Tomlinson-Harashima Precoding Research Articles

Joint transceiver vector precoding based on GMD method for MIMO systems

We heuristically propose a joint transceiver vector precoding (VP) based on geometric mean decomposition (GMD) method for multiple input multiple output (MIMO) systems. In fact, it is the generalization and improvement of the GMD transceiver with Tomlinson-Harashima precoding (THP). We first propose the GMD-VP design with zero forcing (ZF) criterion, then exploit the extended channel matrix to obtain the improved regularized scheme. Simulation results show that the proposed schemes obtain performance improvement and complexity reduction.

Generalized Design of Multi-User MIMO Precoding Matrices

In this paper we introduce a novel linear precoding technique. The approach used for the design of the precoding matrix is general and the resulting algorithm can address several optimization criteria with an arbitrary number of antennas at the user terminals. We have achieved this by designing the precoding matrices in two steps. In the first step we minimize the overlap of the row spaces spanned by the effective channel matrices of different users using a new cost function. In the next step, we optimize the system performance with respect to specific optimization criteria assuming a set of parallel single- user MIMO channels. By combining the closed form solution with Tomlinson-Harashima precoding we reach the maximum sum-rate capacity when the total number of antennas at the user terminals is less or equal to the number of antennas at the base station. By iterating the closed form solution with appropriate power loading we are able to extract the full diversity in the system and reach the maximum sum-rate capacity in case of high multi-user interference. Joint processing over a group of multi-user MIMO channels in different frequency and time slots yields maximum diversity regardless of the level of multi-user interference.

Lattice reduction aided MMSE Tomlinson-Harashima precoding based on VBLAST algorithm for MIMO systems

A lattice reduction aided (LRA) minimum mean square error (MMSE) Tomlinson-Harashima precoding (THP) was proposed based on vertical Bell Labs layered space time (VBLAST) algorithm for multiple input multiple output (MIMO) systems. The extended channel was used to provide optimal tradeoff between residual interference and noise amplification. The processing based on lattice reduction method helps achieve maximal diversity order. The VBLAST algorithm was applied to get the optimal processing ordering for successive interference cancellation (SIC) at transmitter. Simulation results show that the proposed algorithm outperforms conventional THP and the LRA zero-forcing (ZF) THP with full diversity order.

Tomlinson-Harashima Precoding for the Downlink of Multiuser MIMO Systems

In this letter, a Tomlinson-Harashima precoding (THP) scheme is proposed for the downlink of multiuser MIMO systems with multiple antennas at each receiver. Assuming single data stream communication for each user, joint transmitter and receiver design is done to maximize the signal to noise ratio (SNR) for each user. Furthermore, a heuristic user ordering algorithm is proposed to optimize the encoding order and improve the bit error rate (BER) performance. Simulation results have shown that the proposed approach is superior to some existing precoding schemes.

MIMO Relaying With Linear Processing for Multiuser Transmission in Fixed Relay Networks

In this paper, a novel relaying strategy that uses multiple-input multiple-output (MIMO) fixed relays with linear processing to support multiuser transmission in cellular networks is proposed. The fixed relay processes the received signal with linear operations and forwards the processed signal to multiple users creating a multiuser MIMO relay. This paper proposes upper and lower bounds on the achievable sum rate for this architecture assuming zero-forcing dirty paper coding at the base station, neglecting the direct links from the base station to the users, and with certain structure in the relay. These bounds are used to motivate an implementable multiuser precoding strategy that combines Tomlinson-Harashima precoding at the base station and linear signal processing at the relay, adaptive stream selection, and QAM modulation. Reduced complexity algorithms based on the sum rate lower bounds are used to select a subset of users. We compare the sum rates achieved by the proposed system architecture and algorithms with the sum rate upper bound and the sum rate achieved by the decode-and-forward relaying.

Tomlinson–Harashima precoding with imperfect channel state information

Nonlinear Tomlinson–Harashima precoding (THP) is an attractive solution for a scenario where the transmission system employs multiple antennas at transmitter and multiple users with a single antenna at the receiver, so that the cooperation among the receive antennas are impossible (downlink scenario). THP solution based on zero forcing (ZF) and minimum mean square error (MMSE) criteria is one of the important techniques to achieve near multiple input multiple output channels capacity with reasonable complexity. In this paper, the effect of channel imperfection on THP is considered. At first, the achievable rate of THP with respect to ZF criterion in an imperfect channel state information (CSI) scenario is calculated. Moreover, based on MMSE criterion, a new robust solution is derived which provides a significant improvement with respect to the conventional optimisation method. Then, the effect of channel estimation error on THP is considered as an improved optimisation where THP filters are optimised together with a channel estimator. Spatial power loading is found to be important to the THP performance. This loading for robust/joint optimisation of MMSE THP is developed by minimum average symbol error rate sense. Simulation results show the capacity loss, the performance advantage attained by the robust/joint optimisation and the power loading in an imperfect CSI scenario.

A framework for designing mimo systems with decision feedback equalization or tomlinson-harashima precoding

We consider joint transceiver design for point-to-point Multiple-Input Multiple-Output communication systems that implement interference (pre-)subtraction; i.e., Decision Feedback Equalization (DFE) or Tomlinson-Harashima precoding (THP). We develop a unified framework for joint transceiver design of these two dual systems by considering design criteria that are expressed as functions of the (logarithm of the) Mean Square Error (MSE) of the individual data streams. By deriving two inequalities that involve the logarithms of the individual MSEs, we obtain optimal designs for two broad classes of communication objectives, namely those that are Schur-convex and Schur-concave functions of these logarithms. These two classes embrace several design criteria for which the optimal transceiver design has remained an open problem. For Schur-convex objectives, the optimal design results in data streams with equal MSEs. In addition to other desirable properties, this design simultaneously minimizes the total MSE and the average bit error rate, and maximizes the Gaussian mutual information; a property that is not achieved by a linear transceiver. Moreover, we show that the optimal design yields objective values that are superior to the corresponding optimal objective value for a linear transceiver. For Schur-concave objectives, the optimal DFE design results in linear equalization and the optimal THP design results in linear precoding. The proposed design framework can be regarded as a counterpart of the existing framework for linear transceiver design.

Asynchronous Two-Way Ranging Using Tomlinson-Harashima Precoding and UWB Signaling

This paper demonstrates two methods which simultaneously undertake synchronization and ranging based on a time-of-arrival approach with bidirectional communication to bypass the need for accurate synchronous clocking. In order to alleviate multipath effects, Tomlinson-Harashima precoding and UWB signaling are used to measure the distance between pairs of sensors. The proposed schemes are shown to be effective under certain assumptions and the analysis is supported by simulation and numerical studies.

Joint Tomlinson-Harashima Precoding and Frequency-Domain Equalization for Broadband Single-Carrier Transmission

The performance of single-carrier (SC) transmission in a frequency-selective fading channel degrades due to a severe inter-symbol interference (ISI). Using frequency-domain equalization (FDE) based on the minimum mean square error (MMSE) criterion can improve the bit error rate (BER) performance of SC transmission. However, the residual ISI after FDE limits the performance improvement. In this paper, we propose a joint use of Tomlinson-Harashima precoding (THP) and FDE to remove the residual ISI. An approximate conditional BER analysis is presented for the given channel condition. The achievable average BER performance is evaluated by Monte-Carlo numerical computation method using the derived conditional BER. The BER analysis is confirmed by computer simulation of the signal transmission.

A Novel Baud-Rate Timing Error Detector Design for Baseband Transmission System Using Tomlinson-Harashima Precoder

Extraction of correct timing error information is very important for high-speed digital transmission systems. In this letter, a novel effective-data-sequence-based timing error detector (EDS-TED) is presented for a baseband transmission system using nonlinear Tomlinson-Harashima precoding (THP), such as 10GBASE-T. The key idea of our TED is to minimize the mean square error between the received and desired EDS, rather than between the transmitted data signals. This formulation can exploit the autocorrelation between the EDS signals and extract the timing information embedded in the received signal. Moreover, the proposed architecture can lead to a simple and feasible circuit implementation. Simulation results show that a timing loop based on the proposed EDS-TED achieves a superior performance over traditional TED in terms of the peak-to-peak jitter and the TED gain.

Frequency domain pre-equalization with transmit precoding for MIMO broadcast wireless channels

Recent research has shown that frequency domain pre-equalization (FDPE) can provide broadcast transmissions over multi-input multi-output (MIMO) frequency selective channels, where the multiple receivers need limited processing. In this paper, we consider the combination of FDPE with parallel and successive Tomlinson-Harashima Precoding (THP) and propose two novel FDPE MIMO schemes, which are referred to as FDPE-P-THP and FDPE-S-THP, respectively, based on the minimum mean square error (MMSE) criterion. The ordering algorithm in the FDPE-S-THP scheme is considered and it is shown that the system with even a randomly selected order can perform almost as well as that with the optimal one. This paper further develops an accurate theoretical performance analysis methodology for the proposed FDPE-THP schemes. Numerical results along with analytical results demonstrate the significant performance improvement of our proposed schemes compared to the conventional FDPE MIMO schemes. The channel estimation errors and channel variation effects on the proposed system are also investigated. It is shown that the performance degradation due to channel variation can be efficiently reduced by applying channel prediction.

Frequency domain equalization with tomlinson-harashima precoding for single carrier broadband MIMO systems

In this paper, we combine the transmit Tomlinson-Harashima precoding (THP) technique with single carrier frequency domain equalization (SC-FDE) and propose two new FDE multi-input multi-output (MIMO) schemes, which we refer to as parallel THP-FDE and successive THP-FDE, based on the minimum mean square error (MMSE) criterion. For the successive THP-FDE scheme, where all transmit streams are subsequently preceded, we propose an optimal MMSE ordering algorithm. Since the feedback processing is performed at the transmitter, no error propagation problem exists in the proposed THP-FDE MEMO schemes. Numerical results will demonstrate the significant performance improvement of our proposed schemes compared to the conventional FDE MIMO schemes. We will also analyze the error probability, and investigate the channel estimation errors and channel variation effects on the proposed THP-FDE MIMO systems. It will be shown that by applying channel prediction and THP compensation techniques such detrimental effects can be greatly reduced.

A Unified Framework for Tomlinson--Harashima Precoding in MC-CDMA and OFDMA Downlink Transmissions

We consider a unified framework comprising both multicarrier code-division multiple-access (MC-CDMA) and orthogonal frequency-division multiple-access (OFDMA), and discuss nonlinear prefiltering for downlink transmissions based on Tomlinson-Harashima precoding. The base station (BS) is equipped with multiple transmitting antennas and channel state information is assumed to be available at the transmit side. We design the prefiltering matrices so as to minimize the sum of the mean square errors at all mobile terminals when a conventional single-user data detector is employed at the receiver side. In this way, most of the computational burden is moved to the BS, where power consumption and computational resources are not critical requirements. Computer simulations are used to assess the performance of the proposed scheme under different operating scenarios. It turns out that OFDMA outperforms MC-CDMA when the system resources (subcarriers and/or spreading codes) are optimally assigned to the active users according to the channel quality.

Tomlinson-Harashima Precoding for Broadcast Channels with Uncertainty

We consider the design of Tomlinson-Harashima (TH) precoders for broadcast channels in the presence of channel uncertainty. For systems in which uplink-downlink reciprocity is used to obtain a channel estimate at the transmitter, we present a robust design based on a statistical model for the channel uncertainty. We provide a convex formulation of the design problem subject to two types of power constraints: a set of constraints on the power transmitted from each antenna and a total power constraint. For the case of the total power constraint, we present a closed-form solution for the robust TH precoder that incurs essentially the same computational cost as the corresponding designs that assume perfect channel knowledge. For systems in which the receivers feed back quantized channel state information to the transmitter, we present a robust design based on a bounded model for the channel uncertainty. We provide a convex formulation for the TH precoder that maximizes the performance under the worst-case channel uncertainty subject to both types of power constraints. We also present a conservative robust design for this type of channel uncertainty that has reduced computational complexity for the case of power constraints on individual antennas and leads to a closed-form solution for the total power constraint case. Simulation studies verify our analytical results and show that the robust TH precoders can significantly reduce the rather high sensitivity of broadcast transmissions to errors in channel state information.

High-Speed Architecture Design of Tomlinson–Harashima Precoders

Like decision feedback equalizers (DFEs), Tomlinson-Harashima precoders (TH precoders) contain nonlinear feedback loops, which limit their use for high-speed applications. Unlike in DFEs where the output levels of the nonlinear devices are finite, in TH precoders, theoretically, the output levels of the modulo devices are infinite. Thus, it is difficult to apply look-ahead and pre-computation techniques to pipeline TH precoders, which were successfully applied to pipeline infinite-impulse response (IIR) filters and DFEs in the past. In this paper, three approaches are proposed to design high-speed TH precoders. In the first approach, the traditional block processing technique for DFEs is generalized to the design of high-speed TH precoders. In the second approach, based on the equivalent form of a TH precoder where the precoder can be viewed as an IIR filter with an input equal to the sum of the original input to the TH precoder and a finite-level compensation signal, two high-speed pipelined designs are developed. In the third approach, parallel processing techniques for fast IIR filters are generalized to the design of parallel TH precoders.

Receive Antenna Selection for Multiuser MIMO Systems with Tomlinson-Harashima Precoding

SUMMARY In this letter, we discuss the problem of receive antenna selection in the downlink of multiuser multiple-input multiple-output (MIMO) systems with Tomlinson-Harashima precoding (THP), where the number of receivers is assumed equal to that of transmit antennas. Based on the criterion of maximum system sum-capacity, a per-layer receive antenna selection scheme is proposed. This scheme, which selects one receive antenna for each receiver, can well exploit the nonlinear and successive characteristics of THP. Two models are established for the proposed per-layer scheme and the conventional per-user scheme. Both the theoretical analysis and simulation results indicate that the proposed scheme can greatly

Lattice-Reduction-Aided MMSE Tomlinson-Harashima Precoding for MIMO Systems

In this letter, a lattice-reduction-aided (LRA) minimum mean square error (MMSE) Tomlinson-Harashima precoding (THP) is proposed for multiple input multiple output (MIMO) systems. The extended channel is exploited to develop the LRA MMSE-THP based on the lattice reduction method. Simulation results show that the proposed scheme significantly outperforms the conventional MMSE THP and the LRA zero-forcing (ZF) THP and achieves full diversity order.

Performance Analysis of a Pre-BLAST-DFE Technique for MISO Channels With Decentralized Receivers

The performance of a pre-Bell Laboratories Layered Space-Time Architecture (BLAST)-decision feedback equalization (DFE) technique with Tomlinson-Harashima precoding and decentralized receivers, operating over multiple-input single-output (MISO) frequency-selective fading channels, is evaluated. First, we derive the probability of symbol error for Tomlinson-Harashima precoding operating over single-input single-output channels with intersymbol interference. We then generalize this result to MISO frequency-selective fading channels with decentralized receivers by using the QR decomposition technique. The effect of optimal ordering of the decentralized receivers, which minimizes the total transmit energy, is investigated. We obtain a closed-form expression for the probability density function of the squared diagonal elements of the upper right triangular matrix belonging to the optimal QR decomposition when two transmit antennas and two receivers are used. We also provide simulations to corroborate the analytical results.

Robust Design of Spatial Tomlinson-Harashima Precoding in the Presence of Errors in the CSI

In this letter, we study spatial Tomlinson-Harashima precoding (STHP) from an information theoretic point of view encompassing both the single and the multiuser scenarios. Since the performance of any communications preceding scheme relies on the quality of the channel state information (CSI) that is made available at the transmitter side, in this work we focus our attention on the analysis of the robustness of STHP in terms of rate loss when the CSI is imperfect. Precisely, we present a robust design of the set of moduli used in STHP and, consequently, of the corresponding power allocation, that maximizes the achievable rates for the worst-case errors in the CSI in the small errors regime.

Finite-Length MMSE Tomlinson–Harashima Precoding for Frequency Selective Vector Channels

We design Tomlinson-Harashima precoding for decentralized receivers and frequency-selective channels based on the minimum mean square error criterion, where the feedforward filter is restricted to have finite length. Contrary to most other publications on Tomlinson-Harashima precoding which rely on solutions for decision feedback equalization to find the corresponding precoding filters in a heuristic manner, we deduce the optimization for Tomlinson-Harashima precoding from the optimization for the linear minimum mean square error transmit filter. Thereby, we include the precoding order explicitly in the problem formulation and thus obtain the precoding filter solutions, together with the algorithms to compute the latency time, i.e., the time difference between application of the precoder at the transmitter and detection at the receiver and the precoding order from a single optimization. Since the algorithm for THP filter computation resulting from the optimization has a high computational complexity, we present an alternative algorithm to compute the Tomlinson-Harashima precoding filters based on a Cholesky factorization with symmetric permutation, resulting in an order of complexity that is the same as for the computation of the linear transmit filters. The simulations reveal that the latency time optimization can be omitted without performance degradation for most practical channel models, i.e., the latency time can be chosen to be the order of the feedforward filter