Two-hop Relay Channel Research Articles

Secure Transmission on the Two-Hop Relay Channel With Scaled Compute-and-Forward

In this paper, we consider communication on a two-hop channel in which a source wants to send information reliably and securely to the destination via a relay. We consider both the untrusted relay case and the external eavesdropper case. In the untrusted relay case, the relay behaves as an eavesdropper, and there is a cooperative node, which sends a jamming signal to confuse the relay when it is receiving from the source. In the external eavesdropper case, the relay is trusted, and there is an external node eavesdropping the communication. We propose two secure transmission schemes using the scaled compute-and-forward technique. One of the schemes is based on a random binning code, and the other one is based on a lattice chain code. It is proved that in the high signal-to-noise-ratio (SNR) scenario and/or the limited relay power scenario, if the destination is used as the jammer, both schemes outperform all existing schemes and achieve the upper bound. In particular, if the SNR is large and the source, the relay, and the cooperative jammer have identical power and channels, both schemes achieve the upper bound for secrecy rate, which is merely 1/2 bit per channel use lower than the channel capacity without secrecy constraints. We also prove that one of our schemes achieves a positive secrecy rate in the external eavesdropper case in which the relay is trusted and there exists an external eavesdropper.

Throughput Maximization for Block Fading Two-Hop Relay Channels With Non-Ideal Transmitter Circuit Power

This letter studies the throughput maximization problem for a two-hop block fading relay channel over an infinite time horizon. The decode-and-forward relaying scheme is adopted and the non-ideal circuit power is considered. By examining the Karush–Kuhn–Tucker conditions, the optimal power allocation is shown to be with a variational water-filling form, which is jointly determined by the instantaneous channel state information (CSI) of both the two links. Moreover, the decision threshold for transmission is derived offline as a function of the non-ideal circuit power, the power budget, and the statistical CSI. Finally, numerical results show that the proposed scheme outperforms the reference one.

두 홉 릴레이 채널에서 ZF 수신기의 연속 간섭 제거

두 홉 릴레이 채널에서 ZF 수신기의 연속 간섭 제거

두 홉 릴레이 채널에서 끝 노드 Zero-Forcing 빔포밍 방식의 소스 노드 전력분배

소스 노드와 목적 노드 사이에 직접 연결된 채널이 없거나 심층 쇠퇴가 존재하는 경우에 릴레이 노드를 사용함으로써 데이터 전송률의 증가 및 시스템 오류 성능 개선 두 가지 측면의 이득을 본다. 본 논문에서는 소스 노드에서 zero-forcing 빔포밍 기술을 사용하여 여러 개의 릴레이 노드로 서로 다른 신호를 간섭 없이 전송하고, 릴레이 노드들은 각각 특정한 신호만 복호하고 목적 노드로 전달하는 시스템을 고려한다. 이런 다중 릴레이들의 부분 복호 후 전달 시스템에서 소스-릴레이 노드 채널 정보와 릴레이-목적 노드 채널 정보를 이용하여 데이터 전송률을 최대화하는 소스 전력분배 기법을 제안하고 기존에 잘 알려져 있던 소스-릴레이 채널만 고려하는 water-filling 알고리즘보다 높은 전송률을 얻는다는 것을 보여 준다.

Capacity of the Two-Hop Relay Channel With Wireless Energy Transfer From Relay to Source and Energy Transmission Cost

In this paper, we investigate a communication system comprised of an energy harvesting (EH) source, which harvests radio frequency (RF) energy from an out-of-band full-duplex relay node and exploits this energy to transmit data to a destination node via the relay node. We assume two scenarios for the battery of the EH source. In the first scenario, we assume that the EH source is not equipped with a battery and thereby cannot store energy. As a result, the RF energy harvested during one symbol interval can only be used in the following symbol interval. In the second scenario, we assume that the EH source is equipped with a battery having unlimited storage capacity in which it can store the harvested RF energy. As a result, the RF energy harvested during one symbol interval can be used in any of the following symbol intervals. For both system models, we derive the channel capacity subject to an average power constraint at the relay and an additional energy transmission cost at the EH source. We compare the derived capacities to the achievable rates of several benchmark schemes. Our results show that using the optimal input distributions at both the EH source and the relay is essential for high performance. Moreover, we demonstrate that neglecting the energy transmission cost at the source can result in a severe overestimation of the achievable performance.

Optimal Buffer-Aided Relaying with Imperfect CSI

In this letter, we consider a two-hop relay channel that consists of a source, a half-duplex decode-and-forward relay, and a destination. We derive the optimal buffer-aided relaying policy based on imperfect channel state information (CSI) and under long-term per-node power constraints for the source and the relay. In particular, the proposed protocol determines the optimal state of the relay node, namely, the transmit, receive, or silent state, based on the imperfect CSI of the involved links, the quality of the CSI, and the required acquisition overhead. Our simulation results verify the analysis and reveal that there is an optimal tradeoff between the required acquisition overhead and the quality of the CSI that maximizes the throughput.

Optimal Cooperative Beamforming Design for MIMO Relay Channels

Motivated by the rapid growth of wireless applications with multiple antenna terminals, multiple input multiple output (MIMO) relaying has gained much attention now a days due to its improved data rate, coverage extension and improved signal to noise ratio (SNR). In this paper, a transmit beamforming design for MIMO decode-and-forward (DF), MIMO amplify-and-forward (AF) and MIMO compress-and-forward (CF) half-duplex two-hop relay channels with a direct source–destination link is considered. Network model consist of source, relay and destination. Design includes four different cases in terms of the number of antennas deployed at source, relay and destination node which contains 2:2:1 scenario, Ns:1:1 scenario, Ns:Nr:1 scenario and Ns:Nr:Nd scenario. Here, beamforming design is based on exact capacity formulation and low-complexity explicit expressions are used. Effect of parameter such as number of antennas on the performance of MIMO relay channels is also investigated. Optimal beamforming design for MIMO AF relaying scheme achieves high performance gain and higher information rates than MIMO DF and MIMO CF relaying scheme.

On the DMT Optimality of Time-Varying Distributed Rotation Over Slow Fading Relay Channels

We consider a slow fading two-hop relay channel where a source terminal communicates with a destination through a layer of relays without a direct link. First, we introduce the notion of time-varying distributed rotation and propose a linear relaying scheme called rotate-and-forward (RF). The main idea is to create a time-varying channel and to convert the spatial diversity to time diversity. It is shown that this scheme achieves the optimal diversity-multiplexing tradeoff (DMT) of the channel with full-duplex relays. While more involved non-linear relaying schemes previously proposed in the literature are optimal in the same setting, we show here that simple linear relaying can also be DMT optimal. Then, we extend the RF scheme to the relay channel with multiple hops where the DMT optimality of the two-antenna case is shown. Finally, we apply the idea of distributed rotation to the decode-and-forward relays. The same diversity order as previous schemes can be achieved with low signaling complexity.

Achieving Global Optimality for Joint Source and Relay Beamforming Design in Two-Hop Relay Channels

This paper deals with joint source and relay beam- forming (BF) design for an amplify-and-forward (AF) multi- antenna multirelay network. Considering that the channel state information (CSI) from relays to a destination is imperfect, we aim to maximize the worst-case received signal-to-noise ratio (SNR). The associated optimization problem is then solved in two steps. In the first step, by fixing the source BF vector, a semi-closed-form solution of the relay BF matrices is obtained, up to a power- allocation factor. In the second step, the global optimal source BF vector is obtained based on the polyblock outer approximation (PA) algorithm. We also propose two low-complexity methods for obtaining the source BF vector, which differ in their complexity and performances. The optimal joint source and relay BF solution obtained by the proposed algorithms serves as the benchmark for evaluating the existing schemes and the proposed low-complexity methods. Simulation results show that the proposed robust design can significantly reduce the sensitivity of the channel uncertainty to the system performance. Index Terms—Amplify and forward (AF), beamforming (BF), global optimal, multiantenna multirelay system.

Optimal Cooperative Beamforming Design for MIMO Decode-and-Forward Relay Channels

In this paper, we consider a transmit beamforming design for multiple-input-multiple-output (MIMO) decode-and-forward (DF) half-duplex two-hop relay channels with a direct source-destination link. For the scenario where source and relay nodes are equipped with multiple antennas and the destination node is deployed with single antenna, we formulate and solve the optimal beamforming vectors for source and relay nodes jointly. Specifically, we identify several unique properties of the optimal solutions through mathematical derivation, based on which we develop a systematic approach to arrive at the optimal beamforming vectors for the source and relay nodes for different system configurations. We derive a low-complexity explicit expression for the optimal beamforming vectors for some specific scenarios. Numerical results show that our proposed beamforming design scheme can achieve the e-optimal solution with low computational complexity for MIMO DF relay networks.

On optimal policies for control and estimation over a Gaussian relay channel

The problem of causal transmission of a memoryless Gaussian source over a two-hop memoryless Gaussian relay channel is considered. The source and the relay encoders have average transmit power constraints, and the performance criterion is mean-squared distortion. The main contribution of this paper is to show that unlike the case of a point-to-point scalar Gaussian channel, linear encoding schemes are not optimal over a two-hop relay channel in general, extending the sub-optimality results which are known for more than three hops. In some cases, simple three-level quantization policies employed at the source and at the relay can outperform the best linear policies. Further a lower bound on the distortion is derived and it is shown that the distortion bounds derived using cut-set arguments are not tight in general for sensor networks.

Cognitive Radios for Preserving Primary Outage Performance over Two-Hop Relay Channels

We consider cognitive radio (CR) communications over two-hop relay channels. It is assumed that the secondary sender has only one-bit information indicating whether or not it is allowed to access, while the primary nodes still operate even without any prior knowledge on the secondary nodes. We propose three different two-hop relaying protocols according to how much the relay has prior knowledge on its outgoing channels, and show that the proposed relaying protocols make it possible for the secondary sender to transmit data without causing any loss at the primary outage probability. It is also shown that the proposed relaying protocols make the secondary outage probability as small as possible by increasing the signal-to-noise ratio (SNR) if the relay has prior knowledge on its outgoing channel to the primary receiver.

Robust Transmitter Design for Amplify-and-Forward MIMO Relay Systems Exploiting Only Channel Statistics

In this paper, we address statistically robust transmit design problems that maximize the average mutual information of amplify-and-forward (AF) multiple-input multiple-output (MIMO) two-hop relay channels having perfect channel state information at the receiver (CSIR) and statistical channel state information at the transmitter (CSIT). In the selected scenario, the source, relay, and destination terminals are equipped with correlated antennas where a direct link between the source and the destination terminals can be found. Moreover, the statistical CSIT consists of the channel means and covariance matrices of various links. The design problem is taken into account for regimes in large systems because there are no closed-form expressions of the average mutual information in the MIMO relay channel. The contribution of this study includes the derivation of asymptotic mutual information expressions for the MIMO relay channel in the large system limit. Additionally, an efficient optimization algorithm based on the asymptotic mutual information is proposed in order to find the asymptotically optimal source covariance matrix and the relay amplifying matrix. Numerical simulation results show that the new approach achieves indistinguishable performance compared to those of the maximization approaches in finite-dimensional systems, even for a small number of antennas at each link. The impact of the CSI of various links on the throughput of the MIMO relay channel is studied using the new approach.

On the Asymptotic Properties of Amplify-and-Forward MIMO Relay Channels

This paper studies the asymptotic properties of amplify-and-forward (AF) multiple-input multiple-output (MIMO) two-hop relay channels, where the source terminal (ST), relay terminal (RT) and destination terminal (DT) are equipped with a number of correlated antennas and there is a direct link between the ST and DT. The analysis is based on the Kronecker correlated fading model where the correlation properties of the MIMO channel are modeled at the transmitter and receiver ends separately. Our first main contribution is the derivation of the asymptotic mutual information expressions for the MIMO-AF relay channel for any given signaling input distributions (not necessarily Gaussian) in the large-system regime, which is particularly relevant if practical modulation schemes are used. In addition to the formula that uses joint optimal decoding (JOD) at the DT, we also obtain the asymptotic result for a more practical system which performs separate detection and decoding (SDD) (i.e., spatial detection followed by a temporal error-correction decoder). Another major contribution of this paper is an efficient algorithm that can compute the optimal source covariance matrix and the relay precoding matrix to maximize the asymptotic mutual information of the MIMO-AF relay system if channel covariance information (CCI) is known at the ST and RT.

Relay Selection Algorithm with Simplified Precoding for MIMO Multiple Relay Channels

Considering an Amplify-and-Forward (AF) cooperative network with the help of multiple relay nodes, a relay selection algorithm with simplified precoder is proposed for the two-hop relay channels. This new algorithm based on the approximate received signal-noise rate (SNR), which chooses only one relay with the maximal received SNR gain to assist in transmission, can significantly reduce the required system consumption, achieve excellent bit-error-rate (BER) and average throughput, and maintain full diversity order. Simulation results demonstrate that the performance of the proposed scheme with a low complexity approaches to the optimal iteration method. And for practical situation with distance attenuation factor, the performance gain of our scheme is also in evident.

Detect-and-forward in two-hop relay channels: a metrics-based analysis

In this paper, we analyze the coded performance of a cooperative system with multiple parallel relays using “Detect-and-Forward” (DetF) strategy where each relay demodulates the overheard signal and forwards the detected binary words. The proposed method is based on the probabilistic characterization of the reliability metrics given under the form of L-values. First, we derive analytical expressions of the probability density functions (PDFs) of the L-values in the elementary two-hop DetF relay channel with different source-relay channel state information assumptions. Then, we apply the obtained expressions to calculate the theoretically achievable rates and compare them with the practical throughput of a simulated turbo-coded transmission. Next, we derive tight approximations for the end-to-end coded bit error rate (BER) of a general cooperative scheme with multiple parallel relays. Simulation results demonstrate the accuracy of our derivations for different cooperation configurations and conditions.

Bit error probability of distributed Turbo coded relay systems over quasi-static Rayleigh fading channels

As is known, distributed Turbo coding (DTC) performs close to the theoretic outage probability bound of a relay channel when correct decoding is assumed at the relay. However, decoding error is inevitable in practical fading channels due to the error-prone feature of radio channels, and the decoding error propagation in DTC scheme will severely degrade the error performance of the relay system. As a result, it is necessary to evaluate the error performance of the DTC scheme in multi-hop relaying wireless systems in practical fading channels. Moreover, the theoretical method of analysis provides an effective tool for obtaining the error performance besides lengthy simulations. In this article, the concept of equivalent signal-to-noise ratio (SNR) of the two-hop relay channel and the method of computing equivalent SNR are developed, and then the upper bound on the bit error probability (BEP) of DTC relay systems is analyzed by use of Turbo code's distance spectrum, the concept of uniform interleaver, the limit-before-averaging technique, and the union bound method. Both theoretical analysis and numerical simulation are implemented for relay systems with DTC scheme over quasi-static Rayleigh fading channels. The results show that the upper bound approaches the simulation results in the medium to high SNR region.

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.