Two-way Multiple-input Multiple-output Research Articles

Semiblind Uni-ALS receiver for a two-way MIMO relaying system based on the PARATUCK2 model

In this paper, we consider a two-way multiple-input multiple-output (MIMO) relaying system employing simplified space-time (ST) coding at both sources. The signals received at each source form a third-order tensor, which satisfies a parallel tucker2 (PARATUCK2) model. Exploiting this structure, we present a novel semiblind united alternating least squares (Uni-ALS) receiver for jointly estimating the transmitted symbols and the individual channels. The identifiability and uniqueness conditions are analyzed. In contrast to training-based receivers, such as tensor-based channel estimation (TENCE), two-stage training (TST) and zero forcing (ZF) receiver, the proposed receiver improves the spectrum efficiency. Simulation results show that the proposed receiver yields superior performance in comparison with the two-stage training (TST) receiver.

Secure Degrees of Freedom of MIMO Two-Way Wiretap Channel With no CSI Anywhere

This article considers a two-way multiple-input multiple-output (MIMO) Rayleigh block fading wiretap channel with two full-duplex nodes (Alice and Bob) exchanging messages simultaneously and wiretapped by a $ {N}_{ {e}}$ -antennas eavesdropper (Eve). The channel state remains unchanged over a coherence interval T and is unknown to all terminals, including Alice, Bob, and Eve, at the beginning of the coherence interval. We first show the expression of the optimal signal waveform for Alice and Bob, which maximizes the sum secrecy rate, should be the products of independent random diagonal matrices and isotropically distributed unitary matrices. Then, conditioned on large T and small $ {N}_{ {e}}$ , the upper-bound for the secure degree of freedom (s.d.o.f.) of the two-way wiretap channel is derived, and a constant-norm-signaling (CNS) scheme is presented to achieve this theoretical bound. Finally, we formulate an optimization problem of the s.d.o.f. achieved by the CNS scheme for general cases with arbitrary T and $ {N}_{ {e}}$ , and solve this problem by exploring the monotonicity of the achievable s.d.o.f.. Our result shows that the optimal s.d.o.f. can be independent of coherence time T and becomes the product of the numbers of legitimate nodes’s transmitter antennas (NLNTA) for large $ {N}_{ {e}}$ and small NLNTA.

Robust Transceiver Design for AF Asymmetric Two-Way MIMO Relaying

We consider a multiple-input multiple-output (MIMO) asymmetric two-way relay (A-TWR) system, wherein the base station (BS) serves a transmit-only user (TU) and receive-only user (RU). The TU transmits data to the BS and the RU receives data from the BS. Because of the asymmetric nature of A-TWR, the RU experiences interference and necessitates a joint transceiver design at the TU, RU, and relay. The existing literature has designed such transceivers by assuming perfect channel state information (CSI) at all the nodes. Obtaining perfect CSI at all the nodes is, however, not viable in practice due to the distributed nature of the system. This work constructs a transceiver design with perfect CSI at the relay and perturbed CSI at the TU, RU and BS. The perturbed signal-to-interference-plus-noise ratio (SINR) is analyzed by exploiting the properties of the singular value decomposition and the results from theory of matrix normal distributions. The resulting closed-form SINR expressions are then used to perform robust power allocation at all the nodes. Two different settings, namely maximization of the minimum SINR across all streams and minimization of the total network transmit power are considered. The performance gains from the proposed robust designs are validated numerically.

Secure Wideband Beamforming Design for Two-Way MIMO Relaying Systems

In this paper, secure wideband beamforming design is investigated for two-way multiple-input multiple-output (MIMO) relaying systems with one eavesdropper. Due to the wideband signals exchanged by two sources via the relay, inter-symbol-interference (ISI) occurs inevitably and makes the beamforming design more challenging than the narrowband beamforming design. To sufficiently combat the ISI, the tapped delay lines are deployed at the relay. Besides, to reduce the computational complexity at the tapped delay lines based relay, the analog beamforming structure is also considered, and thus the MIMO relay beamforming can be distinctly partitioned into a transmit beamforming and a receive beamforming bridged by a single link. Joint optimization of the transmit and receive beamformings at both the relay and two sources is considered to maximize the secrecy sum rate (SSR) of the two-way MIMO relaying systems. Since the joint optimization is nonconvex and intractable, an iterative algorithm is proposed to decompose the original SSR maximization problem into four individual subproblems that can be reformulated as three types of convex problems, i.e., the generalized Rayleigh quotient problems, the polynomial time differential convex problem, and the semidefinite programming problem. A suboptimal solution for the secure transmit and receive beamformings at all nodes can then be obtained iteratively. Finally, numerical experiments are conducted to corroborate the effectiveness of our proposed iterative algorithm in terms of the achievable maximum SSR and ISI suppression.

Precoding Design for Two-Way MIMO Full-Duplex Amplify-and-Forward Relay Communication Systems

Full duplex (FD) multiple-input multiple-output (MIMO) relaying can significantly increase the spectral efficiency of cooperative communication systems. This paper examines the problem of linear source and relay precoder and destination combiner design for two-way MIMO FD amplify-and-forward (AF) relay communication systems. The effect of the residual loop interference (LI) due to imperfect LI cancellation is considered in the design. Two algorithms are proposed to minimize the mean squared error (MSE) of the received signals at the destinations. The first is a tri-step alternating iterative algorithm and the second is a bi-step iterative algorithm. The convergence and complexity of these algorithms are analyzed. Simulation results are presented, which show that the proposed two-way FD system provides approximately double the achievable rate of the corresponding half-duplex (HD) system when the residual LI is low. Furthermore, the bi-step algorithm shows comparable performance to the tri-step algorithm and has a lower computational complexity.

Individual Channel Estimation Based on Blind Interference Cancellation for Two-Way MIMO Relay Networks

In this paper, we investigate an individual channel estimation problem for multiple-input multiple-output (MIMO) two-way amplify-and-forward (AF) relay networks. To avoid self-interference during the estimation of the individual MIMO channels, a novel blind interference cancellation (BIC) approach is proposed based on an orthogonal preceding framework, where a pair of orthogonal precoding matrices is utilized at the source nodes. By designing an optimal decoding scheme, we propose to decompose the bidirectional transmission into a pair of unidirectional transmissions. Unlike most existing approaches, we make the practical assumption that the nonreciprocal MIMO channel and the mutual interference of multiple antennas are both taken into consideration. Under the precoding framework, we employ an orthogonal superimposed training strategy to obtain the individual MIMO channels. However, the AF strategy causes the noise at the terminal to be the sum of the local noise and the relay-propagated noise. To remove the relay-propagated noise during the estimation of the second-hop channel, a partial noise-nulling method is designed. We also derive a closed-form expression for the total mean square error (MSE) of the MIMO channel from which we compute the optimal power allocation. The simulation results demonstrate that the analytical and simulated curves match fully.

On the DoF of Two-Way MIMO Butterfly Networks

This paper studies the degrees of freedom (DoF) of two-way multiple-input multiple-output (MIMO) butterfly networks, a class of two-way four-unicast networks, that consists of four source/destination nodes and three relay nodes. We first give upper and lower bounds on the sum DoF of such network with any number of antennas in each node. We also study the DoF of the two-way MIMO butterfly network with caching at the relays. For the special case that each source/destination node has $M$ antennas and each relay node has $N$ antennas, we obtain the exact DoF for some special cases. Specifically, if $N \leq M$ , then without caching, ${\rm DoF}=2N$ , which is equal to the DoF of a one-way MIMO butterfly network, and with relay caching, ${\rm DoF}=4N$ . Moreover, if $N > 2M$ , then with or without relay caching, ${\rm DoF}=4M$ which doubles the DoF of a one-way MIMO butterfly network. Hence, for this MIMO butterfly network, when the number of relay antennas is large compared with the number of source/destination antennas, bidirectional transmission improves the DoF; and when the number of relay antennas is small, relay caching improves the DoF.

On MIMO Linear Physical-Layer Network Coding: Full-Rate Full-Diversity Design and Optimization

This paper considers a multiuser communication network, where a receiver is set to compute functions of the messages from $K$ users. All user nodes and the receiver are equipped with multi-antenna. We propose a space–time (ST) coded multiple-input multiple-output (MIMO) linear physical-layer network coding (LPNC) scheme that promises full-rate and full-diversity, while achieving the maximum coding gain of LPNC. In the proposed framework, the users’ messages are encoded by the same linear dispersion ST code and transmitted simultaneously. The receiver exploits the MIMO LPNC mapping in reconstructing an arbitrary number of linearly network-coded (NC) messages. We derive the NC generator matrix that leads to the greatest coding gain and minimized error probability at the receiver. On top of that, we analytically show that the proposed ST coded LPNC scheme guarantees the full-diversity and full-rate transmission. The proposed method applies to a wide range of network configurations. Two case studies on: (1) MIMO two-way relay network and (2) MIMO multiple-access relay network are presented in this paper. For both case studies, numerical results are shown to demonstrate the performance improvement of the proposed scheme over conventional schemes by more than 4 dB, while the full-rate and full-diversity behaviors are in line with our analysis.

Sequential Closed-Form Semiblind Receiver for Space-Time Coded Multihop Relaying Systems

In this letter, we present a sequential closed-form semi-blind receiver for a one-way multi-hop amplify-and-forward (AF) relaying system. Assuming Khatri-Rao space-time (KRST) coding at each relay, it is shown that the system with K relays can be modeled by means of a generalized nested PARAFAC model. Decomposing this model into K +1 third-order PARAFAC models, we develop a closed-form semi-blind receiver for jointly estimating the information symbols and the individual channels, at the destination node. Each step consists of a Khatri-Rao factorization. Parameter identifiability conditions are given, and simulation results are provided to illustrate the effectiveness of the proposed semi-blind receiver. Index Terms—Multi-hop relaying, sequential closed-form semi-blind receiver, space time (ST) coding, amplify-and-forward, generalized nested PARAFAC model. I. INTRODUCTION Relay nodes will play an important role in 5G communication systems. In such systems, the high-capacity wireless backhaul offers operators an alternative solution to conventional backhauling using multi-hop short-distance communications [1]–[4]. Tensor decompositions have been widely exploited for point-to-point wireless communication systems. The practical motivation for tensor modeling comes from the fact that one can simultaneously benefit from multiple (more than two) signal diversities, like space, time and frequency diversities, for instance. In the context of cooperative wireless communications, few results have been published on tensor-based receivers, and most of them are limited to a single relay scenario. In previous works [5]–[8], the problem of channel estimation for multiple input multiple output (MIMO) relaying systems was considered under a supervised approach. The works [5]–[7] considered one-way two-hop systems, while [8] addressed two-way MIMO relaying systems. In [9] and [10], three-hop relaying systems were studied. Recent works proposed semi-blind receivers for joint symbol and channel estimation. For instance, one can cite the PARAFAC-PARATUCK [11] and the nested PARAFAC receivers [12], [13]. However, the generalization of tensor-based semi-blind receivers to the multi-hop relaying scenario has not been addressed so far to the best of authors' knowledge.

Transceiver Design for Nonconcurrent Two-Way MIMO AF Relaying With QoS Guarantees

We consider a cellular system with amplify-and-forward (AF) nonconcurrent two-way relaying (ncTWR), where a base station serves a transmit-only user and a receive-only user. Most of the state-of-the-art transceiver designs for AF multiple-input multiple-output (MIMO) ncTWR optimize a system-wide objective function subject to the transmit power constraints. Transceiver designs that incorporate quality-of-service (QoS) constraints are not well investigated in ncTWR literature. In this paper, we design a MIMO AF transceiver that maximizes weighted sum-rate (WSR) while guaranteeing the QoS constraints that are cast as per-stream rate required by two ncTWR users. The WSR maximization is a nonconvex problem due to its nonconvex objective. We solve this problem by separately approximating the objective at low and high signal-to-noise ratios (SNRs), with each approximation cast as a geometric program. With extensive numerical evaluations, we first demonstrate the improved performance of the proposed transceiver over existing designs without QoS constraints. We later investigate the effect of QoS constraints on the system WSR.

Iterative Beamformer Design for Multi-Node MIMO Two-Way Relay Networks Using Duality

In this paper, an iterative design method for beamformers is proposed for multiple-input multiple-output (MIMO) two-way relay networks with multiple pairs of source nodes. It is known that the joint beamformer design problem based on the minimum mean-square-error (MMSE) is known to be nonconvex, and it cannot be analytically solved. To manage this difficulty, a novel iterative algorithm is proposed, which uses duality relationships. First, the MSE duality for MIMO two-way relay networks with multiple pairs of nodes is presented. Moreover, the optimization problem is divided into three subproblems, which can be separately solved; then, the duality is applied to the proposed iterative algorithm, which provides closed-form solutions for all subproblems. The numerical results demonstrate that the proposed method improves network performance and can be applied to various communication systems that use the two-way relay network.

Joint Relay/Antenna Selection and Precoding Design for Two-Way MIMO Amplify-and-Forward Relaying Systems

In this paper, a unified framework of relay/antenna subset selection and transceiver design is proposed for a dual-hop two-way amplify-and-forward (AF) multiple-input–multiple-output (MIMO) relaying system in correlated fading channels. By making use of the singular value decomposition (SVD) technique, the joint design of two-source transceivers and multirelay precoders is developed based on the minimum-mean-square-error (MMSE) criterion. This MMSE-based optimization leads to a highly nonlinear objective function of sources and relaying precoders under power constraints so that an iterative search algorithm is applied to explore the optimal power allocation. Simulation results show that the SVD-based joint design of relay and source precoders, in conjunction with the SVD-based relay-and-antenna selection scheme, is capable of achieving superior performance in terms of bit error rate (BER) with an alleviated demand on relays and associated antenna pairs.

Joint Transceiver Design for QoS-Constrained MIMO Two-Way Non-Regenerative Relaying Using Geometric Programming

Transceiver designs for multiple-input multiple-output (MIMO) two-way relaying are being actively explored. Most of the state-of-the-art studies optimize a system-wide objective function subject to the transmit power constraints on the two source nodes and the relay. Transceiver designs with quality-of-service (QoS) constraints have lacked attention in two-way relaying literature. In this paper, we study a MIMO transceiver design, based on the generalized singular value decomposition, that allocates power at the source and relay nodes to optimize the following per-stream rate-constrained objectives: 1) network transmit power, and 2) sum-rate. In addition, we also maximize the rate of the transmit stream with the worst signal-to-noise ratio. Through extensive numerical evaluations, we demonstrate the superior performance of proposed design over the existing ones, not only with QoS constraints but also without them.

Novel self-interference suppression schemes based on Dempster-Shafer theory with network coding in two-way full-duplex MIMO relay

A two-way full-duplex multiple-input multiple-output (MIMO) relay provides effective spectral efficiency and system capacity improvement. However, self-interference (SI) as a serious problem limits the development of a full-duplex relay. In this paper, the novel SI suppression schemes based on the Dempster-Shafer (DS) evidence theory are proposed to suppress SI in the two-way full-duplex MIMO relay. DS evidence theory can appropriately characterize uncertainty and make full use of multiple evidence source information by DS combination rule to obtain reliable decisions. The first proposed DS network coding (DS-NC) scheme adopts DS evidence theory to detect the signal of each source node, considering SI suppression in the basic probability assignment computation in the multiple access phase. Moreover, different from the DS-NC scheme, the further proposed DS physical-layer network coding (DS-PNC) scheme considers SI suppression from the vector space perspective and combines the PNC mapping rule with the DS theory to obtain a network-coded signal without estimating each source node signal. In the broadcast phase, antenna selection is adopted at the relay and DS evidence theory is also applied at each source node for SI suppression. Meanwhile, the effects of imperfect SI channel estimation and the intended channel estimation on the proposed schemes are also studied. Finally, the proposed DS-PNC scheme is studied with the SI signal model which considers analog radio frequency cancellation, the effects of I/Q modulator imbalances, and power amplifier nonlinearity of the transmitter. Simulation results reveal that the proposed DS-PNC scheme is a little more sensitive to the channel estimation errors than the traditional spatial-domain schemes. However, with the perfect channel state information, the proposed DS-NC with one iteration and DS-PNC schemes outperform traditional spatial-domain schemes. Furthermore, considering the SI signal model with nonlinear distortion and radio frequency cancellation, the DS-PNC scheme is also superior to the traditional schemes. Meanwhile, the DS-PNC scheme is more robust to the SI and achieves the same diversity gain as the ideal cancellation.

On the energy-efficiency optimisation of OSTBC-MIMO two-way cooperative systems

This paper addresses the optimisation of energy consumption of a two-way Amplify-and-Forward (AF) cooperative Multiple-Input, Multiple-Output (MIMO) system based on Orthogonal Space Time Block Code (OSTBC) under data rate constraint. The energy minimisation problem is written as a geometric problem and then solved employing a useful optimisation tool denoted as geometric programs in posynomial form (gpposy). The effects of the number of antennas, the relay's location and the predefined data rate transmission on the total transmit energy consumption are investigated. A comparison between the energy consumption of one- and two-way relaying is done. Evaluating the total energy consumption including both the transmission energy and the circuit energy consumption is also a contribution of this work. Simulation results show the significant transmit energy saving achieved by the proposed optimisation scheme. Thus, the OSTBC-MIMO cooperative system decreases the total transmit energy consumption compared to a SISO cooperative one. Generally, the cooperative MIMO systems are more energy efficient than the cooperative SISO systems even when circuit energy consumption is considered. Furthermore, our results indicate that the two-way MIMO systems are more energy efficient than one-way MIMO systems for high rates.

Centralized Two-Way AF MIMO Multiple Dispersed Relay Network

This paper considers a two-way amplify-and-forward (AF) multiple-input multiple-output (MIMO) relay network consisting of two sources (each with multiple antennas) and multiple physically dispersed single-antenna relays. A central station finds the optimum relay amplifying matrices and transmit/receive beamforming vectors explicitly and iteratively under the transmit power constraints at the sources and the relays. The minimum-mean-square-error criterion is used. Numerical results show that the proposed scheme outperforms the existing two-way AF MIMO network schemes proposed by Arti et al. and Wang et al.

Sum Rate Maximization of an MIMO Two-Way Relay System Using MSE Duality

In this letter, we propose a novel joint beamforming scheme using mean-square error (MSE) duality to maximize the sum rate of a multiple-input multiple-output (MIMO) two-way relay system. It is difficult to solve the sum rate maximization problem directly due to its non-convexity. To manage this difficulty, the optimization problem is reformulated as a problem that minimizes the product of the minimum mean-square errors. Then, we show that the per stream MSE duality holds in a two-way relay system under cross power constraints. Based on the per stream MSE duality, an alternate algorithm is proposed to jointly optimize the linear transceivers. The simulation results demonstrate that the proposed scheme outperforms the existing linear schemes in view of the sum rate maximization.

Channel Estimation for Two-Way MIMO Relay Systems in Frequency-Selective Fading Environments

In this paper, we investigate the channel estimation problem for two-way multiple-input multiple-output (MIMO) relay communication systems in frequency-selective fading environments. We apply the method of superimposed channel training to estimate the individual channel state information (CSI) of the first-hop and second-hop links for two-way MIMO relay systems with frequency-selective fading channels. In this algorithm, a relay training sequence is superimposed on the received signals at the relay node to assist the estimation of the second-hop channel matrices. The optimal structure of the source and relay training sequences is derived to minimize the mean-squared error (MSE) of channel estimation. Moreover, the optimal power allocation between the source and relay training sequences is derived to improve the performance of channel estimation. Numerical examples are shown to demonstrate the performance of the proposed superimposed channel training algorithm for two-way MIMO relay systems in frequency-selective fading environments.

Optimization of a two-way MIMO amplify-and-forward relay network

In this paper, we consider optimization of a two-way multiple-input multiple-output (MIMO) amplify-and-forward relay network which consists of a pair of transceivers and several relay nodes. Multiple antennas are equipped on the transceivers and relays. Multiple access broadcast scheme which finishes communication in two time slots is considered. In the first time slot, signals received by the relays are scaled by several beamforming matrices. In the second time slot, the relays transmit the scaled signals to the two transceivers. Upon receiving these signals, a MIMO equalizer is implemented at each transceiver to recover the desired signal. In this paper, zero forcing equalizers are used. Joint optimization of the beamforming matrices and the equalizers are realized using the following criteria: 1) the total relay transmission power is minimized subject to the minimal output signal-to-noise ratio (SNR) constraint at each transceiver, 2) the minimal output SNR of the two transceivers is maximized subject to total relay transmission power constraint, and 3) the minimal output SNR of the two transceivers is maximized subject to individual relay transmission power constraint. It is shown that the proposed optimization problems can be formulated as the second-order cone programming problems which can be solved efficiently. The validity of the proposed algorithm is verified by computer simulations.

Joint Transceiver Optimization for Two-Way MIMO Relay Systems With MSE Constraints

Transceiver design for two-way multiple-input multiple-output (MIMO) relay systems has attracted much research interest recently. However, there is little research on the impact of quality-of-service (QoS) constraints on two-way MIMO relay systems, which greatly affects the user experience. In this letter, we propose a transceiver design for two-way MIMO relay systems which minimizes the total network transmission power subjecting to QoS constraints expressed as upper-bounds on the mean-squared error (MSE) of the signal waveform estimation at both destinations. An iterative algorithm is developed to optimize the source, relay, and receive matrices. Simulation results demonstrate the fast convergence of the proposed algorithm.