Code Design for Multihop Wireless Relay Networks

We consider a wireless relay network, where a transmitter node communicates with a receiver node with the help of relay nodes. Most coding strategies considered so far assume that the relay nodes are used for one hop. We address the problem of code design when relay nodes may be used for more than one hop. We consider as a protocol a more elaborated version of amplify-and-forward, called distributed space-time coding, where the relay nodes multiply their received signal with a unitary matrix, in such a way that the receiver senses a space-time code. We first show that in this scenario, as expected, the so-called full-diversity condition holds, namely, the codebook of distributed space-time codewords has to be designed such that the difference of any two distinct codewords is full rank. We then compute the diversity of the channel, and show that it is given by the minimum number of relay nodes among the hops. We finally give a systematic way of building fully diverse codebooks and provide simulation results for their performance

Approaching Gaussian Relay Network Capacity in the High SNR Regime: End-to-End Lattice Codes

We present a natural and low-complexity technique for achieving the capacity of the Gaussian relay network in the high SNR regime. Specifically, we propose the use of end-to-end structured lattice codes with the amplify-and-forward strategy, where the source uses a nested lattice code to encode the messages and the destination decodes the messages by lattice decoding. All intermediate relays simply amplify and forward the received signals over the network to the destination. We show that the end-to-end lattice-coded amplify-and-forward scheme approaches the capacity of the layered Gaussian relay network in the high SNR regime. Next, we extend our scheme to non-layered Gaussian relay networks under the amplify-and-forward scheme, which can be viewed as a Gaussian intersymbol interference (ISI) channel. Compared with other schemes, our approach is significantly simpler and requires only the end-to-end design of the lattice precoding and decoding. It does not require any knowledge of the network topology or the individual channel gains

An Upper Bound on Multi-hop Transmission Capacity with Dynamic Routing Selection

This paper develops upper bounds on the end-to-end transmission capacity of multi-hop wireless networks. Potential source-destination paths are dynamically selected from a pool of randomly located relays, from which a closed-form lower bound on the outage probability is derived in terms of the expected number of potential paths. This is in turn used to provide an upper bound on the number of successful transmissions that can occur per unit area, which is known as the transmission capacity. The upper bound results from assuming independence among the potential paths, and can be viewed as the maximum diversity case. A useful aspect of the upper bound is its simple form for an arbitrary-sized network, which allows insights into how the number of hops and other network parameters affect spatial throughput in the non-asymptotic regime. The outage probability analysis is then extended to account for retransmissions with a maximum number of allowed attempts. In contrast to prevailing wisdom, we show that predetermined routing (such as nearest-neighbor) is suboptimal, since more hops are not useful once the network is interference-limited. Our results also make clear that randomness in the location of relay sets and dynamically varying channel states is helpful in obtaining higher aggregate throughput, and that dynamic route selection should be used to exploit path diversity.Comment: 14 pages, 5 figures, accepted to IEEE Transactions on Information Theory, 201

Multihop Diversity in Wideband OFDM Systems: The Impact of Spatial Reuse and Frequency Selectivity

The goal of this paper is to establish which practical routing schemes for wireless networks are most suitable for wideband systems in the power-limited regime, which is, for example, a practically relevant mode of operation for the analysis of ultrawideband (UWB) mesh networks. For this purpose, we study the tradeoff between energy efficiency and spectral efficiency (known as the power-bandwidth tradeoff) in a wideband linear multihop network in which transmissions employ orthogonal frequency-division multiplexing (OFDM) modulation and are affected by quasi-static, frequency-selective fading. Considering open-loop (fixed-rate) and closed-loop (rate-adaptive) multihop relaying techniques, we characterize the impact of routing with spatial reuse on the statistical properties of the end-to-end conditional mutual information (conditioned on the specific values of the channel fading parameters and therefore treated as a random variable) and on the energy and spectral efficiency measures of the wideband regime. Our analysis particularly deals with the convergence of these end-to-end performance measures in the case of large number of hops, i.e., the phenomenon first observed in \cite{Oyman06b} and named as ``multihop diversity''. Our results demonstrate the realizability of the multihop diversity advantages in the case of routing with spatial reuse for wideband OFDM systems under wireless channel effects such as path-loss and quasi-static frequency-selective multipath fading.Comment: 6 pages, to be published in Proc. 2008 IEEE International Symposium on Spread Spectrum Techniques and Applications (IEEE ISSSTA'08), Bologna, Ital

End-to-End Joint Antenna Selection Strategy and Distributed Compress and Forward Strategy for Relay Channels

Multi-hop relay channels use multiple relay stages, each with multiple relay nodes, to facilitate communication between a source and destination. Previously, distributed space-time codes were proposed to maximize the achievable diversity-multiplexing tradeoff, however, they fail to achieve all the points of the optimal diversity-multiplexing tradeoff. In the presence of a low-rate feedback link from the destination to each relay stage and the source, this paper proposes an end-to-end antenna selection (EEAS) strategy as an alternative to distributed space-time codes. The EEAS strategy uses a subset of antennas of each relay stage for transmission of the source signal to the destination with amplify and forwarding at each relay stage. The subsets are chosen such that they maximize the end-to-end mutual information at the destination. The EEAS strategy achieves the corner points of the optimal diversity-multiplexing tradeoff (corresponding to maximum diversity gain and maximum multiplexing gain) and achieves better diversity gain at intermediate values of multiplexing gain, versus the best known distributed space-time coding strategies. A distributed compress and forward (CF) strategy is also proposed to achieve all points of the optimal diversity-multiplexing tradeoff for a two-hop relay channel with multiple relay nodes.Comment: Accepted for publication in the special issue on cooperative communication in the Eurasip Journal on Wireless Communication and Networkin