Robust Tomlinson-Harashima Precoding Research Articles

Robust Tomlinson-Harashima Precoding for Two-Way Relaying

Most of the non-linear transceivers, which are based on Tomlinson Harashima (TH) precoding and have been proposed in the literature for two-way relay networks, assume perfect channel state information (CSI). In this paper, we propose a novel and robust TH precoding scheme for two-way relay networks with multiple antennas at the transceiver and the relay nodes. We assume imperfect CSI and that the channel uncertainty is bounded by a spherical region. Furthermore, we consider the sum of the mean square error as the objective function, under a limited power constraint for transceiver and relay nodes. Simulations are provided to evaluate the performance and to validate the efficiency of the proposed scheme.

Robust THP Design for Energy Efficiency of Multibeam Satellite Systems with Imperfect CSI

In this letter, we investigate a robust zero-forcing (ZF) Tomlinson-Harashima Precoding (THP) scheme for multibeam satellite downlink systems to improve the energy efficiency (EE) when the channel state information (CSI) at the transmitter is imperfect. By using a norm-bounded error (NBE) model with unknown statistical characterization, the worst case EE optimization problem under transmit power constraint is solved with two steps. Firstly, the optimal CSI uncertainty parameter minimizing the EE is obtained, then sequential convex approximation (SCA) is used to obtain the solution via a nested iteration method. The proposed robust algorithm achieves better EE performance in comparison with the nonrobust one in the literature in the presence of CSI error, which can be shown from simulation results.

Non‐linear transceiver design for multiple‐input–multiple‐output interference channel with statistical channel state information error

This study focuses on robust Tomlinson–Harashima precoding transceiver design for multi-cell multiple-input–multiple-output interference channel with statistical channel state information error. The objective is formulated to minimise the maximum per-user mean square error (MSE) with per-transmitter power constraint. Since the problem is not jointly convex, an approximated method is proposed. The authors optimise the receiver matrix to be minimum MSE form as well as derive the optimisation problems of transmitter matrix and feedback matrix to be second-order cone programming, respectively. By use of the results, the three matrices are updated iteratively. The convergence of the proposed method is also proved. Simulation results show that the proposed scheme outperforms the robust linear transceiver in both MSE and bit error ratio.

Robust Tomlinson–Harashima Precoding With Gaussian Uncertainties for SWIPT in MIMO Broadcast Channels

Nonlinear transceiver based on Tomlinson–Harashima (TH) precoding outperforms the linear minimum mean-square-error (MSE) architecture in terms of minimum achievable MSE. In this paper, we investigate nonlinear TH precoding design problem for simultaneous wireless information and power transfer in multiple-input-multiple-output broadcast channels, where there are one information-decoding (ID) receiver and multiple energy harvesting (EH) receivers. We consider the scenario that the transmitter knows imperfect channel state information of all links and the channel uncertainties are modeled by Gaussian random variables. Our objective is to jointly optimize TH precoding matrices and linear equalizer to minimize average MSE subject to transmit power constraint and EH constraints on average harvested power. We transform the robust transceiver design problem into a difference of convex programming and propose a constrained concave convex procedure (CCCP) based locally optimal solution. To reduce computational complexity, we propose a noniterative upper bound based suboptimal solution that minimizes the upper bound on average MSE. We also extend the CCCP-based locally optimal solution to the single group multicast scenario where there are multiple ID receivers. Simulation results demonstrate that our proposed TH precoding transceiver design achieves lower average MSE than linear precoding transceiver design.

Robust THP Transceiver Design for MIMO Interference Channel

This letter focuses on robust Tomlinson-Harashima precoding (THP) transceiver optimization for multiple-input multiple-output (MIMO) interference channel, where a bounded channel error model is assumed. Two optimization problems are formulated as minimizing the maximum per-user mean square error (MSE) and sum MSE with per-transmitter power constraint, respectively. Since both optimization problems are not convex, a sub-optimal alternating optimization method is proposed to iteratively update the transmit feedback matrix, precoding matrix and receive equalization matrix of THP transceiver until convergence. We show that the two problems of three matrix variables can be formulated as semidefinite program (SDP) when any two of three matrices are fixed, thus making the problems computationally tractable. Simulation results demonstrate that the proposed THP transceivers can improve the performance over the linear transceivers and are robust to the imperfect channel state information (CSI).

Robust non-linear precoding for downlink multiuser multiple-input multiple-output orthogonal frequency-division multiplexing systems with limited feedback

The authors consider the robust Tomlinson–Harashima precoding (THP) for downlink multiuser multiple-input multiple-output orthogonal frequency-division multiplexing systems with quantised feedback. The authors discuss vector channel feedback strategies in the frequency and time domains, and develop a robust version of THP that takes into account of error statistics of the channel state information, that consists of the optimal feedforward filters, feedback filters and the receive filters. Feedback techniques are developed to exploit the spatial correlations in realistic 3GPP channel models by applying dimension reduction and scalar-quantisation. Extensive simulations results are provided to demonstrate the performance of the proposed robust THP design as well as the channel feedback scheme.

Robust THP Transceiver Designs for Multiuser MIMO Downlink with Imperfect CSIT

In this paper, we present robust joint non-linear transceiver designs for multiuser multiple-input multiple-output (MIMO) downlink in the presence of imperfections in the channel state information at the transmitter (CSIT). The base station (BS) is equipped with multiple transmit antennas, and each user terminal is equipped with one or more receive antennas. The BS employs Tomlinson-Harashima precoding (THP) for inter-user interference pre-cancellation at the transmitter. We consider robust transceiver designs that jointly optimize the transmit THP filters and receive filter for two models of CSIT errors. The first model is a stochastic error (SE) model, where the CSIT error is Gaussian-distributed. This model is applicable when the CSIT error is dominated by channel estimation error. In this case, the proposed robust transceiver design seeks to minimize a stochastic function of the sum mean square error (SMSE) under a constraint on the total BS transmit power. We propose an iterative algorithm to solve this problem. The other model we consider is a norm-bounded error (NBE) model, where the CSIT error can be specified by an uncertainty set. This model is applicable when the CSIT error is dominated by quantization errors. In this case, we consider a worst-case design. For this model, we consider robust i) minimum SMSE, ii) MSE-constrained, and iii) MSE-balancing transceiver designs. We propose iterative algorithms to solve these problems, wherein each iteration involves a pair of semi-definite programs (SDP). Further, we consider an extension of the proposed algorithm to the case with per-antenna power constraints.

Robust Tomlinson–Harashima Precoding for the Wireless Broadcast Channel

<para xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> Previous designs of Tomlinson–Harashima precoding (THP) for the broadcast channel with multiple (cooperative) transmitters and noncooperative (decentralized) scalar receivers assume complete channel state information (CSI) at the transmitter. Due to its nonlinearity, THP is more sensitive to errors in CSI at the transmitter than linear precoding, which may be large in wireless communications. Thus, THP performance degrades severely—and it is even outperformed by corresponding linear precoders. We propose a novel robust optimization for THP with partial CSI based on mean-square error (MSE), which performs a conditional mean (CM) estimate of the cost function including a novel model of the receivers. This enables a smooth transition of robust THP from complete, via partial, to statistical CSI. The performance is now always superior or in the worst case equal to corresponding linear precoding techniques. With these features, the proposed robust THP is very attractive for application in the wireless broadcast channel. </para>