MIMO Two-way Relay Channels Research Articles

Optimal DoF Region for the Asymmetric Two-Pair MIMO Two-Way Relay Channel

In this paper, we study the optimal degrees of freedom (DoF) region for the two-pair MIMO two-way relay channel (TWRC) with asymmetric antenna setting, where two pairs of users exchange information with the help of a common relay. Each user $i$ is equipped with $M_i$ antennas, for $i=1,2,3,4$, and the relay is equipped with $N$ antennas. First, we derive an outer bound of the DoF region by using the cut-set theorem and the genie-message approach. Then, we propose a new transmission scheme to achieve the outer bound of the DoF region. Due to the asymmetric data exchange, where the two users in each pair can communicate a different number of data streams, we not only need to form the network-coded symbols but also need to process the additional asymmetric data streams at the relay. This is realized through the joint design of relay compression matrix and source precoding matrices. After obtaining the optimal DoF region, we study the optimal sum DoF by solving a linear programming problem. From the optimal DoF region of this channel, we show that in the asymmetric antenna setting, some antennas at certain source nodes are redundant and cannot contribute to enlarge the DoF region. We also show that there is no loss of optimality in terms of the sum DoF by enforcing symmetric data exchange, where the two users in each pair are restricted to communicate the same number of data streams.

A Novel Secure Transmission Scheme in MIMO Two-Way Relay Channels with Physical Layer Approach

Security issue has been considered as one of the most pivotal aspects for the fifth-generation mobile network (5G) due to the increasing demands of security service as well as the growing occurrence of security threat. In this paper, instead of focusing on the security architecture in the upper layer, we investigate the secure transmission for a basic channel model in a heterogeneous network, that is, two-way relay channels. By exploiting the properties of the transmission medium in the physical layer, we propose a novel secure scheme for the aforementioned channel mode. With precoding design, the proposed scheme is able to achieve a high transmission efficiency as well as security. Two different approaches have been introduced: information theoretical approach and physical layer encryption approach. We show that our scheme is secure under three different adversarial models: (1) untrusted relay attack model, (2) trusted relay with eavesdropper attack model, and (3) untrusted relay with eavesdroppers attack model. We also derive the secrecy capacity of the two different approaches under the three attacks. Finally, we conduct three simulations of our proposed scheme. The simulation results agree with the theoretical analysis illustrating that our proposed scheme could achieve a better performance than the existing schemes.

Optimal Power Allocation between Training and Data for MIMO Two-Way Relay Channels

Power allocation between training and data in MIMO two-way relay systems is proposed, which takes into consideration both the symmetric and asymmetric cases of the two sources. For the former, we present a closed form for the optimal ratio of data energy to total energy, which is suitable for the single antenna case as well, and can be simplified when the number of antennas is large. We also show that the achievable rate is a monotonically increasing function of the data time. Concerning the asymmetric case, we prove that the difference of the two SNRs is either a concave or convex function of the energy ratio, depending on the imbalance between the two sources. Using this, the minimum SNR between the two sources is maximized.

Greedy Relay Antenna Selection for Sum Rate Maximization in Amplify-and-Forward MIMO Two-Way Relay Channels Under a Holistic Power Model

This letter investigates the sum rate maximization in amplify-and-forward (AF) MIMO two-way relay channels (TWRCs) combined with relay antenna selection (AS). We consider the circuit power consumption in this letter and hence the optimization of the number of active RF chains is necessary. In particular, a greedy relay AS algorithm is proposed to avoid the exhaustive search. The proposed algorithm relies on a derived equation for the sum rate of AF MIMO TWRCs when relay AS is adopted, which guides us to select a pair of receive and transmit antennas that brings the largest sum rate increment at each selection. Simulation results show that the greedy algorithm is capable of achieving nearly the same performance of exhaustive search but with significantly reduced computational complexity.

Joint Beamforming Optimization and Power Control for Full-Duplex MIMO Two-Way Relay Channel

In this paper, we explore the use of full-duplex radio to improve the spectrum efficiency in a two-way relay channel where two sources exchange information through an multi-antenna relay, and all nodes work in the full-duplex mode. The full-duplex operation can reduce the overall communication to only one phase but suffers from the self-interference. Instead of purely suppressing the self-interference, we aim to maximize the end-to-end performance by jointly optimizing the beamforming matrix at the relay which uses the amplify-and-forward protocol as well as the power control at the sources. To be specific, we propose iterative algorithms and 1-D search to solve two problems: finding the achievable rate region and maximizing the sum rate. At each iteration, either the analytical solution or convex formulation is obtained. We compare the proposed full-duplex two-way relaying with the conventional half-duplex two-way relaying, a full-duplex one-way relaying and a performance upper bound. Numerical results show that the proposed full-duplex scheme significantly improves the achievable data rates over the conventional scheme.

Application of Analog Network Coding to MIMO Two-Way Relay Channel in Cellular Systems

An efficient analog network coding transmission protocol is proposed in this letter for a MIMO two way cellular network. Block signal alignment is first proposed to null the inter-user interference for multi-antenna users, which makes the dimensions of aligned space larger compared with the existing signal alignment. Two algorithms are developed to jointly design the precoding matrices at the relay and BS for outage optimization. Especially, the last algorithm is designed to maximize the effective channel gain to the effective noise gain ratio. The performance of this transmission protocol is also verified by simulations.

Reduced-Dimension Cooperative Precoding for MIMO Two-Way Relay Channels

We investigate efficient communications over MIMO two-way relay channels (TWRCs) of n <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">T</sub> <; n <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">R</sub> , where n <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">T</sub> denotes the number of antennas at each user and n <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">R</sub> denotes that at the relay. We propose a new reduced-dimension (RD) cooperative precoding scheme. In the proposed scheme, the two users cooperatively create n <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">T</sub> aligned eigen-modes, supporting n <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">T</sub> streams of physical-layer network coding. We investigate the design of the RD cooperative precoder and derive an asymptotically optimal solution. We analytically show that, in the worst case, the proposed scheme is within ½ bit per transmit antenna of the asymptotic sum-capacity of the MIMO TWRC. For fading MIMO TWRCs with i.i.d. Gaussian coefficients, we derive a closed-form expression of the average sum-rate of the proposed scheme using large system analysis. Our analytical result shows that, for a large system with n <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">T</sub> /n <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">R</sub> = ½, the proposed scheme is less than 0.16 bit per transmit antenna away from the capacity. Furthermore, this gap reduces as n <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">T</sub> /n <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">R</sub> increases, and vanishes as n <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">T</sub> /n <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">R</sub> tends to 1. It is demonstrated that the proposed scheme can significantly outperform other existing schemes in the literature.

Computationally Efficient Relay Antenna Selection for AF MIMO Two-Way Relay Channels

This correspondence develops a computationally efficient scheme to select a subset of relay antennas to maximize the achievable sum rate (ASR) of amplify-and-forward multiple-input multiple-output two-way relay channels. To reduce the computational complexity of antenna selection (AS), two sequential AS algorithms, joint AS (JAS) and separate AS (SAS), are proposed. JAS jointly selects a pair of receive-transmit antennas at each sequential step. In contrast, SAS separates receive and transmit AS into a two-stage algorithm; the receive antenna set is selected first, followed by selection of the transmit antennas. Simulation results show that the proposed algorithms achieve nearly the same ASR as compared to an exhaustive search, but with significantly reduced computational complexity.

MSMSE-based optimal beamforming design and simplification on AF MIMO two-way relay channels

An optimal cooperative beamforming for the amplify-and-forward (AF) MIMO two-way relay channels was designed. Supposing the channel state information (CSI) was perfectly known by the receiver and transmitter as well as the relay, optimal beamforming vectors (matrices) of all nodes were jointly designed based on the criterion of minimizing the sum mean square errors (MSMSE). The analysis result shows that the performance effect of transmitting and receiving beamforming pairs is to maximize the receive signal-to-noise ratio (SNR) at two communication nodes, and the rank of the optimal relay beamforming matrix is no larger than two when there is only one data stream at each source node. A simplified algorithm was put forward to accomplish the design based on the analysis conclusions. Simulation results provide that the system performance, which is characterized in terms of bit error rates (BER), is significantly improved by cooperative beamforming, and the performance of the simplified method is not only very close to the optimal one but also with faster iteration speed and much lower computational complexity.

Asymptotic Capacity of the Separated MIMO Two-Way Relay Channel

A multiple-input multiple-output two-way relay channel consisting of two communication nodes and a full-duplex relay node in which no direct link exists between the two communication nodes is considered. We propose an achievable scheme that employs horizontally encoded lattice codes combined with generalized singular value decomposition-based precoding for the first phase. The second phase of the proposed scheme follows the fundamentals of the previous scheme, which uses vertically encoded structural bining, with the only difference that the added codeword of the two codewords from the communication nodes, instead of those two individual codewords, is decoded and retransmitted in the proposed scheme. We show that the proposed scheme achieves the cut-set bound asymptotically as the signal-to-noise ratios of the channels tend to infinity.

MIMO two-way relay channel with superposition coding and imperfect channel estimation

This paper deals with the superposition coding (SPC) scheme in multiple-input multiple-output two-way relay channels subject to imperfect channel estimation. In this scenario, two multiple antenna terminals, which are unable to communicate directly, exchange information with each other via a multiple antenna relay. We determine the impact of the channel estimation error degradation on the achievable rate region for two main SPC techniques: (a) SPC without channel state information (CSI) at the users, (b) SPC with an imperfect CSI at the users where a waterfilling power allocation is employed. We demonstrate that imperfect CSI significantly improves the achievable rate at low signal-to-noise ratios (SNRs) while it becomes less critical at high SNRs. In addition, a SPC power allocation technique that incorporates the average channel statistics and does not require any instantaneous CSI is also investigated. We show how the available power is split between the two bi-directional (superimposed) data flows in order to maximize the system performance and to support fairness as well as to maximize the achievable sum-rate.

Phase Alignment Schemes in Multiple Antenna Two-Way Relay Channels

In this paper, we propose regularized vector perturbation in MIMO two-way relay channels in order to align phases of received signals. The proposed scheme not only simplifies the detection process at the relay, but also removes the perturbation vector without its knowledge. Numerical results show that the proposed scheme improves the block error performance.