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.

The capacity regions are investigated for two relay broadcast channels (RBCs), where relay links are incorporated into standard two-user broadcast channels to support user cooperation. In the first channel, the Partially Cooperative Relay Broadcast Channel, only one user in the system can act as a relay and transmit to the other user through a relay link. An achievable rate region is derived based on the relay using the decode-and-forward scheme. An outer bound on the capacity region is derived and is shown to be tighter than the cut-set bound. For the special case where the Partially Cooperative RBC is degraded, the achievable rate region is shown to be tight and provides the capacity region. Two Gaussian cases of the Partially Cooperative RBC are studied. For the system where the additive Gaussian noise term at one receiver is a degraded version of the other, which we refer to as the D-AWGN Partially Cooperative RBC, the capacity region is established. For the system where the additive Gaussian noise term at one receiver is independent of the other, which we refer to as the AWGN Partially Cooperative RBC, inner and outer bounds on the capacity region are derived and are shown to be close. Furthermore, it is shown that feedback does not increase the capacity region for the degraded

We consider a general multiple-antenna network with multiple sources, multiple destinations, and multiple relays in terms of the diversity–multiplexing tradeoff (DMT). We examine several subcases of this most general problem taking into account the processing capability of the relays (half-duplex or full-duplex), and the network geometry (clustered or nonclustered). We first study the multiple-antenna relay channel with a full-duplex relay to understand the effect of increased degrees of freedom in the direct link. We find DMT upper bounds and investigate the achievable performance of decode-and-forward (DF), and compress-and-forward (CF) protocols. Our results suggest that while DF is DMT optimal when all terminals have one antenna each, it may not maintain its good performance when the degrees of freedom in the direct link are increased, whereas CF continues to perform optimally. We also study the multiple-antenna relay channel with a half-duplex relay. We show that the half-duplex DMT behavior can significantly be different from the full-duplex case. We find that CF is DMT optimal for half-duplex relaying as well, and is the first protocol known to achieve the half-duplex relay DMT. We next study the multiple-access relay channel (MARC) DMT. Finally, we investigate a system with a single source–destination pair and multiple relays, each node with a single antenna, and show that even under the ideal assumption of full-duplex relays and a clustered network, this virtual multiple-input multiple-output (MIMO) system can never fully mimic a real MIMO DMT. For cooperative systems with multiple sources and multiple destinations the same limitation remains in effect.

Abstract — We consider a general multiple antenna network with multiple sources, multiple destinations and multiple relays in terms of the diversity-multiplexing tradeoff (DMT). We examine several subcases of this most general problem taking into account the processing capability of the relays (half-duplex or full-duplex), and the network geometry (clustered or non-clustered). We first study the multiple antenna relay channel with a full-duplex relay to understand the effect of increased degrees of freedom in the direct link. We find DMT upper bounds and investigate the achievable performance of decode-and-forward (DF), and compress-and-forward (CF) protocols. Our results suggest that while DF is DMT optimal when all terminals have one antenna each, it may not maintain its good performance when the degrees of freedom in the direct link is increased, whereas CF continues to perform optimally. We also study the multiple antenna relay channel with a half-duplex relay. We show that the half-duplex DMT behavior can significantly be different from the full-duplex case. We find that CF is DMT optimal for half-duplex relaying as well, and is the first protocol known to achieve the halfduplex relay DMT. We next study the multiple-access relay channel (MARC) DMT. Finally, we investigate a system with a single source-destination pair and multiple relays, each node with a single antenna, and show that even under the idealistic assumption of full-duplex relays and a clustered network, this virtual multi-input multi-output (MIMO) system can never fully mimic a real MIMO DMT. For cooperative systems with multiple sources and multiple destinations the same limitation remains to be in effect. Index Terms — cooperation, diversity-multiplexing tradeoff, fading channels, multiple-input multiple-output (MIMO), relay

Abstract — A framework is developed for analyzing capacity gains from user cooperation in slow fading wireless networks when the number of nodes (network size) is large. The framework is illustrated for the case of a simple multipath-rich Rayleigh fading channel model. Both unicasting (one source and one destination) and multicasting (one source and several destinations) scenarios are considered. We introduce a meaningful notion of Shannon capacity for such systems, evaluate this capacity as a function of signal-to-noise ratio (SNR), and develop a simple two-phase cooperative network protocol that achieves it. We observe that the resulting capacity is the same for both unicasting and multicasting, but show that the network size required to achieve any target error probability is smaller for unicasting than for multicasting. Finally, we introduce the notion of a network “scaling exponent ” to quantify the rate of decay of error probability with network size as a function of the targeted fraction of the capacity. This exponent provides additional insights to system designers by enabling a finer grain comparison of candidate cooperative transmission protocols in even moderately sized networks. Index Terms — Wireless networking, multicasting, ad-hoc networks, sensor networks, cooperative diversity, outage capacity, scaling laws. I.

We analyze the diversity-multiplexing tradeoff in a fading relay channel at finite signal-to-noise ratios (SNRs). In this framework, the rate adaptation policy is such that the target system data rate is a multiple of the capacity of an additive white Gaussian noise (AWGN) channel. The proportionality constant determines how aggressively the system scales the data rate and can be interpreted as a finite-SNR multiplexing gain. The diversity gain is given by the negative slope of the outage probability with respect to the SNR. Finite-SNR diversity performance is estimated using a constrained max-flow min-cut upper bound on the relay channel capacity. Moreover, the finite-SNR diversity-multiplexing tradeoff is characterized for three practical decode and forward half-duplex cooperative protocols with different amounts of broadcasting and simultaneous reception. For each configuration, system performance is computed as a function of SNR under a system-wide power constraint on the source and relay transmissions. Our analysis yields the following findings; (i) improved multiplexing performance can be achieved at any SNR by allowing the source to transmit constantly, (ii) both broadcasting and simultaneous reception are desirable in half-duplex relay cooperation for superior diversitymultiplexing performance, and (iii) the diversity-multiplexing tradeoff at finite-SNR is impacted by the power partitioning between the source and the relay terminals. Finally, we verify our analytical results by numerical simulations.

This chapter provides an overview of the information theoretic foundations of cooperative communications. Earlier information theoretic achievements as well as the more recent developments are discussed. The analysis accounts for full/half-duplex nodes, and for multiple relays. Various channel models such as discrete memoryless, additive white Gaussian noise (AWGN) and fading channels are considered. Cooperative communication protocols are investigated using capacity, diversity and diversity-multiplexing tradeoff (DMT) as performance metrics. Overall, this chapter provides a comprehensive view on the foundations of, and the state-of-the-art reached in the theory of cooperative communications.

This paper focuses on analog network coding (ANC) and time division broadcasting (TDBC) which are two major protocols used in bidirectional cooperative networks. Lower bounds of the outage probabilities of those two protocols are derived first. Those lower bounds are extremely tight in the whole signal-to-noise ratio (SNR) range irrespective of the values of channel variances. Based on those lower bounds, finite-SNR diversity-multiplexing tradeoffs of the ANC and TDBC protocols are obtained. Secondly, we investigate how to efficiently use channel state information (CSI) in those two protocols. Specifically, an optimum power allocation scheme is proposed for the ANC protocol. It simultaneously minimizes the outage probability and maximizes the total mutual information of this protocol. For the TDBC protocol, an optimum method to combine the received signals at the relay terminal is developed under an equal power allocation assumption. This method minimizes the outage probability and maximizes the total mutual information of the TDBC protocol at the same time. I.

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Abstract — Resource allocation is investigated for fading relay channels under separate power constraints at the source and relay nodes. As a basic information-theoretic model for fading relay channels, the parallel relay channel is first studied, which consists of multiple independent three-terminal relay channels as subchannels. Lower and upper bounds on the capacity are derived, and are shown to match, and thus establish the capacity for the parallel relay channel with degraded subchannels. This capacity theorem is further demonstrated via the Gaussian parallel relay channel with degraded subchannels, for which the synchronized and asynchronized capacities are obtained. The capacity achieving power allocation at the source and relay nodes among the subchannels is partially characterized for the synchronized case and fully characterized for the asynchronized case. The fading relay channel is then studied, which is based on the three-terminal relay channel with each communication link being corrupted by a multiplicative fading gain coefficient as well as an additive Gaussian noise term. For each link, the fading state information is assumed to be known at both the transmitter and the receiver. The source and relay nodes are allowed to allocate their power adaptively according to the instantaneous channel state information. The source and relay nodes are assumed to be subject to separate power constraints. For both the full-duplex and half-duplex cases, power allocations that maximize the achievable rates are obtained. In the half-duplex case, the power allocation needs to be jointly optimized with the channel resource (time and bandwidth) allocation between the two orthogonal channels over which the relay node transmits and receives. Capacities are established for fading relay channels that satisfy certain conditions. Index Terms — Capacity, max-min, parallel relay channels, resource allocation, wireless relay channels.