MIMO Two-way Relay Channel: Diversity-Multiplexing Tradeoff Analysis

📝 Abstract

A multi-hop two-way relay channel is considered in which all the terminals are equipped with multiple antennas. Assuming independent quasi-static Rayleigh fading channels and channel state information available at the receivers, we characterize the optimal diversity-multiplexing gain tradeoff (DMT) curve for a full-duplex relay terminal. It is shown that the optimal DMT can be achieved by a compress-and-forward type relaying strategy in which the relay quantizes its received signal and transmits the corresponding channel codeword. It is noteworthy that, with this transmission protocol, the two transmissions in opposite directions can achieve their respective single user optimal DMT performances simultaneously, despite the interference they cause to each other. Motivated by the optimality of this scheme in the case of the two-way relay channel, a novel dynamic compress-and-forward (DCF) protocol is proposed for the one-way multi-hop MIMO relay channel for a half-duplex relay terminal, and this scheme is shown to achieve the optimal DMT performance.

💡 Analysis

A multi-hop two-way relay channel is considered in which all the terminals are equipped with multiple antennas. Assuming independent quasi-static Rayleigh fading channels and channel state information available at the receivers, we characterize the optimal diversity-multiplexing gain tradeoff (DMT) curve for a full-duplex relay terminal. It is shown that the optimal DMT can be achieved by a compress-and-forward type relaying strategy in which the relay quantizes its received signal and transmits the corresponding channel codeword. It is noteworthy that, with this transmission protocol, the two transmissions in opposite directions can achieve their respective single user optimal DMT performances simultaneously, despite the interference they cause to each other. Motivated by the optimality of this scheme in the case of the two-way relay channel, a novel dynamic compress-and-forward (DCF) protocol is proposed for the one-way multi-hop MIMO relay channel for a half-duplex relay terminal, and this scheme is shown to achieve the optimal DMT performance.

📄 Content

arXiv:0812.3642v1 [cs.IT] 18 Dec 2008 MIMO Two-way Relay Channel: Diversity-Multiplexing Tradeoff Analysis Deniz G¨und¨uz∗†, Andrea Goldsmith†, H. Vincent Poor∗, ∗Department of Electrical Engineering, Princeton University, Princeton, NJ. †Department of Electrical Engineering, Stanford University, Stanford, CA. Email: dgunduz@princeton.edu, andrea@wsl.stanford.edu, poor@princeton.edu Abstract— A multi-hop two-way relay channel is considered in which all the terminals are equipped with multiple antennas. Assuming independent quasi-static Rayleigh fading channels and channel state information available at the receivers, we characterize the optimal diversity-multiplexing gain tradeoff (DMT) curve for a full-duplex relay terminal. It is shown that the optimal DMT can be achieved by a compress-and-forward type relaying strategy in which the relay quantizes its received signal and transmits the corresponding channel codeword. It is noteworthy that, with this transmission protocol, the two transmissions in opposite directions can achieve their respective single user optimal DMT performances simultaneously, despite the interference they cause to each other. Motivated by the optimality of this scheme in the case of the two-way relay channel, a novel dynamic compress-and-forward (DCF) protocol is proposed for the one-way multi-hop MIMO relay channel for a half-duplex relay terminal, and this scheme is shown to achieve the optimal DMT performance. I. INTRODUCTION Relays have found applications in many wireless networks to enhance coverage, reliability and throughput. Following [1] and [2] there has been a growing interest in developing cooperative relaying techniques for wireless systems. While one-way relaying has been widely considered in the litera- ture, in most practical communication scenarios data flows in both directions. Hence, the relay can be used to improve the performance of both transmissions simultaneously. This pragmatic approach has been modeled as the two-way relay channel in the literature and has attracted significant recent interest [3], [4], [5]. Although many involved transmission schemes have been proposed for communication over two- way relay channels [3], [6], [7], the capacity region remains open. In this paper, we consider a “separated” two-way relay channel (sTRC) [6], in which the two users can receive signals only from the relay terminal (see Fig. 1). In practice, this corresponds to a scenario in which the users are physically separated and the signals received from each other are negli- gible, such as two distant land stations communicating with a satellite, or two mobile users located on opposite sides of a building communicating with the same base station on top This research was supported by the National Science Foundation under Grants ANI-03-38807 and CNS-06-25637, the DARPA ITMANET program under Grant 1105741-1-TFIND, and the U.S. Army Research Office under MURI award W911NF-05-1-0246. } } } M1 Mr M2 H1 H2 H3 H4 S1 R S2 Fig. 1. The (M1, M2, M3) separated MIMO two-way relay channel model. There is no direct link between the user terminals S1 and S2. of the building. When there is no direct connection between the two wireless terminals, relays are essential to enable communication. We consider multiple antennas at each terminal and model the channels between the users as quasi-static, independent, frequency non-selective Rayleigh fading channels, and assume that perfect channel state information (CSI) is available only at the receivers. Our focus here is on the diversity-multiplexing tradeoff (DMT) analysis for the multiple-input multiple-output (MIMO) sTRC. DMT analysis, introduced in [8], is useful in characterizing the fundamental tradeoff between the reliabil- ity and the number of degrees-of-freedom of a system. We measure the reliability by the diversity gain, defined as the rate of decay of the error probability with increasing SNR, and measure the degrees-of-freedom of the system by the spatial multiplexing gain, defined as the rate of increase in the transmission rate with SNR. The optimal DMT of a point-to- point MIMO system is characterized in [8], and it is shown to be a piecewise linear function. When only one of the users is active, the sTRC model reduces to a MIMO multi-hop relay channel, for which the optimal DMT is characterized in [9]. For a full-duplex re- lay terminal the optimal DMT for this multi-hop setup is achievable by decode-and-forward (DF) relaying. On the other hand, if the relay is constrained to half-duplex operation, fixed time allocation schemes fall short of the optimal DMT performance, while the dynamic decode-and-forward (DDF) protocol, introduced in [10], can be shown to be DMT-optimal. In this paper, we show that in sTRC the DF protocol fails to achieve the optimal DMT performance even in the case of a full-duplex relay. Enforcing the relay terminal to decode both messages limits the achievable multiplexing gains due to the additional sum-rate const

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