DMT of multi-hop cooperative networks-Part II: Layered and multi-antenna networks

Sreeram, K.; Birenjith, S.; Kumar, P. Vijay

doi:10.1109/isit.2008.4595356

Cited by 11 publications

(5 citation statements)

References 10 publications

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“…The above discussion shows that static QMF and DDF are sufficient to achieve the optimal trade-off in the singlerelay channel when a = b. Moreover, in all other scenarios studied in the literature such as [14], [15] where the optimal DMT is achieved by another strategy, it can be shown that either DDF or static QMF is also optimal with the added benefit of avoiding extra requirements on transmit CSI at the relays. Therefore, the current results in the literature for halfduplex relay networks (including our result above) exhibit the following dichotomy: in all cases where the DMT of halfduplex relay networks is known it is either achieved by DDF where the relay waits until it can fully decode the source message, or by QMF with a fixed schedule independent of the channel realizations.…”

Section: Introductionmentioning

confidence: 80%

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When Are Dynamic Relaying Strategies Necessary in Half-Duplex Wireless Networks?

Kolte

Özgür

Diggavi

2015

IEEE Trans. Inform. Theory

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Abstract-In this paper we study a simple question: when are dynamic relaying strategies essential in optimizing the diversitymultiplexing tradeoff (DMT) in half-duplex wireless relay networks? This is motivated by apparently two contrasting results even for a simple 3 node network, with a single half-duplex relay. When all channels in the system are assumed to be independent and identically fading, a static schedule where the relay listens half the time and transmits half the time combined with quantizemap-and-forward (QMF) relaying is known to achieve the fullduplex performance. However, when there is no direct link between the source and the destination, a dynamic decodeand-forward (DDF) strategy is needed to achieve the optimal tradeoff. In this case, a static schedule is strictly suboptimal and the optimal tradeoff is significantly worse than the fullduplex performance. In this paper we study the general case when the direct link is neither as strong as the other links nor fully non-existent, and identify regimes where dynamic schedules are necessary and those where static schedules are enough. We identify four qualitatively different regimes for the single relay channel where the tradeoff between diversity and multiplexing is significantly different. We show that in all these regimes one of the above two strategies is sufficient to achieve the optimal tradeoff by developing a new upper bound on the best achievable tradeoff under channel state information available only at the receivers. A natural next question is whether these two strategies are sufficient to achieve the DMT of more general half-duplex wireless networks with a larger number of relays. We propose a generalization of the two existing schemes through a dynamic QMF strategy, where the relay listens for a fraction of time depending on received CSI but not long enough to be able to decode. We show that such a dynamic QMF (DQMF) strategy is needed to achieve the optimal DMT in a parallel channel with two relays, outperforming both DDF and static QMF strategies.

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Section: Introductionmentioning

confidence: 80%

“…Finally, it is easy to check that introducing non-negativity conditions on α, β, γ and redefining r ′ h.d. as (12) instead of (29) does not change the problem, which gives us (15).…”

Section: Appendix B Characterizing Dmt Under Global Csimentioning

confidence: 99%

When Are Dynamic Relaying Strategies Necessary in Half-Duplex Wireless Networks?

Kolte

Özgür

Diggavi

2015

IEEE Trans. Inform. Theory

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“…• In Lemma 2, we show that to ensure the instantaneous transmit power almost surely displays no exponential growth, and that the end-to-end capacity of the dominant eigenchannel almost surely displays no exponential decay (i.e., from (18) and (19), λ αH,1 = 0), the average transmit power must grow exponentially with n. Furthermore, this rate of average power growth can be reduced by: 1) implementing variable-gain instead of fixed-gain, 2) increasing the number of antennas at each node.…”

Section: Key Resultsmentioning

confidence: 91%

“…Meanwhile, in [14], c n was assessed for general n-hop AF networks in terms of the limiting (in d) eigenvalue distribution of products of random matrices when noise was not negligible at the relay nodes. Related work on the diversity-multiplexing tradeoff, [15], for various MIMO multihop relaying strategies can be found in [8], [16]- [18].…”

Section: Introductionmentioning

confidence: 99%

Capacity and Power Scaling Laws for Finite Antenna MIMO Amplify-and-Forward Relay Networks

Simmons

Coon

Warsi

2016

IEEE Trans. Inform. Theory

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In this paper, we present a novel framework that can be used to study the capacity and power scaling properties of linear multiple-input multiple-output (MIMO) d × d antenna amplify-and-forward (AF) relay networks. In particular, we model these networks as random dynamical systems (RDS) and calculate their d Lyapunov exponents. Our analysis can be applied to systems with any per-hop channel fading distribution, although in this contribution we focus on Rayleigh fading. Our main results are twofold: 1) the total transmit power at the nth node will follow a deterministic trajectory through the network governed by the network's maximum Lyapunov exponent, 2) the capacity of the ith eigenchannel at the nth node will follow a deterministic trajectory through the network governed by the network's ith Lyapunov exponent. Before concluding, we concentrate on some applications of our results. In particular, we show how the Lyapunov exponents are intimately related to the rate at which the eigenchannel capacities diverge from each other, and how this relates to the amplification strategy and number of antennas at each relay. We also use them to determine the extra cost in power associated with each extra multiplexed data stream.

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“…We give explicit protocols and code constructions for all cases. Some of these results were presented in conference versions of this paper [12]- [15] (see also [16], [17]).…”

Section: E Resultsmentioning

confidence: 99%

DMT of Multi-hop Cooperative Networks - Part II: Half-Duplex Networks with Full-Duplex Performance

Sreeram,

Birenjith,

Kumar

2008

Preprint

Self Cite

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We consider single-source single-sink (ss-ss) multihop relay networks, with slow-fading links and single-antenna half-duplex relay nodes. While two-hop cooperative relay networks have been studied in great detail in terms of the diversitymultiplexing gain tradeoff (DMT), few results are available for more general networks. In a companion paper, we characterized end points of DMT of arbitrary networks, and established some basic results which laid the foundation for the results presented here. In the present paper, we identify two families of networks that are multi-hop generalizations of the two-hop network: K-Parallel-Path (KPP) networks and layered networks.KPP networks may be viewed as the union of K nodedisjoint parallel relaying paths. Generalizations of these networks include KPP(I) networks, which permit interference between paths and KPP(D) networks, which possess a direct link between source and sink. We characterize the DMT of these families of networks completely for K > 3 and show that they can achieve the cut-set bound, thus proving that the DMT performance of full-duplex networks can be obtained even in the presence of the half-duplex constraint. We then consider layered networks, which are comprised of layers of relays, and prove that a linear DMT between the maximum diversity dmax and the maximum multiplexing gain of 1 is achievable for single-antenna fullyconnected(fc) layered networks. This is shown to be equal to the cut-set bound on DMT if the number of relaying layers is less than 4, thus characterizing the DMT of this family of networks completely. For multiple-antenna KPP and layered networks, we provide lower bounds on DMT, that are significantly better than the best-known bounds.All protocols in this paper are explicit and use only amplifyand-forward (AF) relaying. We also construct codes with short block-lengths based on cyclic division algebras that achieve the optimal DMT for all the proposed schemes. In addition, it is shown that codes achieving full diversity on a MIMO Rayleigh channel achieve full diversity on arbitrary fading channels as well.Two key implications of the results in the paper are that the half-duplex constraint does not entail any rate loss for a large class of cooperative networks and that simple AF protocols are often sufficient to attain the optimal DMT.

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DMT of multi-hop cooperative networks-Part II: Layered and multi-antenna networks

Cited by 11 publications

References 10 publications

When Are Dynamic Relaying Strategies Necessary in Half-Duplex Wireless Networks?

When Are Dynamic Relaying Strategies Necessary in Half-Duplex Wireless Networks?

Capacity and Power Scaling Laws for Finite Antenna MIMO Amplify-and-Forward Relay Networks

DMT of Multi-hop Cooperative Networks - Part II: Half-Duplex Networks with Full-Duplex Performance

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