An Optimized User Selection Method for Cooperative Diversity Systems Diomidis S. Michalopoulos ∗§ , George K. Karagiannidis ∗ , Theodoros A. Tsiftsis † and Ranjan K. Mallik ‡ ∗ Telecommunications Division, Department of Electrical & Computer Engineering, Aristotle University of Thessaloniki, GR-54124, Thessaloniki, Greece Email:{dmixalo, geokarag}@auth.gr † Wireless Telecommunications Laboratory, Department of Electrical & Computer Engineering, University of Patras, Rion, GR-26500, Patras, Greece Email: tsiftsis@ee.upatras.gr ‡ Department of Electrical Engineering, Indian Institute of Technology - Delhi, Haus Khas, New Delhi 110016, India (e-mail: rkmallik@ee.iitd.ernet.in) § The work of Mr Michalopoulos is supported by the Greek General Secretariat of Research and Technology under PENED’04 Abstract— Multi-user cooperative diversity is a recent techni- que promising great improvement of the performance of wireless communication systems operating in fading environments. Based on combinatorial optimization theory and specifically on the so-called knapsack problem, this paper presents a method of optimizing the selection among the potential cooperating users, when amplify-and-forward relays are used. In particular, two optimization problems are studied: the error probability mini- mization subject to total energy consumption constraints, and the dual one, the energy consumption minimization under error performance constraints. Depending on the frequency of repea- ting this selection, the above problems are categorized into short- term and long-term node selection. Numerical examples verify the expected knapsack scheme’s advantage of adapting the number of cooperating users, depending on the desired performance- consumption tradeoff. Moreover, long-term node selection seems to lead to similar error or consumption performance compared to the short-term one, despite its simplicity. I. I NTRODUCTION In the last few years, a new concept that is being acti- vely studied in multihop-augmented networks is multi-user cooperative diversity, where several terminals form a kind of coalition to assist each other with the transmission of their messages. In general, cooperative relaying systems have a source node multicasting a message to a number of cooperative relays, which in turn resend a processed version to the intended destination node. The destination node combines the signal received from the relays, taking into account the source’s original signal [1]- [4]. The main contribution of this paper is the proposal of a novel node-selection strategy for multi-user cooperative diversity systems, according to which only a subset of the set of available users is activated, in order to achieve the optimal balance between error performance and total consumed energy. More specifically, two variations of this problem are intro- duced: the end-to-end error performance optimization under total power constraints, and the dual one, the minimization of the total consumed energy provided that the end-to-end error probability will not exceed a predefined threshold. This is accomplished by utilizing the general concept of optimizing the selection among the elements of a given set under specific constraints, which was first introduced in combinatorial opti- mization theory: Given an item set, and assuming that each item is characterized by a unique pair of profit and weight va- lues, the subset that maximizes the profit summation provided that the weight summation does not exceed a maximum value needs to be distinguished. These problems are widely known as knapsack problems [5]. In this work, dual-hop amplify-and-forward cooperative diversity is assumed, where a number of individual relays amplify and retransmit the signal received from the source node to the destination one. The structure of the studied model is further analyzed in Section II; in Section III, the knapsack application on cooperative diversity systems is presented. In such applications, the gain and the energy each relay consumes depends usually only on the fading state of its input channel, in order to limit the output power of the relay. Moreover, assuming maximal ratio combining (MRC) at the receiver, the instantaneous 1 overall signal to noise ratio (SNR) is the sum of the end-to-end SNRs corresponding to each separate branch. These end-to-end SNRs, reflect the branches’ ability to contribute to the total performance enhancement, and are also determined by a combination of the fading state of the chan- nels in the input and the output of the corresponding relays. We thus realize that two scalar metrics can be attributed to each branch, depending only on the fading conditions corresponding to it, and characterizing its contribution to the end-to-end performance and its energy consumption respectively. Then, the error performance optimization problem under total energy consumption constraints, and the dual problem of minimizing the energy consumption provided that the received SNR is not arbitrarily small, can be reduced to knapsack ones. This requires that the selection is repeated on a frequent basis, at a rate that ensures constant fading characteristics in every selection interval. Next, this type of selection is referred as short-term node selection (STNS), and is further analyzed in Section IV. In Section V, a solution that tackles the above problems in an average sense is presented. More specifically, since all channels are considered ergodic, the metrics that are attributed to the corresponding relays are determined by their fading 1 In the following, the term instantaneous will be used in a loose sense, describing the time interval in which the fading state can be considered constant. © 1-4244-0357-X/06/$20.00 2006 IEEE This full text paper was peer reviewed at the direction of IEEE Communications Society subject matter experts for publication in the IEEE GLOBECOM 2006 proceedings.