Tomlinson-Harashima Precoding Research Articles

Non‐linear transceiver design for secure communications with artificial noise‐assisted MIMO relay

This study investigates the problem of physical layer security for amplify-and-forward (AF) multiple-input multiple-output (MIMO) relay systems operating in the presence of a passive eavesdropper. Specifically, the authors consider the robust design of an artificial noise (AN)-assisted non-linear transceiver employing Tomlinson–Harashima precoding (THP), with imperfect knowledge of the legitimate channel states. The design problem can be reformulated as a two-level optimisation, where the outer problem aims to optimise the source precoder as a function of the relay precoder, while the inner problem at the relay aims to jointly optimise the relay precoder as well as the power allocation between the AN and the information-bearing signals. To solve the inner problem, the authors adopt a bisection method which attempts to maximise the AN power level, to confuse the eavesdropper, while satisfying the mean-squared-error requirement for the intended user. Some relaxation for the objective function is applied to transform the problem into a standard convex optimisation one. Regarding the outer problem, closed-form solutions for the precoders can be derived by an iterative method based on the Karush–Kuhn–Tucker conditions. Simulation results illustrate the superior secrecy performance provided by the proposed non-linear transceiver design with AN and THP.

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.

Downlink MU-MIMO With THP Combined With Pre- and Post-processing and Selection of the Processing Vectors for Maximization of Per-Stream SNR

In this paper, we consider a downlink multiuser multiple-input–multiple-output (MU-MIMO) system with multiple antennas at the transmitter and multiple antennas at each user, where the transmitter can send one or more data streams to each user. We propose a non-iterative method by combining Tomlinson–Harashima precoding (THP) with pre- and post-processing and selecting processing vectors based on the maximization of instantaneous signal-to-noise ratio (SNR) of the data stream at the input of the detector of each user. The postprocessing vectors for all users are found to be eigenvectors corresponding to the maximum eigenvalue of a certain matrix involving the channel matrix of the user. The transmitter computes the vectors of the linear processing matrix through an orthonormalization procedure in a single step. The feedback matrix at the transmitter is then obtained from the effective channel matrix and the linear processing matrix. We express the instantaneous SNR of all data streams in terms of eigenvalues of a Wishart matrix, obtained from the channel matrix of the user, and find the diversity order for each data stream. Considering multiple scenarios, we find the outage probability of the instantaneous SNR for all data streams and the cumulative distribution function (cdf) of the sum-rate capacity for all users using the proposed method and compare the results with those of recently proposed methods that provide a closed-form solution and with that of block diagonalization, channel inversion, and THP in scenarios where they are applicable.

Nonlinear Equalization Approaches for Physical Layer Network Coding

We consider a two-way relaying system employing physical layer network coding in channels suffering from frequency-selective fading. We study decision-feedback equalization (DFE), a technique based on delayed decision-feedback sequence estimation (DDFSE), and Tomlinson-Harashima precoding (THP) approaches for mitigating the distortions introduced by the channel. For DFE, we introduce transmit filtering schemes that generate identical overall source-to-relay channel impulse responses for both source nodes, while achieving the maximum signal-to-noise ratio after equalization for the zero-forcing and the minimum mean-squared error criterion, respectively. The advocated DDFSE approach also relies on transmit filtering at the source nodes. For the THP scheme, we derive the optimal precoding filters that guarantee an intersymbol interference free source-to-relay transmission. In order to obtain a two-way relaying system, which uses the same equalization techniques in both transmission directions, we design a THP-based compromise precoding scheme for the relay-to-destination transmission. The performance of the proposed techniques is compared with that of benchmark schemes with simpler filtering/precoding, where identical overall source-to-relay channel impulse responses are enforced by straightforward but suboptimum choices for the transmit filters. Our results reveal that the developed schemes enable significant gains compared with the benchmark schemes.

Pre-equalized Faster-than-Nyquist Transmission

Faster-than-Nyquist (FTN) transmission applies non-orthogonal linear modulation to increase spectral efficiency compared with the well-known orthogonal transmission at Nyquist rate. This comes at a price of inter-symbol interference (ISI), which usually is equalized through receiver processing. In this paper, we investigate the alternative approach of pre-equalization at the transmitter. First, we consider Tomlinson–Harashima precoding (THP) for FTN and propose two novel soft demapping algorithms to generate the soft-input for the error-correction decoder. The developed demappers effectively compensate the modulo-loss associated with conventional THP transmission. Second, we propose a linear pre-filtering strategy to pre-equalize the ISI induced by FTN. We show that the linear pre-equalization approach is equivalent to an orthogonal transmission with a modified pulse shape. It thus yields the optimal error-rate performance while affording higher spectral efficiency. We validate our proposed precoding algorithms through computer simulations of a coded coherent optical communication system as a practical application example for FTN.

Double-Rate Tomlinson-Harashima Precoding for Multi-Valued Data Transmission

Double-Rate Tomlinson-Harashima Precoding for Multi-Valued Data Transmission

Feedback delay reduction of Tomlinson–Harashima precoder in 14 nm CMOS via pipelined MAC units operated entirely with CSA arithmetic

The data rate of a Tomlinson–Harashima (TH) precoder is limited by the delay in the feedback path of its infinite impulse response (IIR) filter that cancels the channel's post-cursor intersymbol interference (ISI). One reason for long loop delays is the requirement to perform the ISI subtraction from the data signal in binary arithmetic in order to properly execute the modulo (MOD) operation, which stabilises the IIR filter and limits the transmitter amplitude. The restriction to binary arithmetic is unfortunate, because some filter subcomponents such as, e.g. adder trees are often implemented in a faster data format that has no slow carry propagation [e.g. the carry-save adder (CSA) format]. This paper proposes a novel architecture for TH precoders in which the MOD operation is taken out of the loop, so that the remaining IIR filtering is performed entirely in CSA arithmetic to reduce the feedback delay as no conversion to binary format is required within the loop. With the pipelining technique applied, the filter's feedback delay reduces to the propagation delay of a multiply-accumulate unit operated with CSA arithmetic. The proposed concept was verified in a 14 nm CMOS test chip with multi-level signalling (NRZ, 4-/8-/16-PAM).

Successive optimization Tomlinson-Harashima precoding strategies for physical-layer security in wireless networks

In this paper, we propose novel non-linear precoders for the downlink of a multi-user MIMO system in the existence of multiple eavesdroppers. The proposed non-linear precoders are designed to improve the physical-layer secrecy rate. Specifically, we combine the non-linear successive optimization Tomlinson-Harashima precoding (SO-THP) with the generalized matrix inversion (GMI) technique to maximize the physical-layer secrecy rate. For the purpose of comparison, we examine different traditional precoders with the proposed algorithm in terms of secrecy rate as well as bit error rate (BER) performance. We also investigate simplified generalized matrix inversion (S-GMI) and lattice-reduction (LR) techniques in order to efficiently compute the parameters of the precoders. We further conduct computational complexity and secrecy-rate analysis of the proposed and existing algorithms. In addition, in the scenario without knowledge of the channel state information (CSI) to the eavesdroppers, a strategy of injecting artificial noise (AN) prior to the transmission is employed to enhance the physical-layer secrecy rate. Simulation results show that the proposed non-linear precoders outperform existing precoders in terms of BER and secrecy-rate performance.

Robust Faster-Than-Nyquist PDM-mQAM Systems With Tomlinson–Harashima Precoding

A training-based channel estimation algorithm is proposed for the faster-than-Nyquist PDM-mQAM (m = 4, 16, 64) systems with Tomlinson-Harashima precoding (THP). This is robust to the convergence failure phenomenon suffered by the existing algorithm, yet remaining format-transparent. Simulation results show that the proposed algorithm requires a reduced optical signal-to-noise ratio (OSNR) to achieve a certain bit error rate (BER) in the presence of first-order polarization mode dispersion and phase noise introduced by the laser linewidth.

MIMO Precoder Design With a Compensated QR-Decomposition Combination for CoMP Downlink Scenarios

This paper presents a multiple-input–multiple-output (MIMO) precoder with a compensated QR decomposition (CQRD) combination for coordinated multipoint (CoMP) downlink transmission. Unlike conventional QR decomposition (QRD) combination, CQRD combination adopts compensated channel matrix orderings. This paper first proposes CQRD combination for CoMP scenarios. The statistics for combined spatial subchannel gains with a CQRD combination of two coordinated base stations (BSs) are derived, and these statistics show that more balanced subchannel gains are generated with a CQRD combination than with a QRD combination. Furthermore, this paper proposes a generalized CQRD combination scheme with a joint sorting strategy that can be applied to scenarios with more than two coordinated BSs. Unlike the unsorted strategy, the joint sorting strategy determines an enhanced compensated combination to further increase spatial subchannel gains; therefore, the performance can be upgraded. Because conventional Tomlinson–Harashima precoding (THP) cannot be used in the CQRD combination, interference presubtraction and vector precoding (VP) is adopted. Theoretical analysis and simulation results are both provided to demonstrate the advantages of balanced spatial subchannel gains and enhanced bit-error-rate (BER) performance in the proposed CQRD-based schemes. Compared with existing QRD-based MIMO precoders in CoMP scenarios, the proposed CQRD-based schemes have substantial signal-to-noise ratio (SNR) improvements of 2–5 dB.

Performance and efficiency analysis of THP algorithms: A practical perspective

As an attractive interference cancellation (IC) technique, Tomlinson–Harashima precoding (THP) has been investigated thoroughly in theory. Several high performance THP variants have been proposed, e.g., sorted QR decomposition (SQRD), Cholesky decomposition, vertical Bell Laboratories space time (V-BLAST) and lattice reduction aided THPs. From a practical perspective, however, limited hardware implementations have been reported in the literature so far. To bridge the progress gap between the theory and the practice, we present a comprehensive analysis of these THP variants in terms of performance and implementation efficiency in this paper. We first evaluate their bit-error rate (BER) performance under perfect and imperfect channel state information (CSI) scenarios. Subsequently, the emphasis is put on their implementation efficiency, including the computational complexity, the numerical precision requirement and the parallelism potential. Our analysis shows a wide trade-off space exists between the performance and the implementation efficiency in different THP variants, which is especially valuable for hardware designers to implement cost-efficient architectures biased towards practical systems.

Rate Balancing Based Tomlinson–Harashima Precoding for G.Fast Systems

Due to the much higher crosstalk impairing in G.fast high-frequency channels compared with digital subscriber line low-frequency channels, the nonlinear Tomlinson–Harashima precoding (THP) has a good potential to enhance the G.fast system performance. However, ordering plays an important role for the data rate performance in THP. The users precoded earlier experience enhanced data rate performance, while the users precoded later are punished with lower data rates. This would be undesirable from the service providers’ point of view. In this letter, a systemic rate balancing method named projected sorting is developed by sorting the G.fast lines with respect to the projected channel vectors. Simulation results show that the proposed projected sorting can achieve performance among users in a more controlled way.

Achievable rates of SVD‐based codebooks for zero‐forcing and Tomlinson‐Harashima precoding schemes with limited feedback MU‐MIMO system

SummaryIn this manuscript, we developed a new SVD‐based codebook design criterion for linear zero‐forcing (ZF) precoding and Tomlinson‐Harashima (TH) precoding with limited feedback. In limited feedback systems where only quantized channel state information is available, precoding on transmitter causes sum‐rate degradation because of quantization errors. Thus, we propose more efficient codebooks that reduce the quantization error with lower feedback overheads. We also develop a closed‐form expression for sum‐rate of the proposed codebooks in case of TH and ZF precoding schemes in a multiuser MIMO system with limited feedback. The numerical consequences prove that TH precoding can achieve sum‐rate gain of 0.5–2.5 bps/Hz at 25 dB signal‐to‐noise ratio as compared with linear ZF precoding with 10 and 20 feedback bits per user, respectively. Moreover, the numerical results also prove that the performance of nonlinear TH precoding is better than linear ZF precoding for low signal‐to‐noise ratio value or for the large number of feedback bits. Copyright © 2016 John Wiley & Sons, Ltd.

PERFORMANCE EVALUATION OF TRANSMISSION FOR MULTIUSER MIMO BROADCAST CHANNEL

Multiple Input Multiple Output (MIMO) system has been brought a great improvement in spectral efficiency and the system capacity by serving multiple users simultaneously. The mathematical model of downlink Multi-user MIMO system and its capacity has been presented as well as different precoded transmission schemes. It is to implementing the downlink MU-MIMO system, such as channel inversion (CI), block diagonalization (BD), dirty paper coding (DPC) and tomlinsonharashimaprecoding (THP). It is because, in wireless and mobile communication system has been requires a reliable transmission of high data rates under various channel type different scenarios and reduce MU interference in the system. These compares the method of transmission for broadcast channel (BC) and propose the best one method that outperforms existing technique with percentage improvement from the worst performance.

Multiple-Valued Signaling for High-Speed Serial Links Using Tomlinson-Harashima Precoding

The data rate of VLSI interconnections has been increasing following the demand for the high-speed operation of semiconductors, such as in CPUs. At high-speed data rates, achieving accurate communication without bit errors is difficult because of intersymbol interference (ISI). This paper presents high-speed data communication techniques for VLSI systems using Tomlinson-Harashima precoding (THP). Because THP can eliminate ISI by limiting the average and peak power of the transmitter signal, it is suitable for implementing advanced low-voltage VLSI systems. In this study, a 4-PAM (Pulse amplitude modulation) signal with THP was employed to achieve high-speed data communication in VLSI systems. Simulation and measurement results show that THP can remove the ISI without increasing the peak and average power of a transmitter signal. Furthermore, we clarify that multiple-valued signaling using THP is effective in reducing implementation costs to realize high-speed serial links.

Transceiver Optimization for Multi-Hop Communications With Per-Antenna Power Constraints

In multiple-input multiple-output (MIMO) systems, power constraints are critically important for transceiver designs. The most popular and widely used power constraint is sum power constraint. However, each antenna usually has its own amplifier, per-antenna power constraints are a more accurate and reasonable power constraint model. In this paper, under per-antenna power constraints a framework is proposed for the transceiver designs for multi-antenna multi-hop cooperative communications. In the framework, both linear transceiver and nonlinear transceiver designs with various objective functions are investigated. In specific, the considered nonlinear transceiver designs include transceivers with decision feedback equalizer (DFE) or Tomlinson–Harashima precoding (THP). To find the optimal solutions, we tackle the problem both numerically and analytically. In the proposed framework, based the matrix-monotonic optimization framework, the optimal architectures of the optimal solutions are derived, and the relationship between the designs under sum power constraint and per-antenna constraints is clearly revealed. It is proved that per-antenna power constraints are in nature equivalent to a weighted sum power constraint. After introducing a weighting matrix for the power constraints, closed-form optimal solutions can be derived. Finally, simulation results assess the performance of the proposed transceiver designs.

Transceiver Design for Nonregenerative MIMO Cognitive Relay Networks With Tomlinson–Harashima Precoding

Transceiver with Tomlinson-Harashima (TH) precoding outperforms the linear minimum mean-square-error (MSE) architecture in terms of minimum achievable MSE. In this paper, we investigate transceiver design optimization problem for nonregenerative multiple-input multiple-output cognitive relay networks (CRNs) with TH precoding. In the CRN, a secondary user (SU) source, an SU relay and an SU destination employ a TH precoder, a relay precoder, and a linear equalizer, respectively. For scenario in which SUs know perfect channel state information (CSI) from SUs to primary users, we propose an alternating optimization (AO)-based suboptimal algorithm. Given TH precoder and relay precoder, we derive a closed-form optimal solution of linear equalizer. Given relay precoder, TH precoder can be found by convex optimization. Given TH precoder, we transform nonconvex relay precoder design problem into a difference of convex programming and propose a constrained concave convex procedure-based iterative algorithm to find its local optimum. For scenario in which SUs know imperfect CSI, the channel uncertainties are modeled by worst case model. We derive equivalent worst case interference power constraints and extend the proposed AO-based suboptimal algorithm to cope with the worst case interference power constraints. Simulation results demonstrate that the proposed transceiver design with TH precoding outperforms linear transceiver designs.

Sensitivity Analysis for RVQ-Based Tomlinson–Harashima Precoded MIMO Systems

Tomlinson-Harashima precoded (THP) multiple-input-multiple-output (MIMO) systems are developed to cancel the intersymbol interference (ISI) at the transmitter. However, the THP at least requires perfect channel direction information (CDI) to completely mitigate the interference at the transmitter, which is not practical in the real world. The limited feedback systems are then practically developed to convey the quantized CDI to the transmitter. Using the quantized CDI to conduct the THP, an unavoidable interference degrades the performance at the receiver. In this paper, we investigate the performance degradation resulted from the random vector quantization (RVQ), which is a kind of CDI-based limited feedback mechanism. Here, we measure the performance degradation as the excess mean-squared error (EMSE). Since the formulation of the EMSE is a complicated function of the quantization error, we proposed using the second-order Taylor expansion to derive an analytical result. Simulation results have also verified our proposed analysis, showing that the derived analysis can match the actual EMSE.

Distributed Bi-Directional Training of Nonlinear Precoders and Receivers in Cellular Networks

Joint optimization of nonlinear precoders and receive filters is studied for both the uplink and downlink in a cellular system. For the uplink, the base transceiver station (BTS) receiver implements successive interference cancellation, and for the downlink, the BTS station pre-compensates for the interference with Tomlinson-Harashima precoding (THP). Convergence of alternating optimization of receivers and transmitters in a single cell is established when filters are updated according to a minimum mean squared error (MMSE) criterion, subject to appropriate power constraints. Adaptive algorithms are then introduced for updating the precoders and receivers in the absence of channel state information, assuming time-division duplex transmissions with channel reciprocity. Instead of estimating the channels, the filters are directly estimated according to a least squares criterion via bi-directional training: Uplink pilots are used to update the feedforward and feedback filters, which are then used as interference pre-compensation filters for downlink training of the mobile receivers. Numerical results show that nonlinear filters can provide substantial gains relative to linear filters with limited forward-backward iterations.

A Novel Investigation on BER Measurement of SC-FDMA System with Combined Tomlinson-Harashima Precoding and Reed Solomon Coding

Objective: Designing energy efficient mobile communication system is the main challenge for the LTE researchers due to increasing of users and their demands in accessing broadband services on mobile phones. High data rate, reduced Bit Error Rate (BER) and low Peak to Average Power Ratio (PAPR) are the requirement of the current telecommunication technology in both uplink and downlink. In this paper, various modulations techniques (QPSK, BPSK and QAM) and pre-coding schemes (DPC, THP, and RS) are proposed to analyze the uplink characteristics. Methods/Analysis: This paper investigates Single Carrier Frequency Division Multiple Access (SC-FDMA) and performs its link level models with Tomlinson-Harashima Precoder (THP) and Reed Solomon coding (RS) in separate and integrative manner which is proposed. Findings: In order to prove the hypothetical results, various simulations performed for BER of SC-FDMA system. Results proved that the integration of THP and RS coder in the SC-FDMA transmission, improves the system performance in case of BER. The proposed techniques can be implemented in GPRS, UMTS, GSM, EDGE, HSPA and LTE.