Previous work on relay networks has concentrated primarily on the diversity benefits of such techniques. This paper explores the possibility of also obtaining multiplexing gain in a relay network, while retaining diversity gain. Specifically, consider a network in which a single source node is equipped with one antenna and a destination is equipped with two antennas. It is shown that, in certain scenarios, by adding a relay with two antennas and using a successive relaying protocol, the diversity multiplexing tradeoff performance of the network can be lower bounded by that of a 2 by 2 MIMO channel, when the decode-and-forward protocol is applied at the relay. A distributed D-BLAST architecture is developed, in which parallel channel coding is applied to achieve this tradeoff. A space-time coding strategy, which can bring a maximal multiplexing gain of more than one, is also derived for this scenario. As will be shown, while this space-time coding strategy exploits maximal diversity for a small multiplexing gain, the proposed successive relaying scheme offers a significant performance advantage for higher data rate transmission. In addition to the specific results shown here, these ideas open a new direction for exploiting the benefits of wireless relay networks.
Generally speaking, a relay network can act as a virtual multiple-input multiple-output (MIMO) system if the nodes are allowed to cooperate [1], [5], [6]. It is well known that a MIMO system has two advantages over single-input singleoutput systems, namely multiplexing gain and diversity gain. The diversity gain can improve the system outage performance (i.e, reliability), while the multiplexing gain enhances the spectral efficiency for high SNR. The tradeoff between diversity and multiplexing gain is a key characteristic of MIMO systems [2]- [4], and hence for relay networks (virtual MIMO systems). The optimal diversity-multiplexing trade-off (DMT) for half-duplex relay networks is yet to be discovered [5], [6], especially in the scenario in which multiple antennas can be deployed at one node. However, instead of looking at both multiplexing and diversity behavior simultaneously, most of the past work emphasizes primarily the diversity benefits of the relay network(e.g. [1]), while ignoring the possible multiplexing benefits it could bring. Unlike a point-to-point MIMO link, in a half-duplex relay network, multiplexing gain is difficult to obtain due to the additional transmission time slots the relays require. In fact, it has been shown recently [6] that no multiplexing gain (of more than 1) can be achieved for high SNR in general, when the source is deployed with only one antenna, even if full-duplex relay transmission is assumed. We note that, compared with full-duplex relaying, half-duplex relaying is recognized to be a suboptimal but more practical choice for wireless networks.
As one might hope that relaying could bring both diversity and multiplexing gain, investigating and realizing this possibility is of significant importance. Very recently, some capacity analyses [7], [8] on scalar channels have shown that only under certain signal to noise ratio (SNR) constraints, is it possible to achieve a MIMO rate through full-duplex relaying. However, the DMT for these SNR values in fading environments is not exploited and discussed in these papers.
In this paper, we show that it is even possible to obtain multiplexing gain in a half-duplex relay network. We consider a scenario in which the relays perform decode-and-forward. Specifically, we consider a one-antenna source, a two-antenna relay, and a two-antenna destination. We apply a successive relaying protocol to make the two antennas at the relay transmit in turn. We show that in this scenario a DMT that is at least as good as that of a 2 × 2 MIMO channel can be obtained under certain finite SNR or channel constraint. Based on our network model, we show that the constraint can be expressed by an upper bound for the SNR and a function of the channel coefficients. We also show that the above DMT can be achieved with a very high probability for most of the realistic SNR values, in a scenario in which the relay is close to the source. We also develop a more practical signalling method, which we refer to as the distributed D-BLAST architecture, to achieve the 2 × 2 MIMO DMT lower bound. Furthermore, we derive a space-time coding scheme, which can also offer a multiplexing gain of more than 1, provided that the source to relay channel is good enough. We discuss the constraints for this scheme and compare it with the successive relaying scheme. While the space-time coding strategy exploits maximal diversity for a small multiplexing gain, the successive relaying scheme offers significant performance advantages for higher data rate transmission (i.e, higher multiplexing gain).
The decode-and-forward successive relaying scheme has been discussed for single antenna relay networks [9], [10], while neither of the above works explore the possibility of obtaining multiplexing gains of more than 1 by using such a scheme. We note that the difference between our work and [9], [10] is that we use independent Gaussian codebooks at the relays to re-encode the message, instead of using the same codebook as at the source. In fact, in our work the additional multiplexing gain is obtained through distributed coding.
The rest of the paper is organized as follows. In Section II, the system model and transmission protocol are introduced. In Section III, the DMT performance for the proposed scheme is analyzed. In Section IV, a distributed D-BLAST signalling method is proposed to approach the DMT bound obtained in Section III. The space-time coding scheme is discussed and compared with the proposed successive relaying scheme in Section V, and conclusions are drawn in Section VI. Due to limited space, we omit all the proofs of the theorems in the paper. Details of the proofs can be found in [11].
We concentrate on a network in which there is one source having a single antenna, one relay having 2 antennas, and one destination having 2 antennas. We assume that the relay is close to the source, while both the source and the relay are far away from the destination 1 . Note that this
This content is AI-processed based on open access ArXiv data.