Multiple-input Multiple-output Two-way Relay Channel Research Articles

The Dirty MIMO Multiple-Access Channel

In the scalar dirty multiple-access channel, in addition to Gaussian noise, two additive interference signals are present, each known non-causally to a single transmitter. It was shown by Philosof et al. that for strong interferences, an independent identically distributed ensemble of codes does not achieve the capacity region. Rather, a structured-codes approach was presented that was shown to be optimal in the limit of high signal-to-noise ratios, where the sum capacity is dictated by the minimal (“bottleneck”) channel gain. In this paper, we consider the multiple-input multiple-output (MIMO) variant of this setting. In order to incorporate structured codes in this case, one can utilize matrix decompositions that transform the channel into effective parallel scalar dirty multiple-access channels. This approach, however, suffers from a “bottleneck” effect for each effective scalar channel and, therefore, the achievable rates strongly depend on the chosen decomposition. It is shown that a recently proposed decomposition, where the diagonals of the effective channel matrices are equal up to a scaling factor, is optimal at high signal-to-noise ratios, under an equal rank assumption. This approach is then extended to any number of transmitters. Finally, an application to physical-layer network coding for the MIMO two-way relay channel is presented.

Multiple-Input Multiple-Output Two-Way Relaying: A Space-Division Approach

We propose a novel space-division-based network-coding scheme for multiple-input multiple-output (MIMO) two-way relay channels (TWRCs), in which two multiantenna users exchange information via a multiantenna relay. In the proposed scheme, the overall signal space at the relay is divided into two subspaces. In one subspace, the spatial streams of the two users have nearly orthogonal directions and are completely decoded at the relay. In the other subspace, the signal directions of the two users are nearly parallel, and linear functions of the spatial streams are computed at the relay, following the principle of physical-layer network coding. Based on the recovered messages and message-functions, the relay generates and forwards network-coded messages to the two users. We show that, at high signal-to-noise ratio, the proposed scheme achieves the asymptotic sum-rate capacity of the MIMO TWRC within [ 1/ 2]log(5/4) ≈ 0.161 bits per user-antenna, for any antenna configuration and any channel realization. We perform large-system analysis to derive the average sum-rate of the proposed scheme over Rayleigh-fading MIMO TWRCs. We show that the average asymptotic sum-rate gap to the capacity is at most 0.053 bits per relay-antenna. It is demonstrated that the proposed scheme significantly outperforms the existing schemes.

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.

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.

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.

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.