Two-way Multiple-input Multiple-output Research Articles

Channel estimation for MIMO multi-relay systems using a tensor approach

In this paper, we address the channel estimation problem for multiple-input multiple-output (MIMO) multi-relay systems exploiting measurements collected at the destination only. Assuming that the source, relays, and destination are multiple-antenna devices and considering a three-hop amplify-and-forward (AF)-based training scheme, new channel estimation algorithms capitalizing on a tensor modeling of the end-to-end communication channel are proposed. Our approach provides the destination with the instantaneous knowledge of all the channel matrices involved in the communication. Instead of using separate estimations for each matrix, we are interested in a joint estimation approach. Two receiver algorithms are formulated to solve the joint channel estimation problem. The first one is an iterative method based on a trilinear alternating least squares (TALS) algorithm, while the second one is a closed-form solution based on a Kronecker least squares (KRLS) factorization. A useful lower-bound on the channel training length is derived from an identifiability study. We also show the proposed tensor-based approach is applicable to two-way MIMO relaying systems. Simulation results corroborate the effectiveness of the proposed estimators and provide a comparison with existing methods in terms of channel estimation accuracy and bit error rate (BER).

Secure Beamforming Design for Physical Layer Network Coding Based MIMO Two-Way Relaying

In this letter, we propose a secure beamforming scheme for physical layer network coding (PNC)-based multiple-input multiple-output (MIMO) two-way relaying system. The relay node performs PNC mapping. An eavesdropper is attempting to intercept the user information. The channel state information (CSI) of the user-to-eavesdropper channel is imperfect at the user nodes. A robust optimization problem is formulated to design beamforming vectors at the user nodes and relay. The problem is non-convex, and an algorithm is proposed to solve that. In the numerical analysis, we discuss the convergence of the proposed algorithm and the impact of the CSI error on the performance.

Joint Optimization of Source and Relay for MIMO Two-Way Relay Networks Using MSE Duality

In this letter, the joint optimization of a source-relay pair is proposed for multiple-input multiple-output (MIMO) two-way relay networks. In these networks, since the joint beamformer design problem based on the minimum mean square error (MMSE) is known to be non-convex, it cannot be solved analytically. In order to solve the problem, a novel iterative algorithm is proposed that uses duality relationships. First, the MSE duality for MIMO two-way relay networks is presented; then, this duality is applied to the proposed optimization method, which provides closed-form solutions for all subproblems. Because the proposed algorithm does not involve convex optimization software packages, it efficiently reduces the computational complexity. The numerical results demonstrate that the proposed method improves the MSE performance compared with the conventional method.

MIMO Two-Way Compress-and-Forward Relaying with Approximate Joint Eigen-Decomposition

While compress-and-forward (CF) is one of the basic relay protocols in cooperative transmission, little is known about the optimal design of CF in multiple-input multiple-output (MIMO) two-way relay channels (TWRC). An intuitive method is to compress each element of the superimposed signal vector during the multiple-access (MAC) phase independently and with identical compression noise variance. In this paper, we introduce an improved compression method. The key idea is to apply approximate joint diagonalization (AJD) to realize simultaneous eigen-decomposition of the two channel matrices in the MAC phase of two-way relaying in an approximate manner. After that, a novel covariance matrix design of the compression noise vector is derived for sum-rate maximization. Numerical results show that the proposed CF design can improve the spectral efficiency, especially when the relay node is close to any of the two source nodes instead of in the midpoint.

Sum Rate Analysis of Two-Way MIMO AF Relay Networks with Zero-Forcing

The sum rate of multiple-input multiple-output (MIMO) amplify-and-forward (AF) two-way relay networks (TWRNs) with zero-forcing (ZF) transmission is analyzed. Namely, (1) ZF at the two sources for transmission and reception and (2) ZF at the relay for transmission and reception, are treated. Specifically, the exact sum rate expressions and corresponding high signal-to-noise ratio (SNR) approximations are derived for uncorrelated and min-semi-correlated (i.e., correlation exists only at the minimum antenna terminal) Rayleigh fading cases in closed-form. Moreover, the closed-form upper and lower bounds of the sum rate are derived for max-semi-correlated (i.e., correlation exists only at the maximum antenna terminal) and doubly-correlated Rayleigh fading cases. Notably, these sum rate bounds and high SNR approximations provide valuable insights into practical MIMO AF TWRN system-design and the maximum achievable spatial multiplexing gain. All the analyses are verified by using Monte-Carlo simulations.

Channel Training Algorithms for Two-Way MIMO Relay Systems

Two-way relay systems are known to be capable of providing higher spectral efficiency compared with conventional one-way relay systems. However, the channel estimation problem for two-way relay systems is more complicated than that of one-way relay systems. In this paper, we propose and compare two channel estimation algorithms, namely the superimposed channel training scheme and the two-stage channel estimation algorithm, for two-way multiple-input multiple-output (MIMO) relay communication systems, where the individual channel state information (CSI) for the first-hop and second-hop links is estimated. For both algorithms, we derive the optimal structure of the source and relay training sequences which minimize the mean-squared error (MSE) of channel estimation. In the superimposed channel training scheme, the power allocation between the source and relay training sequences is optimized. For the two-stage channel estimation algorithm, we optimize the power allocation at the relay node between two stages to improve the performance of the algorithm. Numerical examples are shown to demonstrate and compare the performance of the proposed channel training algorithms.

Beamforming and Combining in Two-Way AF MIMO Relay Networks

In this letter, we propose a beamforming and combining scheme for a two-way amplify-and-forward (AF) multiple-input multiple-output (MIMO) relay network. An approximate expression for the symbol error rate of the scheme in Rayleigh fading for M-ary phase-shift keying is obtained based on the moment generating function of the instantaneous received signal-to-noise ratio. The diversity order is also analytically derived. It is shown by simulations that the proposed scheme outperforms existing schemes for beamforming and combining in two-way AF MIMO relay systems. We also discuss beamforming and combining in a two-way AF MIMO relay system with estimated channel gains.

Transmission Scheme of MIMO Two-Way Relaying Systems Based on Symmetric Channel

There are fading and noise in MIMO two-way relaying system. A novel transmission scheme was proposed. The scheme performs equivalent to a 2×2 V-BLAST MIMO(Multiple-Input Multiple-Output) and a two 2×1 AlAMOUTI MISO(Multiple-Input Single-Output) in multiple-access phase and broadcast phase respectively. Network coding and minimum mean square error detection are employed at the relay. Binary phase shift keying and 8 phase shift keying modulation is used. The performance is analyzed under the assumption of a symmetric relay channel model. Simulation results show that the proposed transmission scheme can facilitate more reliable transmission.

Achievable Degrees of Freedom on MIMO Two-way Relay Interference Channels

In this paper, we study new network information flow called multiple-input multiple-output (MIMO) two-way relay interference channels where two links of relay systems are interfering with each other. In this system, we characterize the achievable total degrees of freedom (DOF) when all user nodes and relays have M and N antennas, respectively. We provide three different methods, namely, time-division multiple access, signal space alignment for network coding (SSANC), and a new interference neutralization (IN) scheme. In the SSA-NC scheme, one relay is selected to fully exploit the dimension of the chosen relay for network coding. For the IN, we propose a new relay transmission scheme where two relays cooperatively design the beamforming vectors so that the interference signals are neutralized at each receiver. By adopting three different relaying strategies, we show that the DOF of max {min(4N, 2M), min(2N, 2⌊4/3M⌋), min(2N - 1, 4M)} is achieved for MIMO two-way relay interference channels.

A New Physical-Layer Network Coding Scheme with Eigen-Direction Alignment Precoding for MIMO Two-Way Relaying

We investigate efficient communication over multiple-input multiple-output (MIMO) two-way relay channels (TWRCs), where two multi-antenna users exchange information via a multi-antenna relay. We propose a new MIMO physical-layer network coding (PNC) scheme that includes novel eigen-direction alignment (EDA) precoding. The proposed EDA precoding efficiently aligns the two-user's eigen-modes into the same set of orthogonal directions, and multiple independent PNC streams are implemented over the aligned eigen-modes. We derive an achievable rate-pair of the proposed scheme, for given EDA precoding parameters, over a MIMO TWRC. To maximize the achievable rate-region, we formulate a design criterion for the EDA precoding parameters, and present solutions to the formulation. Closed-form bounds on the sum-rates of the designed EDA-PNC schemes are derived. Numerical results show that there is only a small gap between the achievable rate of the proposed scheme and the capacity upper bound of the MIMO TWRC. It is shown that the proposed scheme can significantly outperforms existing schemes in the literature.

Degrees of Freedom for MIMO Two-Way X Relay Channel

We study the degrees of freedom (DOF) of a multiple-input multiple-output (MIMO) two-way X relay channel, where there are two groups of source nodes and one relay node, each equipped with multiple antennas, and each of the two source nodes in one group exchanges independent messages with the two source nodes in the other group via the relay node. It is assumed that every source node is equipped with M antennas while the relay is equipped with N antennas. We first show that the upper bound on the total DOF for this network is 2min{2M,N} and then focus on the case of N \leq 2M so that the DOF is upper bounded by the number of antennas at the relay. By applying signal alignment for network coding and joint transceiver design for interference cancellation, we show that this upper bound can be achieved when N \leq8M/5. We also show that with signal alignment only but no joint transceiver design, the upper bound is achievable when N\leq4M/3. Simulation results are provided to corroborate the theoretical results and to demonstrate the performance of the proposed scheme in the finite signal-to-noise ratio regime.

Zero-Forcing Based MIMO Two-Way Relay with Relay Antenna Selection: Transmission Scheme and Diversity Analysis

Combining of physical-layer network coding (PNC) and multiple-input multiple-output (MIMO) can significantly improve the performance of the wireless two-way relay network (TWRN). This paper proposes novel Max-Min optimization based relay antenna selection (RAS) schemes for zero-forcing (ZF) based MIMO-PNC transmission. RAS relaxes ZF's constraints on the number of antennas and extends the applications of ZF based MIMO-PNC to more practical scenarios, where the dedicated relay has more antennas than the end node. Moreover, RAS also brings diversity advantages to TWRN and the achievable diversity gains of the proposed schemes are theoretically analyzed. In particular, an equivalence relation is carefully built for the diversity gains obtained by 1) RAS for ZF based MIMO-PNC and 2) transmit antenna selection (TAS) for MIMO broadcasting (BC) with ZF receivers. This equivalence transforms the original problem to a more tractable form which eventually allows explicit analytical results. It is interesting to see that Max-Min RAS keeps the network diversity gain of ZF based MIMO-PNC to be the same as the diversity gain of the point-to-point link within the TWRN. This insight extends the understanding on the behaviors of ZF transceivers with antenna selection (AS) to relatively complicated MIMO-TWRN/BC scenarios.

A Closed-Form Power Allocation and Signal Alignment for a Diagonalized MIMO Two-Way Relay Channel With Linear Receivers

A novel channel diagonalization scheme for an amplify-and-forward, multiple-input multiple-output (MIMO), two-way relay channel (TWRC) is proposed using generalized singular value decomposition (GSVD). Diagonalization of the MIMO TWRC is a sub-optimal approach that achieves two main purposes: reducing the computational complexity for optimizing the linear precoders at each node; and reducing the detection complexity at the source nodes by separating the multiple data streams. For the given diagonalized structure, we first align the entries of the diagonalized channels using a permutation to maximize a lower bound of average achievable sum rate (ASR), and a joint source-relay power allocation is then performed to maximize the ASR of the aligned TWRC; the overall problem is divided into two convex subproblems, the solutions to which are provided in closed-form. Our analysis for the proposed scheme underlines the benefits of acquiring channel state information. Simulation results demonstrate that the proposed GSVD-based relaying scheme, with the signal alignment and closed-form power allocation, significantly improves the ASR while retaining the diagonalized channel structure. In addition, the proposed scheme achieves the same level of ASR with much less computational complexity as compared to the iterative schemes.

On Achievable Rate Regions for Half-Duplex Gaussian MIMO Relay Channels: A Decomposition Approach

We consider uni- and bidirectional communication in the half-duplex multiple-input multiple-output (MIMO) relay channel. Assuming perfect channel state information at all nodes and the use of time division duplex communication protocols with a peak power constraint for every protocol phase, we propose a dual decomposition approach to efficiently determine the cut-set bound and the maximum achievable decode-and-forward rate for the Gaussian MIMO relay channel. A general outer bound on the rate regions that can be achieved in the restricted two-way MIMO relay channel is established, and we present an achievable rate region based on the decode-and-forward scheme which is a superset of several previously derived achievable rate regions. Finally, it is shown how the stated outer bound and achievable rate region can also be evaluated by means of the proposed dual decomposition approach, and we discuss how our work may be used for designing optimal protocols.

Precoding and decoding design for two-way MIMO AF multiple-relay system

In this paper, a joint precoding and decoding design scheme is proposed for two-way Multiple-Input Multiple-Output (MIMO) multiple-relay system. The precoding and decoding matrices are jointly optimized based on Minimum Mean-Square-Error (MMSE) criteria under transmit power constraints. The optimization problem is solved by using a convergent iterative algorithm which includes four sub-problems. It is shown that due to the difficulty of the block diagonal nature of the relay precoding matrix, sub-problem two cannot be solved with existing methods. It is then solved by converting sub-problem two into a convex optimization problem and a simplified method is proposed to reduce the computational complexity. Simulation results show that the proposed scheme can achieve lower Bit Error Rate (BER) and larger sum rate than other schemes. Furthermore, the BER and the sum rate performance can be improved by increasing the number of antennas for the same number of relays or increasing the number of relays for the same number of antennas.

Channel Estimation of Dual-Hop MIMO Relay System via Parallel Factor Analysis

The optimal source precoding matrix and relay amplifying matrix have been developed in recent works on multiple-input multiple-output (MIMO) relay communication systems assuming that the instantaneous channel state information (CSI) is available. However, in practical relay communication systems, the instantaneous CSI is unknown, and therefore, has to be estimated at the destination node. In this paper, we develop a novel channel estimation algorithm for two-hop MIMO relay systems using the parallel factor (PARAFAC) analysis. The proposed algorithm provides the destination node with full knowledge of all channel matrices involved in the communication. Compared with existing approaches, the proposed algorithm requires less number of training data blocks, yields smaller channel estimation error, and is applicable for both one-way and two-way MIMO relay systems with single or multiple relay nodes. Numerical examples demonstrate the effectiveness of the PARAFAC-based channel estimation algorithm.

Sum-Rate Maximization in Two-Way AF MIMO Relaying: Polynomial Time Solutions to a Class of DC Programming Problems

Sum-rate maximization in two-way amplify-and-forward (AF) multiple-input multiple-output (MIMO) relaying belongs to the class of difference-of-convex functions (DC) programming problems. DC programming problems occur also in other signal processing applications and are typically solved using different modifications of the branch-and-bound method which, however, does not have any polynomial time complexity guarantees. In this paper, we develop two efficient polynomial time algorithms for the sum-rate maximization in two-way AF MIMO relaying. The first algorithm guarantees to find at least a Karush-Kuhn-Tucker (KKT) solution. There is a strong evidence, however, that such a solution is actually globally optimal. The second algorithm that is based on the generalized eigenvectors shows the same performance as the first one with reduced computational complexity. The objective function of the problem is represented as a product of quadratic fractional ratios and parameterized so that its convex part (versus the concave part) contains only one (or two) optimization variables. One of the algorithms is called POlynomial Time DC (POTDC) and is based on semi-definite programming (SDP) relaxation, linearization, and an iterative Newton-type search over a single parameter. The other algorithm is called RAte-maximization via Generalized EigenvectorS (RAGES) and is based on the generalized eigenvectors method and an iterative search over two (or one, in its approximate version) optimization variables. We derive an upper-bound for the optimal value of the corresponding optimization problem and show by simulations that this upper-bound is achieved by both algorithms. It provides an evidence that the algorithms find a global optimum. The proposed methods are also superior to other state-of-the-art algorithms.

Performance Analysis of MIMO Relay Network via Propagation Measurement in L-Shaped Corridor Environment

Setting relays can address the shadowing problem between a transmitter (Tx) and a receiver (Rx). Moreover, the Multiple-Input Multiple-Output (MIMO) technique has been introduced to improve wireless link capacity. The MIMO technique can be applied in relay network to enhance system performance. However, the efficiency of relaying schemes and relay placement have not been well investigated with experiment-based study. This paper provides a propagation measurement campaign of a MIMO two-hop relay network in 5GHz band in an L-shaped corridor environment with various relay locations. Furthermore, this paper proposes a Relay Placement Estimation (RPE) scheme to identify the optimum relay location, i.e. the point at which the network performance is highest. Analysis results of channel capacity show that relaying technique is beneficial over direct transmission in strong shadowing environment while it is ineffective in non-shadowing environment. In addition, the optimum relay location estimated with the RPE scheme also agrees with the location where the network achieves the highest performance as identified by network capacity. Finally, the capacity analysis shows that two-way MIMO relay employing network coding has the best performance while cooperative relaying scheme is not effective due to shadowing effect weakening the signal strength of the direct link.

Joint Source and Relay Precoding Designs for MIMO Two-Way Relaying Based on MSE Criterion

Properly designed precoders can significantly improve the spectral efficiency of multiple-input multiple-output (MIMO) relay systems. In this paper, we investigate joint source and relay precoding design based on the mean-square-error (MSE) criterion in MIMO two-way relay systems, where two multi-antenna source nodes exchange information via a multi-antenna amplify-and-forward relay node. This problem is non-convex and its optimal solution remains unsolved. Aiming to find an efficient way to solve the problem, we first decouple the primal problem into three tractable sub-problems, and then propose an iterative precoding design algorithm based on alternating optimization. The solution to each sub-problem is optimal and unique, thus the convergence of the iterative algorithm is guaranteed. Secondly, we propose a structured precoding design to lower the computational complexity. The proposed precoding structure is able to parallelize the channels in the multiple access (MAC) phase and broadcast (BC) phase. It thus reduces the precoding design to a simple power allocation problem. Lastly, for the special case where only a single data stream is transmitted from each source node, we present a source-antenna-selection (SAS) based precoding design algorithm. This algorithm selects only one antenna for transmission from each source and thus requires lower signalling overhead. Comprehensive simulation is conducted to evaluate the effectiveness of all the proposed precoding designs.

Joint Source and Relay Optimization for Two-Way MIMO Multi-Relay Networks

In this letter, we study two-way nonregenerative multiple-input multiple-output (MIMO) relay communications with multiple relay nodes. An iterative algorithm is developed to jointly optimize the source, relay, and receive matrices such that the two-way sum mean-squared error (MSE) of the signal waveform estimation is minimized. Numerical examples demonstrate a better performance of the proposed algorithm compared with existing algorithms for two-way MIMO multi-relay networks.