4548 IEEE TRANSACTIONS ON INFORMATION THEORY, VOL. 54, NO. 10, OCTOBER 2008 Decode-and-Forward Relaying With Quantized Channel State Feedback: An Outage Exponent Analysis Tùng T. Kim, Student Member, IEEE, Giuseppe Caire, Fellow, IEEE, and Mikael Skoglund, Senior Member, IEEE Abstract—The problem of resource allocation to maximize the outage exponent over a fading relay channel using the decode-and-forward protocol with quantized channel state feedback (CSF) is studied. Three different scenarios are considered: relay-to-source, destination-to-relay, and desti- nation-to-source-and-relay CSF. In the relay-to-source CSF scenario, it is found that using merely one bit of CSF to control the source transmit power is sufficient to achieve the multi- antenna upper bound in a range of multiplexing gains. In the destination-to-relay CSF scenario, the systems slightly outper- form dynamic decode-and-forward (DDF) at high multiplexing gains, even with only one bit of feedback. Finally, in the destina- tion-to-source-and-relay CSF scenario, if the source-relay channel gain is unknown to the feedback quantizer at the destination, the diversity gain only grows linearly in the number of feedback levels, in sharp contrast to an exponential growth for multiantenna chan- nels. In this last scenario, a simple scheme is shown to perform close to the corresponding upper bound. Index Terms—Cooperative communications, diversity methods, diversity-multiplexing tradeoff, fading channels, large-deviation analysis, power control, relay channels. I. INTRODUCTION M OTIVATED by the potential of having simple single-an- tenna communication nodes cooperate and approach the promising performance of multiantenna systems, there has been a renewed interest in the classical relay channels [1], [2], for ex- ample in the recent work [3]–[8]. Resource allocation for relay channels is known to enhance the performance significantly in many different scenarios [9]–[15]. Most previous work on re- source allocation, however, assumed perfect network state infor- mation at both the source and the relay. In [16], power control Manuscript received May 18, 2007; revised January 16, 2008. Current version published September 17, 2008. This work was supported in part by the Swedish Research Council. The work of G. Caire was partially supported by the NSF under Grant NeTS-NOSS-0722073. The material in this paper was presented in part at the IEEE Information Theory Workshop, Lake Tahoe, CA, September 2007. This work was carried out when T. T. Kim was a Visiting Researcher at University of Southern California, Los Angeles, CA. T. T. Kim and M. Skoglund are with the School of Electrical Engineering and also with the ACCESS Linnaeus Center, Royal Institute of Technology (KTH), 10044 Stockholm, Sweden (e-mail: tung.kim@ee.kth.se; mikael.skoglund@ee. kth.se). G. Caire is with the Department of Electrical Engineering, University of Southern California, Los Angeles, CA, 90089 USA (e-mail: caire@usc.edu). Communicated by A. J. Goldsmith, Associate Editor for Communications. Color versions of Figures 2–4, 6, and 7 in this paper are available online at http://ieeexplore.ieee.org. Digital Object Identifier 10.1109/TIT.2008.928978 for amplify-and-forward relaying (AF) with quantized feedback from the destination is considered, but a diversity analysis is not pursued. The fundamental tradeoff between diversity and multi- plexing gains over a slow fading channel, first characterized for the point-to-point multiantenna scenario in [17], gives useful insight into the relation between throughput and re- liability of a system in the regime of asymptotically high signal-to-noise ratio (SNR). For the relay channel, the tradeoff curves of some baseline schemes are obtained in [6] and [18]. A sophisticated scheme named dynamic decode-and-forward (dynamic DF—DDF) is studied in [19] and shown to achieve the multiantenna upper bound at all multiplexing gains less than one-half. (In the present work the term DDF refers to the DDF scheme without any feedback from the destination [19], unless otherwise specified.) The diversity-multiplexing tradeoff over relay channels with AF protocols is extensively treated in [19]–[21]. From a diversity-multiplexing tradeoff point of view, compress-and-forward (CF) relaying is shown to be optimal [22], under the critical assumption that the relay knows the full channel state information (CSI). In the recent work [23], optimizing the dimension allocation for DF using only statistical knowledge about the channel is considered. The present work considers a three-node half-duplex coop- erative communication channel subject to very slowly varying, but random, channel gains (quasi-static fading), under different forms of heavily quantized channel state feedback (CSF). The partial CSF is used to allocate the number of channel uses in the two phases of the DF protocol, i.e., dimension allocation, and also to control the transmit power across fading states. Note that temporal power control across fading blocks is a useful means to improve the diversity gain over slow fading channels [24]–[26]. Both orthogonal (source and relay do not transmit simultane- ously) and nonorthogonal (source and relay can transmit at the same time) schemes are considered. Three different feedback scenarios are considered: relay-to- source CSF, destination-to-source-and-relay CSF, and destina- tion-to-relay CSF. The last case is motivated by the fact that in certain scenarios, the feedback link from the destination to the source is of significantly lower quality than that from the desti- nation to the relay (which inspires the relaying model in the first place). The possibilities that we do not study are the destina- tion-to-source CSF case and the scenario of joint feedback from both the relay and the destination. The former case is omitted because of the relative distances between the nodes in practice. It is unrealistic that the feedback from the destination is reliably 0018-9448/$25.00 © 2008 IEEE