizes the aggregate communication rate will be established.
Power control problems in the areas of femtocells and cognitive radio will also be investigated, and it will be
shown that optimal solutions have a binary (or almost binary) character. These results are obtained by
exploiting an underlying Schur-convex structure of the sum-rate. 

In the second part, we will focus on sum-rate maximizing selective decentralized feedback policies for vector
broadcast channels under finite feedback constraints. First, it will be shown that any sum-rate maximizing
selective decentralized feedback policy must be a threshold feedback policy. This result holds for all fading
channel models with continuous distribution functions. Secondly, the resulting optimum threshold selection
problem will be analyzed in detail. This is a non-convex optimization problem over finite dimensional Euclidean
spaces. By utilizing the theory of majorization, an underlying Schur-concave structure in the sum-rate function
will be identified, and the sufficient conditions for the optimality of homogenous threshold feedback policies
will be obtained.  Rather surprisingly, it will be shown that using the same threshold value at all mobile users is
not always a rate-wise optimal feedback strategy, even for a network in which mobile users experience
statistically the same channel conditions. For the Rayleigh fading channel model, on the other hand, homogenous
threshold feedback policies will be proven to be rate-wise optimal if multiple orthonormal data carrying beams
are used to communicate with multiple mobile users simultaneously. 

Hazer Inaltekin is an Assistant Professor of Electrical and Electronics Engineering at Antalya International University.
He received his B.S. degree (with High Hons.) in electrical and electronics engineering from Bogazici University,
Istanbul, Turkey, in 2001, and his M.S./Ph.D. degree in electrical and computer engineering from Cornell University,
Ithaca, NY, in 2006. He was a Postdoctoral Research Associate at Cornell University from 2006 to 2007, and at
Princeton University, Princeton, NJ, from 2007 to 2009. In 2009, he joined the Department of Electrical and Electronic
Engineering at the University of Melbourne as a Research Fellow. He was a Senior Research Fellow at the same
department between January 2011 and August 2011. Since August 2011, he has been on the faculty at Antalya
International University. He is the recipient of Marie Curie Career Integration Grant, and the principle investigator of
TUBITAK EVRENA 1010 project for radio resource management in next generation wireless networks. His current
research interests include wireless communications, wireless networks, social networks, game theory, and information
theory. More information on his research can be obtained through