Multi-hop Relay Channel Research Articles

On the Energy Efficiency and Effective Throughput Tradeoff of Fading Channels

This paper investigates the tradeoff between the energy efficiency (EE) and the effective throughput (ET) of fading channels. In particular, we consider the case of zero channel state information (CSI) at the transmitter, and thus, the receiver can only successfully decode the source messages with certain probability. Accordingly, the ET, which is defined as the rate of the successfully decoded information, is adopted to measure the spectrum efficiency of the considered channels. We characterize the EE–ET region by exploiting its structure, and each boundary point is obtained by solving a quasi-concave problem. As a special case, we also obtain the maximum ET per unit energy in closed form. Finally, we generalize our results to the case of multihop relay channels.

Achievable Rate of the Half-Duplex Multi-Hop Buffer-Aided Relay Channel With Block Fading

The half-duplex (HD) multi-hop relay channel consists of a source, multiple HD relays connected in series, and a destination where links are present only between adjacent nodes. In this paper, we focus on decode-and-forward relays and assume that the links are impaired by block fading and additive white Gaussian noise. We design a new protocol which, unlike the conventional protocols for the multi-hop relay channel, does not adhere to a fixed and predefined pattern of using the transmit, receive, and silent states of the nodes. In particular, the proposed protocol selects the optimal states of the nodes and the corresponding optimal transmission rates based on the instantaneous channel state information (CSI) of the involved links in each fading block such that the achievable average rate from source to destination is maximized. To enable adaptive scheduling of the states of the nodes, the relay nodes have to be equipped with buffers for temporary storage of the information received from the preceding node. Additionally, we discuss and address two practical challenges arising in the implementation of the optimal protocol, namely the unconstrained end-to-end delay due to data buffering at the relays and the required CSI overhead. Numerical results confirm the superiority of the proposed buffer-aided protocols compared to existing multi-hop relaying protocols.

A Pedagogic Approach to Cascaded Fading Channels and Diversity in Wireless Systems

College programs in electrical engineering offer courses in wireless communications. One of the complex topics of instruction in these courses is fading which deals with signal strength fluctuations. While many simple fading models exist, a cascaded approach to fading provides a general means to describe these fluctuations in wireless channels including keyhole and multi-hop relay channels. In this approach, the signal strength is expressed as the product of several random components. Such a methodology is complicated by the fact that the probability density functions of the signal-to-noise ratio cannot be expressed in simple forms. Furthermore, the study of diversity to mitigate fading is made difficult by the absence of analytical expressions for the densities, error rates and outages. To overcome these difficulties, a MATLAB-based simulation techniques is proposed and demonstrated. The beneficial effects of diversity in mitigating fading are established through density and distribution functions as well as quantitative measures of performance such as the error rates and outage probabilities. It is suggested that the MATLAB-based approach can provide a didactic means to facilitate the understanding of fading and fading mitigation.

Achieving Optimal Diversity-Multiplexing Tradeoff for Full-Duplex MIMO Multihop Relay Networks

In this paper, we investigate the diversity-multiplexing tradeoff (DMT) of a multiple-input-multiple-output (MIMO) full-duplex single-user multihop relay channel, where a pair of source and destination communicates via multiple layers of relays. All communication terminals could be equipped with multiple antennas. The relays operate in a full-duplex mode. By incorporating time-domain linear transformation into amplify-and-forward (AF) based relaying, we propose an AF-based space-time relay scheme and show that the DMT upper bound of the channel can be achieved by properly designing space-time (ST) codes at the source.

To Code in Space and Time or Not in Multihop Relay Channels

Multihop relay channels use multiple relay stages, each with multiple relay nodes, to facilitate communication between a source and destination. Previously, distributed space-time coding was used to maximize diversity gain. Assuming a low-rate feedback link from the destination to each relay stage and the source, this paper proposes end-to-end antenna selection strategies as an alternative to distributed space-time coding. One-way (where only the source has data for destination) and two-way (where the destination also has data for the source) multihop relay channels are considered with both the full-duplex and half-duplex relay nodes. For the full-duplex case, end-to-end antenna selection strategies are designed and proven to achieve maximum diversity gain by using a single-antenna path (using single antenna of the source, each relay stage and the destination) with the maximum signal-to-noise ratio at the destination. For the half-duplex case, two paths with the two best signal-to-noise ratios in alternate time slots are used to overcome the rate loss with half-duplex nodes, with a small diversity gain penalty. A multiple stream end-to-end antenna selection strategy for full-duplex multihop relay channel is also proposed to obtain a lower bound on the diversity multiplexing tradeoff of multihop relay channels. Finally, to answer the question of whether to code in space and time or not in a multihop relay channel, end-to-end antenna selection strategy and distributed space-time coding is compared with respect to several important performance metrics such as encoding/decoding complexity, rate of transmission, latency, bit-error-rate performance, and resource requirements.

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

Multihop 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 amplifying 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.

An Approximation of the Average BER Performance of Multi-Hop AF Relaying Systems with Fixed Gain

In this letter, we present a closed-form bound of the average bit error rate (BER) performance for the multi-hop amplify-and-forward (AF) relaying systems with fixed gain in Rayleigh fading channel. The proposed bound is derived from the probability density function (PDF) of the overall multi-hop relay channel under the assumption of asymptotic high signal-to-noise ratio (SNR) at every intermediate relays. When intermediate relays actually operate at finite SNR, the proposed BER bound becomes looser as the SNR of the last hop increases. In order to reflect the effect of all the noise variances of relay links to the BER evaluation, a hop-indexed recursive BER approximation is proposed, in which the proposed bound of BER under asymptotic high SNR is used. The simulation results manifest that the proposed hop-indexed recursive BER approximation can not only guarantee accuracy regardless of the SNR of the last hop but also provide higher accuracy than the previous works.

Bounds on Maximum Rate-Per-Energy for Orthogonal AWGN Multiple-Relay Channels

This paper presents two lower bounds and one upper bound on the maximum Rate-Per-Energy (RPE) that can be achieved over the orthogonal, additive white Gaussian noise, multi-hop relay channel. The study of the maximum RPE for relay networks not only determines the energy efficiency of a communication system but can also define efficient energy allocation, relay selection, and routing solutions. For the three bounds studied here, these solutions have an attractive distributed structure. The optimal relaying strategy remains unknown, even for the most simple one-relay network and, thus, only bounds on the maximum RPE can be obtained. Here, lower bounds are obtained by considering relays that decode a previously transmitted message (regenerative) from just one of its received signals (non-accumulative). The first lower bound is obtained from the analysis of the traditional multi-hop network, where each relay is required to decode and retransmit the complete source message. Then, this lower bound is tightened, by considering relays that, instead of trying to retransmit the source message, facilitate the transmission between the previous relay and the destination. The destination decodes the source message by using every transmitted signal. Finally, an upper bound valid for any relaying strategy is derived by solving the max-flow min-cut bound.