Cooperative Transmission in a Wireless Relay Network based on Flow Management

arXiv:0903.2820v2 [cs.IT] 16 Nov 2009 Cooperative Transmission in a Wireless Relay Network based on Flow Management Debdeep Chatterjee, Tan F. Wong, and Tat M. Lok Abstract In this paper, a cooperative transmission design for a general multi-node half-duplex wireless relay network is presented. It is assumed that the nodes operate in half-duplex mode and that channel information is available at the nodes. The proposed design involves solving a convex flow optimization problem on a graph that models the relay network. A much simpler generalized-link selection protocol based on the above design is also presented. Both the proposed flow-optimized protocol and the generalized-link selection protocol are shown to achieve the optimal diversity-multiplexing tradeoff (DMT) for the relay network. Moreover, simulation results are presented to quantify the gap between the performances of the proposed protocols and that of a max-flow-min-cut type bound, in terms of outage probability. I. INTRODUCTION A wireless relay network is one in which a set of relay nodes assist a source node transmit information to a destination node. Practically the wireless nodes can only support half-duplex communication [1], i.e., no nodes can receive and transmit information simultaneously on the same frequency band. Different cooperative transmission schemes for systems with half-duplex nodes have been proposed in the literature. Fundamentally, these schemes consist of two basic steps. First, the source transmits to the destination, and the relay listens and “captures” [2] the This research is supported in part by the National Science Foundation under Grant CNS-0626863 and by the Air Force Office of Scientific Research under Grant FA9550-07-10456. A part of this work was presented at the IEEE Wireless Communications and Networking Conference (WCNC), Las Vegas, March 2008. D. Chatterjee and T. F. Wong are with the Department of Electrical and Computer Engineering, University of Florida, Gainesville, FL 32611-6130, U.S.A. e-mail:{debdeep,twong}@ufl.edu T. M. Lok is with Department of Information Engineering, The Chinese University of Hong Kong, Shatin, Hong Kong e-mail:tmlok@ie.cuhk.edu.hk 2 transmission from the source at the same time. Next, the relays send processed source information to the destination while the source may still transmit to the destination directly. Variants of these techniques have been proposed and have been shown to yield good performance under different circumstances [1], [3], [4]. Assuming channel state information (CSI) at the nodes, an opportunistic decode-and-forward (DF) protocol for half-duplex relay channels is proposed in [5]. In [6], the authors present routing algorithms to optimize the rate from a source to a destination, based on the DF technique that uses regular block Markov encoding and windowed decoding [7], [8], for the Gaussian full- duplex multiple-relay channel. The achievable rate of [7] for the Gaussian physically degraded full-duplex multi-relay channel has been established as the capacity of this channel in [9]. In [10], it is shown that the cut-set bound on the capacity of the Gaussian single source-multiple relay-single destination mesh network can be achieved using the compress-and-forward (CF) method, as the relay powers go to infinity. Some simpler cooperative diversity methods based on network path selection have been recently reported [11], [12]. These selection methods include: (i) the max-min selection method [11], wherein the relay node with the maximum of the minimum of the source-relay and relay- destination channel gains is selected; (ii) the harmonic mean selection method [11], wherein the relay node with the highest harmonic mean of the source-relay and relay-destination channel gains is selected; and (iii) the selection scheme of [12], in which the relay that can correctly decode the information from the source and has the best relay-destination channel is selected. These methods achieve a DMT of d(r) = (N −1)(1 −2r) for an N node relay network and multiplexing gain 0 < r < 0.5. This is close to what the distributed space-time coding protocol [13] achieves, when N is large. Unfortunately, these network selection protocols perform poorly in high-rate scenarios (r > 0.5). We have proposed a cooperative diversity design based on a flow optimization approach for a three-node network in [14]. In this design, the source node broadcasts two distinct flows to the destination and the relay node respectively during the relay’s listen period. Then the relay forwards this information using the DF approach while the source may also send another flow 3 of information to the destination during the relay’s transmit period. This scheme is shown to achieve the optimal diversity order for the three-node relay channel and yield performance very close to optimal full-duplex relaying in both low- and high-rate situations. Here, we apply this cooperative transmission design to a general relay network, where

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