Tomlinson-Harashima Precoding Research Articles

Multi-user transmitter preprocessing assisted uplink multi-cell multiple-input multiple-output system with base station cooperation over frequency-selective channels

The performance of cellular uplink multiple-input multiple-output systems, where co-channel interference (CCI) at the base stations (BSs) is a major performance impairment, is investigated in this correspondence principally from a multi-user transmitter preprocessing (MUTP) perspective over correlated frequency-selective channels. Transmitter preprocessing at the mobile station is formulated by singular value decomposition (SVD) of only the individual user’s channel state information (CSI) while post-processing exploits all the users’ CSI using BS cooperation. Our simulations show that this approach completely removes CCI and also outperforms classical zero-forcing multi-user detection, which has about the same detection complexity. Further, the results show that our system, coupled with the optimal ‘water-filling’ strategy for power allocation, results in higher capacity than the maximum signal-to-noise ratio strategy. Furthermore, SVD-based MUTP outperforms dirty paper coding and Tomlinson–Harashima precoding in terms of achievable symbol error rate.

Tomlinson-Harashima precoding minimizing total MSE with transmitter spatial correlation

This paper proposes a Tomlinson-Harashima precoding (THP) transceiver for multiple-input multiple-output (MIMO) system, where the spatial correlation information at the transmitter is included in the channel state information (CSI) model. It derives the total mean square error (MSE) and its lower bound as a function of precoding matrix. Then, a precoding matrix and the closed-form expression of minimum MSE lower bound are obtained by use of optimization and matrix theory. By right-multiplying a proper unitary matrix to the above precoding matrix, the paper develops the optimal precoding matrix, thus the optimal transceiver matrices are achieved. Simulation results show that the total MSE performance of the proposed method outperforms the existing linear method and the naive THP method.

Joint Level 2 and 3 Dynamic Spectrum Management for Downstream DSL

In this paper, we investigate joint level 2 and 3 dynamic spectrum management (joint DSM 2/3) for downstream (DS) DSL. We consider a DS scenario in which users are divided into a few separate groups, where vector encoding based signal coordination can be applied in each group and spectrum coordination is possible for all users. This can be seen as a mixed interference/broadcast channel (IF/BC) scenario. In order to obtain the optimal transmitter structure, we develop a generalized duality between the vector broadcast and multiple-access channel (MAC) for scenarios in which partial signal coordination is available among users. This theory together with optimal spectrum balancing (OSB) is exploited to calculate the jointly optimal filters and transmit powers for non-linear vector dirty paper coding structures (in the form of Tomlinson-Harashima precoder (THP)) in the groups. The proposed scheme is compared to several other joint DSM 2/3 algorithms for DS DSL. Simulation results show that the proposed scheme (referred to as the IF/BC-OSB algorithm) achieves considerably higher bit rates than the other schemes. IF/BC-OSB encompasses the earlier developed BC-OSB algorithm as a special case. A simplified version of IF/BC-OSB avoiding exhaustive search with near-optimal performance is also proposed.

ZF-THP를 이용한 다중 안테나 다중 사용자 시스템에서 전송률 합 최적화를 위한 전력 할당 알고리즘

이 논문에서 우리는 Tomlinson-Harashima precoding (THP)를 이용한 다중 입력 단일 출력 다중 사용자 하향링크 시스템을 위한 전력할당 기법에 대해 알아본다. Zero-forcing THP 시스템의 sum rate를 최대화하기 위해 우리는 이전 방법과는 달리 mutual information 방법을 적용하였다. 나아가서, 모듈로 오퍼레이션을 사용하는 유저에 적절한 전력 레벨을 할당하기 위해 간단한 전력 할당 알고리즘을 제안한다. 실험 결과는 제안된 기법이 기존의 water-filling 기법보다 성능이 우수하고, 시스템의 최적의 성능을 내는 기법과 성능은 유사하면서 보다 작은 복잡도로 이루는 것을 보여준다. In this paper, we study a power allocation technique for Tomlinson-Harashima precoding (THP) in multi-user multiple input single output (MISO) downlink systems. In contrast to previous approaches, a mutual information based method is exploited for maximizing the sum rate of zero-forcing THP systems. Then, we propose a simple power allocation algorithm which assigns proper power level for modulo operated users. Simulation results show that the proposed scheme outperforms a conventional water-filling method, and it provides similar performance with near optimal method with much reduced complexity.

Robust Transceiver with Tomlinson-Harashima Precoding for Amplify-and-Forward MIMO Relaying Systems

In this paper, robust transceiver design with Tomlinson-Harashima precoding (THP) for multi-hop amplify-and-forward (AF) multiple-input multiple-output (MIMO) relaying systems is investigated. At source node, THP is adopted to mitigate the spatial intersymbol interference. However, due to its nonlinear nature, THP is very sensitive to channel estimation errors. In order to reduce the effects of channel estimation errors, a joint Bayesian robust design of THP at source, linear forwarding matrices at relays and linear equalizer at destination is proposed. With novel applications of elegant characteristics of multiplicative convexity and matrix-monotone functions, the optimal structure of the nonlinear transceiver is first derived. Based on the derived structure, the transceiver design problem reduces to a much simpler one with only scalar variables which can be efficiently solved. Finally, the performance advantage of the proposed robust design over non-robust design is demonstrated by simulation results.

Realizable Spatio-Temporal Tomlinson-Harashima Precoders: Theory and Fast Computation

We derive the optimal realizable Tomlinson-Harashima precoder for frequency-selective multiple-input multiple-output (MIMO) channels with respect to a simplified mean square error (MSE) criterion. Realizability means that, in contrast to other works, we do not restrict the internal filters of the precoder to have finite impulse responses (FIRs) but nevertheless ensure that the precoder can be operated in real-time subject to a finite latency time which can be chosen by the system designer. In particular, this allows us to consider channels with infinite impulse responses (IIRs) as they occur, e.g., in digital subscriber lines. The feedforward filter is located at the transmitter in our system model and an additional scalar gain is employed at the receiver. The relocation of the feedforward filter allows us to consider decentralized receivers. However, it also makes it necessary to impose a transmit power constraint. The power constraint often has the effect that the input signals at the receiver have to be rescaled. We argue that the inclusion of the additional scalar gain allows us to incorporate the effect of the rescaling operation into the optimization. Special emphasis is put on the fast computation of the realizable Tomlinson-Harashima precoder via displacement structure theory. We propose a fast algorithm which includes a successive construction of a close-to-optimal ordering of the data streams. The complexity of this algorithm is only cubic in the number of channel inputs and quadratic in the latency time. The algorithm can also be applied in situations where certain FIR constraints have to be fulfilled because we find that the optimal realizable Tomlinson-Harashima precoder involves only FIR filters as soon as the channel is FIR. Our results are reproducible.

Power Loss Analysis of Tomlinson-Harashima Precoder with Tilted Constellation in Flat Fading MIMO Channels

We analyze the power loss of Tomlinson-Harashima precoding with constellation tilting (THP-CT) method using M-QAM modulation in flat fading MIMO channels. To derive a new approximation of the power loss of THP-CT method, the effective channel components, the information symbols, the precoded symbols, and some of their combinations are analyzed stochastically. From the analysis of the signal components, the transmission power of the conventional THP is firstly approximated as the mean of the block average power for a fixed tilting angle. Then, the variance for a fixed angle and the dependence between the block average power terms with two tilting angles are approximated. Also, we modify the Clark's algorithm that approximates the expected minimum of dependent samples. By using the modified algorithm and also the mean, variance, and correlation factors, we provide a more accurate power loss approximation for THP-CT. Simulation results show that the proposed algorithm exploiting the analyzed dependence expression can reduce the approximation error up to about 60% and 70% for the case of 4-QAM and 16-QAM case, respectively.

Novel User Scheduling Schemes Based on Nonlinear Precoding for Multiuser MIMO Systems

This paper proposes a novel greedy user ordering algorithm for the multiuser multiple-input multiple-output (MIMO) systems employing block diagonal geometric mean decomposition method and Tomlinson-Harashima precoding (THP). Theoretical analysis and computer simulations illustrate its low computation complexity relative to the optimal user ordering achieving by brute search over all the possible ordering permutations resulting in extremely high computation complexity. Meanwhile the bit error rate (BER) performance of the proposed algorithm is very close to the optimal user ordering. Moreover, in order to mitigate the impact of users with smaller sub-channel gains to the whole systems BER performance, a joint pre-processing scheme design of adaptive data streams reduction and greedy user ordering (ADSR-GUO) is proposed. By means of choosing different values for the controlling factor, we can obtain different system sum-rate and BER performance to satisfy different quality-of-service (QoS) requirements.

Performance of multi-user transmitter preprocessing assisted MIMO system over correlated frequency-selective channels

In this contribution we present the performance of a multi-user transmitter preprocessing (MUTP) assisted multiple-input multiple-output (MIMO) space division multiple access (SDMA) system, aided by double space time transmit diversity (DSTTD) and space time block code (STBC) processing for downlink (DL) and uplink (UL) transmissions respectively. The MUTP is invoked by singular value decomposition (SVD) which exploits the channel state information (CSI) of all the users at the base station (BS) and only an individual user’s CSI at the mobile station (MS). Specifically, in this contribution, we investigate the performance of multi-user MIMO cellular systems in frequency-selective channels from a transmitter signal processing perspective, where multiple access interference (MAI) is the dominant channel impairment. In particular, the effects of three types of delay spread distributions on MUTP assisted MIMO SDMA systems pertaining to the Long Term Evolution (LTE) channel model are analyzed. The simulation results demonstrate that MUTP can perfectly eliminate MAI in addition to obviating the need for complex multi-user detectors (MUDs) both at the BS and MS. Further, SVD-based MUTP results in better achievable symbol error rate (SER) compared to popularly known precoding schemes such as block diagonalization (BD), dirty paper coding (DPC), Tomlinson–Harashima precoding (THP) and geometric mean decomposition (GMD). Furthermore, when turbo coding is invoked, coded SVD aided MUTP results in better achievable SER than an uncoded system.

A limited feedback scheme based on spatially correlated channels for coordinated multipoint systems

High spectral efficiency can be achieved in the downlink of multi-antenna coordinated multi-point systems provided that the multiuser interference is appropriately managed at the transmitter side. For this sake, downlink channel information needs to be sent back by the users, thus reducing the rate available at the uplink channel. The amount and type of feedback information required has been extensively studied and many limited feedback schemes have been proposed lately. A common pattern to all of them is that achieving low rates of feedback information is possible at the cost of increasing complexity at the user side and, sometimes, assuming that some statistics of the channel are known. In this article, we propose a simple and versatile limited feedback scheme that exploits the spatial correlation at each multi-antenna base station (BS) without requiring any previous statistical information of the channel and without adding significant computational complexity. It is based on the separate quantization of the channel impulse response modulus and phase and it shows better mean square error performance than the standard scheme based on quantization of real and imaginary parts. In order to evaluate the performance of the downlink regarding multiuser interference management, different precoding techniques at the BSs, such as zero-forcing (ZF), Tomlinson-Harashima precoding (THP) and lattice reduction Tomlinson- Harashima precoding (LRTHP), have been evaluated. Simulations results show that LRTHP and THP present a higher robustness than ZF precoding against channel quantization errors but at the cost of a higher complexity at the BS. Regarding sum-capacity and bit error rate performances, our versatile scheme achieves better results than the standard one in the medium and high SNR regime, that is, in the region where quantization errors are dominant against noise, for the same feedback cost measured in bits per user.

Interference Optimization for Transmit Power Reduction in Tomlinson-Harashima Precoded MIMO Downlinks

A novel strategy for reducing the power loss in Tomlinson-Harashima precoding (THP) is explored in this paper, based on optimizing the interference to be canceled. A multiple input multiple output (MIMO) downlink transmission is considered and the proposed strategy is motivated by the fact that both the desired and interfering signals originate from the base station (BS) of the downlink system itself. The resulting interference can therefore be influenced to reduce the transmission power required to cancel it, without altering the information content of the downlink message. This optimization aims at bringing the interference closer to the replicas of the desired symbols for all users in the THP modulo-extended constellation. By doing so, the quantized distance between the useful signal and interference is reduced and therefore the power required to presubtract interference is decreased. Based on this concept, a new practical THP transmitter for multiple input multiple output systems (MIMO-THP) is designed. The effect of the interference optimization is studied by means of mathematical analysis and simulation and towards this end, the Gaussian-Modulo distribution is derived and used to describe the distribution of the modulo-precoded transmitted symbols. This is proven to provide a closer approximation of the power loss for both conventional and proposed MIMO-THP techniques, compared to the approximation based on the uniform distribution used in the literature. Theoretical and simulation results both confirm that, by optimizing the interference to be canceled, the proposed technique offers a considerable transmit power reduction compared to conventional THP while securing a slightly improved error rate performance.

Robust Tomlinson-Harashima Source and Linear Relay Precoders Design in Amplify-and-Forward MIMO Relay Systems

Existing transceiver designs in amplify-and-forward (AF) multiple-input-multiple-output (MIMO) relay systems often assume the availability of perfect channel state informations (CSIs). Robust designs for imperfect CSI have less been considered. In this paper, we propose a robust nonlinear transceiver design for the system with a Tomlinson-Harashima precoder (THP), a linear relay precoder, and a minimum-mean-squared-error (MMSE) receiver. Since two precoders and imperfect CSIs are involved, the robust transceiver design is difficult. To overcome the difficulty, we first propose cascading an additional unitary precoder after the THP. The unitary precoder can not only simplify the optimization but also improve the performance of the MMSE receiver. We then adopt the primal decomposition dividing the original optimization problem into a subproblem and a master problem. With our formulation, the subproblem can be solved and the two-precoder problem can be transferred to a single relay precoder problem. The master problem, however, is not solvable. We then propose a lower bound for the objective function and transfer the master problem into a convex optimization problem. A closed-form solution can then be obtained by the Karush-Kuhn-Tucker (KKT) conditions. Simulations show that the proposed transceiver can significantly outperform existing linear transceivers with perfect or imperfect CSIs.

Vector Precoding for Gaussian MIMO Broadcast Channels: Impact of Replica Symmetry Breaking

The “replica method” of statistical physics is employed for the large-system analysis of vector precoding for the Gaussian multiple-input multiple-output broadcast channel. The transmitter comprises a linear front-end combined with nonlinear precoding, minimizing transmit energy by means of input alphabet relaxation. For the common discrete lattice-based relaxation, the problem violates replica symmetry and a replica symmetry breaking (RSB) ansatz is taken. The limiting empirical distribution of the precoder's output and the limiting transmit energy are derived for one-step RSB. Particularizing to a “zero-forcing” (ZF) linear front-end, a decoupling result is derived. For discrete lattice-based relaxations, the impact of RSB is demonstrated for the transmit energy. The spectral efficiencies of the aforementioned precoding methods are compared to linear ZF and Tomlinson-Harashima precoding (THP). Focusing on quaternary phase shift-keying (QPSK), significant performance gains of both lattice and convex relaxations are revealed for medium to high signal-to-noise ratios (SNRs) when compared to linear ZF precoding. THP is shown to be outperformed as well. Comparing certain lattice-based relaxations for QPSK against a convex counterpart, the latter is found to be superior for low and high SNRs but slightly inferior for medium SNRs in terms of spectral efficiency.

Tight Lower Bounds on Achievable Information Rates for Regularized Tomlinson-Harashima Precoding in Multi-User MIMO Systems

Tomlinson-Harashima precoding (THP) is considered to be a prominent precoding scheme due to its ability to efficiently cancel out the known interference at the transmitter side. Therefore, the information rates achieved by THP are superior to those achieved by conventional linear precoding schemes. In this paper, new lower bounds on the achievable information rates for the regularized THP scheme are derived. Analytical results show that the lower bounds derived in this paper are tighter than the original lower bounds particularly for the low SNR range, while all lower bounds converge to $\\log _{2}(t)-\\log _{2}\\sqrt{2\\pi e}\\sigma$ as SNR → ∞.

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.

A Novel Nonlinear Precoding Detection Algorithm for VBLAST in MIMO-MC-CDMA Downlink System

Considering the error propagation effect and high complexity of the Vertical Bell Labs Layered Space Time (V-BLAST), a novel nonlinear ZF-THP algorithm for VBLAST in MIMO-MC-CDMA downlink system is proposed in this paper. QR decomposition is used for precoding matrix, the nonlinear Tomlinson-Harashima Precoding (THP) is used between the sub-carrier channels of MC-CDMA to eliminate interference from other signals at the transmitter, and can obtain frequency diversity gain and eliminate effectively the error propagation effect. At the receiver, zero forcing criterion is used, and the complexity of the receiver can be reduced. Simulation results show that the proposed algorithm is better than the traditional zero forcing algorithm and the linear precoding algorithm in the system BER.

A novel spatial Tomlinson-Harashima precoding scheme in multi-user MIMO broadcast channels

Spatial Tomlinson-Harashima Precoding (STHP) is a promising transmission technique that can mitigate Inter-User Interferences (IUI) in a multi-user Multiple Input Multiple Output broadcast channel. However, traditional STHPs cannot guarantee user fairness that is supposed to be a desirable feature for future wireless communication systems. This paper proposes an improved STHP transceiver structure. It is based on zero-forcing criterion and has the perfect user fairness. In addition to this, we also derive an elegant ordering method that can significantly improve the system performance.

A Novel Distributed Precoding Scheme Based on THP for Downlink Multi-Cell Multi-User OFDMA Wireless Systems

In this paper, a distributed precoding scheme based on Tomlinson-Harashima Precoding (THP) is proposed for downlink multi-cell multi-user Orthogonal Frequency-Division Multiple Access (OFDMA) wireless systems. In the proposed scheme, relying on the local channel state information (CSI), each base station (BS) designs one forward precoder and one feedback filter per user group for the transmission from itself to corresponding user group. Here, each forward precoder is adopted to mitigate the inter-cell interference (ICI), and each feedback filter is employed to perform the presubtraction of inter-user interference (IUI) within the corresponding user group. Then, based on information exchange among the BSs, each BS is able to do distributed Coordinated Multi-Point transmission (CoMP) to simultaneously serve both the intra-cell (IC) user group and the other-cell (OC) user group. Therefore, the proposed scheme can eliminate the overhead for the CSI exchange, efficiently exploit the available spatial degrees of freedom (DOF) and support multiple users per cell. The simulation results also demonstrate good performance of the proposed scheme.

Per-layer transmit and receive filters design for Tomlinson-Harashima precoding in multiuser MIMO systems

In this paper, the per-layer design for Tomlinson-Harashima precoding (THP) in the downlink of multiuser multiple-input multiple-output (MIMO) systems is investigated. In these systems, the number of the receivers is equal to that of the transmit antennas. Based on the criterion of maximum system sum-capacity, we study two per-layer joint transmit and receive filters design schemes with receive antenna beamforming (RAB) and receive antenna selection (RAS), respectively. Moreover, the differences of the equivalent channel gains and capacities between these two schemes are analyzed theoretically. Simulation results show that by these per-layer schemes, the system sum-rate is improved significantly with respect to the per-user processing scheme.

A New Resource Allocation Technique in MU-MIMO Relay Networks

In this paper, we investigate a novel relaying technique employing scheduling, precoding, beamforming, and power allocation for a multiuser multiple-input-multiple-output (MU-MIMO) relay network. In the proposed scheme, the interference is canceled by using a combination of transmit-receive weights and Tomlinson-Harashima precoding (THP). To achieve data rate fairness among different users and further improve the performance of MU-MIMO relay networks, we propose a low-complexity power allocation (LC-PA) to allocate power to each user. In addition, an algorithm to select a subset of users that has maximum sum rate performance is proposed. The performance of the proposed scheme is investigated by examining the sum rate of the system for different user selection algorithms and different power allocation schemes.