Abstract-We propose novel cooperative transmission protocols for delay-limited coherent fading channels consisting of (half-duplex and single-antenna) partners and one cell site. In our work, we differentiate between the relay, cooperative broadcast (down-link), and cooperative multiple-access (CMA) (up-link) channels. The proposed protocols are evaluated using Zheng-Tse diversity-multiplexing tradeoff. For the relay channel, we investigate two classes of cooperation schemes; namely, amplify and forward (AF) protocols and decode and forward (DF) protocols. For the first class, we establish an upper bound on the achievable diversity-multiplexing tradeoff with a single relay. We then construct a new AF protocol that achieves this upper bound. The proposed algorithm is then extended to the general case with relays where it is shown to outperform the space-time coded protocol of Laneman and Wornell without requiring decoding/encoding at the relays. For the class of DF protocols, we develop a dynamic decode and forward (DDF) protocol that achieves the optimal tradeoff for multiplexing gains . Furthermore, with a single relay, the DDF protocol is shown to dominate the class of AF protocols for all multiplexing gains. The superiority of the DDF protocol is shown to be more significant in the cooperative broadcast channel. The situation is reversed in the CMA channel where we propose a new AF protocol that achieves the optimal tradeoff for all multiplexing gains. A distinguishing feature of the proposed protocols in the three scenarios is that they do not rely on orthogonal subspaces, allowing for a more efficient use of resources. In fact, using our results one can argue that the suboptimality of previously proposed protocols stems from their use of orthogonal subspaces rather than the half-duplex constraint.Index Terms-Cooperative diversity, diversity-multiplexing tradeoff, dynamic decode and forward (DDF), half-duplex node, multiple-access channel, nonorthogonal amplify and forward (NAF), relay channel.

Abstract-In this correspondence, the performance of the automatic repeat request-dynamic decode and forward (ARQ-DDF) cooperation protocol is analyzed in two distinct scenarios. The first scenario is the multiple access relay channel where a single relay is dedicated to simultaneously help two multiple access users. For this setup, it is shown that the ARQ-DDF protocol achieves the channel's optimal diversity multiplexing tradeoff (DMT). The second scenario is the cooperative vector multiple access channel where two users cooperate in delivering their messages to a destination equipped with two receiving antennas. For this setup, a new variant of the ARQ-DDF protocol is developed where the two users are purposefully instructed not to cooperate in the first round of transmission. Lower and upper bounds on the achievable DMT are then derived. These bounds are shown to converge to the optimal tradeoff as the number of transmission rounds increases.Index Terms-Automatic repeat request (ARQ), cooperative diversity, cooperative vector multiple-access (CVMA) channel, diversity-multiplexing tradeoff (DMT), dynamic decode and forward (DDF), half-duplex node, multiple-access relay (MAR) channel. I. BACKGROUNDThe dynamic decode and forward (DDF) protocol was proposed in [1] as an efficient method to exploit cooperative diversity in the half-duplex relay channel (the same protocol was independently devised for other scenarios in [2] and [3]). In this paper, the DDF protocol is combined with the automatic repeat request (ARQ) mechanism to derive new variants that are matched to the multiple access relay (MAR) and cooperative vector multiple access (CVMA) channels. These variants, some of them presented in [11]-[13], are shown to achieve the optimal tradeoff between throughput and reliability, in the high signal-to-noise ratio (SNR) regime. For simplicity of presentation, in this correspondence, the number of users is restricted to two.Throughout this correspondence, all channels are assumed to be flat Rayleigh-fading and quasi-static. The quasi-static assumption implies that the channel gains remain fixed over a coherence interval, but change independently from one coherence interval to the next. In order to highlight the benefits of cooperation and ARQ, as opposed to temporal interleaving, the long-term static channel model of [6] is adopted where all ARQ rounds corresponding to a message take place over the same coherence interval. The channel gains are assumed to be mutually independent and of unit variance. The additive Gaussian noise processes are mutually independent, circularly symmetric, white, and of variance 2 . All nodes operate synchronously and are subject to a short-term power constraint. This constraint ensures that the average energy available to a symbol for transmission E is fixed. Under these assumptions, the average SNR of a link is defined as E 2 :Also, f () is said to be exponentially equal toIn (2), b is called the exponential order of f (). _ and _ are defined similarly. Except for Section III, where ...

This paper demonstrates the significant gains that multi-access users can achieve from sharing a single amplify-forward relay in slow fading environments. The proposed protocol, namely the multiaccess relay amplify-forward, allows for a low-complexity relay and achieves the optimal diversitymultiplexing trade-off at high multiplexing gains. Analysis of the protocol reveals that it uniformly dominates the compress-forward strategy and further outperforms the dynamic decode-forward protocol at high multiplexing gains. An interesting feature of the proposed protocol is that, at high multiplexing gains, it resembles a multiple-input single-output system, and at low multiplexing gains, it provides each user with the same diversity-multiplexing trade-off as if there is no contention for the relay from the other users.

In this paper, an outage limited MIMO channel is considered. We build on Zheng and Tse's elegant formulation of the diversity-multiplexing tradeoff to develop a better understanding of the asymptotic relationship between the probability of error, transmission rate, and signal-to-noise ratio. In particular, we identify the limitation imposed by the multiplexing gain notion and develop a new formulation for the throughput-reliability tradeoff that avoids this limitation. The new characterization is then used to elucidate the asymptotic trends exhibited by the outage probability curves of MIMO channels. * The authors are with the ECE Department at the Ohio State University (email:azariany, helga-mal@ece.osu.edu).

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In this paper, we propose novel cooperative transmission protocols for delay limited coherent fading channels consisting of N (half-duplex and singleantenna) partners and one cell site. In our work, we differentiate between the relay, cooperative broadcast (down-link), and cooperative multiple-access (up-link) channels. The proposed protocols are evaluated using Zheng-Tse diversity-multiplexing tradeoff. For the relay channel, we investigate two classes of cooperation schemes; namely, Amplify and Forward (AF) protocols and Decode and Forward (DF) protocols. For the first class, we establish an upper bound on the achievable diversity-multiplexing tradeoff with a single relay. We then construct a new AF protocol that achieves this upper bound. The proposed algorithm is then extended to the general case with (N − 1) relays where it is shown to outperform the space-time coded protocol of Laneman and Worenell without requiring decoding/encoding at the relays. For the class of DF protocols, we develop a dynamic decode and forward (DDF) protocol that achieves the optimal tradeoff for multiplexing gains 0 ≤ r ≤ 1/N. Furthermore, with a single relay, the DDF protocol is shown to dominate the class of AF protocols for all multiplexing gains. The superiority of the DDF protocol is shown to be more significant in the cooperative broadcast channel. The situation is reversed in the cooperative multiple-access channel where we propose a new AF protocol that achieves the optimal tradeoff for all multiplexing gains. A distinguishing feature of the proposed protocols in the three scenarios is that they do not rely on orthogonal subspaces, allowing for a more efficient use of resources. In fact, using our results one can argue that the sub-optimality of previously proposed protocols stems from their use of orthogonal subspaces rather than the half-duplex constraint.

In this paper, an outage limited MIMO channel is considered. We build on Zheng and Tse's elegant formulation of diversity-multiplexing tradeoff to develop a better understanding of the asymptotic relationship between probability of error, transmission rate and signal-to-noise ratio. We identify the limitation imposed by the notion of multiplexing gain and develop a new formulation for the throughput-reliability tradeoff that avoids this limitation. The new characterization is then used to shed more light on the asymptotic trends exhibited by the outage probability curves of MIMO channels. I. PROBLEM FORMULATIONThis paper revolves around the following question: What does a 3 dB increase in the signal-to-noise ratio (SNR) buy in an outage limited Multi-Input Multi-Output (MIMO) channel? In an Additive White Gaussian Noise (AWGN) setting, it is well known that, a 3 dB increase in SNR translates into one extra bit in channel's capacity in the high SNR regime. The scenario considered in this paper, however, is more involved. We address an outage limited channel, where the randomness of the instantaneous mutual information results in a non-zero lower bound on the probability of error, for non-zero constant transmission rates. Hence, a fundamental tradeoff between the throughput, as quantified by the transmission rate, and reliability, as quantified by the so-called outage probability, arises. Our work explores this tradeoff in the high SNR regime.In this paper, we consider a MIMO wireless communication system with m transmit and n receive antennas. We address a quasi-static flat-fading setup where the path gains remain constant over l consecutive symbol-intervals (i.e. a block), but change independently from one block to another. We further assume a coherent communication model implying the availability of channel state information (CSI) at the destination. Under these assumptions, the channel input-output relation is given by:In (1), y ∈ C n has entries y i representing the signal received at antenna i ∈ {1, · · · , n}, x ∈ C m has entries x j denoting the signal transmitted by antenna j ∈ {1, · · · , m}, and H ∈ C n×m has entries h ij which represents the path gain from receive antenna i ∈ {1, · · · , n} to transmit antenna j ∈ {1, · · · , m}. We model {h ij } as i.i.d unit-variance Rayleigh distributed random variables. w ∈ C n represents the unit-variance additive white Gaussian noise. Finally, ρ corresponds to the SNR at each receive antenna. Our work builds on Zheng and Tse's formulation of diversity-multiplexing tradeoff [1]. This formulation assumes a family of space-time codes {C ρ } indexed by their operating SNR ρ, such that the code C ρ has rate R(ρ), in bits per channel use (bpcu), and error probability P e (ρ). For this family, the multiplexing gain r and the diversity gain d are defined by(2)The optimal diversity-multiplexing tradeoff yields the maximum possible diversity gain for every value of r.The main result of [1] is summarized in the following theorem: Theorem 1: The optimal diversity gain for the...

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