Tomlinson-Harashima Precoding Research Articles

High-Speed Interconnection for VLSI Systems Using Multiple-Valued Signaling with Tomlinson-Harashima Precoding

High-Speed Interconnection for VLSI Systems Using Multiple-Valued Signaling with Tomlinson-Harashima Precoding

High-Speed Data Transmissions Using Tomlinson-Harashima Precoding

High-speed interfaces become an important role to achieve high performance VLSIsystems. This paper demonstrates a high-speed data transmission technique using Tomlinson-Harashima Precoding (THP). The THP can compensate for low-pass effect of an interconnec-tion at a transmitter, and it can also limit peak and average power of a transmitted signal. Inthis paper, a 200Mbps 4-PAM(Pulse-amplitude modulation) transmitter is designed and simu-lated to demonstrate the THP performance. The experimental implementation using an FPGAdemonstrates high-speed transmission over a long 3D2V coaxial cable.

AirSync: Enabling Distributed Multiuser MIMO With Full Spatial Multiplexing

The enormous success of advanced wireless devices is pushing the demand for higher wireless data rates. Denser spectrum reuse through the deployment of more access points (APs) per square mile has the potential to successfully meet such demand. In principle, distributed multiuser multiple-input-multiple-output (MU-MIMO) provides the best approach to infrastructure density increase since several access points are connected to a central server and operate as a large distributed multiantenna access point. This ensures that all transmitted signal power serves the purpose of data transmission, rather than creating interference. In practice, however, a number of implementation difficulties must be addressed, the most significant of which is aligning the phases of all jointly coordinated APs. In this paper, we propose AirSync, a novel scheme that provides timing and phase synchronization accurate enough to enable distributed MU-MIMO. AirSync detects the slot boundary such that all APs are time-synchronous within a cyclic prefix (CP) of the orthogonal frequency-division multiplexing (OFDM) modulation and predicts the instantaneous carrier phase correction along the transmit slot such that all transmitters maintain their coherence, which is necessary for multiuser beamforming. We have implemented AirSync as a digital circuit in the field programmable gate array (FPGA) of the WARP radio platform. Our experimental testbed, comprising four APs and four clients, shows that AirSync is able to achieve timing synchronization within the OFDM CP and carrier phase coherence within a few degrees. For the purpose of demonstration, we have implemented two MU-MIMO precoding schemes, Zero-Forcing Beamforming (ZFBF) and Tomlinson-Harashima Precoding (THP). In both cases, our system approaches the theoretical optimal multiplexing gains. We also discuss aspects related to the MAC and multiuser scheduling design, in relation to the distributed MU-MIMO architecture. To the best of our knowledge, AirSync offers the first realization of the full distributed MU-MIMO multiplexing gain, namely the ability to increase the number of active wireless clients per time-frequency slot linearly with the number of jointly coordinated APs, without reducing the per client rate.

A 10 Gb/s 8-Tap 6b 2-PAM/4-PAM Tomlinson–Harashima Precoding Transmitter for Future Memory-Link Applications in 22-nm SOI CMOS

Tomlinson-Harashima (TH) precoding is a transmitter equalization technique in which the post-cursor intersymbol interference (ISI) is canceled by means of an infinite impulse response (IIR) filter with modulo (MOD)-based amplitude limitation. TH equalizers are suited for asymmetric links, such as DRAM interfaces, where the transmitter contains the equalization complexity and the receiver is kept simple. To increase the data rate, we propose the application of pipelining and half-rate operation to the ISI subtraction in the equalizer's feedback path. A TH equalizer with 8 taps, 6 bit resolution, and 2-PAM/4-PAM support has been implemented in 22-nm silicon-on-insulator (SOI) CMOS technology. In measurements, the feedback delay reduction techniques allow us to equalize 34-cm-long PCB traces having 12-dB loss with 7 × ISI reduction for 5.0-Gb/s 2-PAM signaling, and in 10.0-Gb/s 4-PAM mode completely closed eye diagrams are opened. The measured efficiency of the 145 μm× 115 μm transmitter is 1.2 pJ/bit in 4-PAM mode at 5.0 Gbaud with disabled equalization and increases linearly with 14 μW/Gbaud per 1% increase of the equalization tap weights.

The Effect of Decision Delay in MMSE-THP Systems

In this paper, the effect of decision delay in minimum mean square error Tomlinson-Harashima precoding systems is investigated. The optimal decision delays are partly solved under three cases that are divided by comparing the feedback filter order with channel order. The mean square error and the bit error rate of the system under different decision delays have been thoroughly examined. Simulation results verify the validity of the derived optimal decision delay.

Iterative Decoding of Coded THP with Quantized Output

This paper proposes an improved receiver for the Tomlinson-Harashima precoder (THP). In this paper we demonstrate that most of the capacity loss associated with conventional THP is due to the suboptimal receiver, which is a simple modulo operation. We then demonstrate how this loss can can be avoided with the optimization of the receiver. In the suboptimal receiver the modulo operation ignores the dependency between the implicitly added sequence of symbols removed by it. We then implement a THP with quantized outputs. The quantized outputs enable to implement a Maximum A-Posteriori Probability (MAP) receiver that exploits the dependency between the received symbols. The MAP receiver is named Enhanced MODulo operation (EMOD), and operates as an inner decoder within an iterative scheme, either with outer Low Density Parity Check (LDPC) code or outer Turbo Code. Simulation results show considerable gains relative to coded conventional THP, and also relative to the Turbo-Equalizer (TE) (which does not use a precoder in the transmitter).

Tomlinson-Harashima Precoded MIMO in wireless networks: to THP or not to THP?

We investigate a wireless network architecture that utilizes Tomlinson Harashima Precoded Multiple Input Multiple Output (THP MIMO) technique for improved system capacity. We consider THP MIMO in a multi user scenario, together with a proposed smart scheduling technique and we explore the capacity performance through extensive capacity analysis considering varying SNR levels, varying number of users and number of transmit/receive antennas, under fading and shadowing, also considering errors in channel state information (CSI). We also evaluate the complexity of THP MIMO and present a low-complexity scheduling algorithm that employs Gram-Schmidt algorithm for incremental implementation of THP's QR factorization. In the end, we identify the network and channel conditions under which THP MIMO can be preferred over classical conventional MIMO, and we conclude that for practical transceivers with up to four antennas, THP MIMO can provide significant capacity enhancement over conventional MIMO at lower complexity, performing slightly below the sum rate capacity bound. Another important advantage that is observed in this study is better immunity of THP MIMO to CSI errors, as compared to conventional MIMO.

THP Transceiver Design for MIMO Relaying with Direct Link and Partial CSI

In this letter we consider Tomlinson Harashima precoding (THP) for multiple-input multiple-output (MIMO) relay systems with a direct link between the source and destination. It is assumed that the destination can acquire full channel state information (CSI) of all channels, whereas the source and relay have full CSI of the source-relay channel but only acquire statistical knowledge of the source-destination and relay-destination channels. Simulation results demonstrate that, for high signal to noise ratio (SNR) in the relay-destination link, the performance of the proposed design approaches that of non-linear transceivers utilising full CSI.

SSLNR 기반의 ZF-THP를 위한 새로운 빔형성 기법

본 논문에서는 협력 빔형성(Coordinated Multi-Point Coordinated Beamforming : CoMP CB) 시나리오에서 인접한 사용자들 때문에 발생되는 간섭(Inter User Interference : IUI)을 제거하기 위해 사용된 Block Diagonal Geometric Mean Decomposition(BD-GMD)기반의 IUI 제거 알고리즘을 Successive Signal to Leakage plus Noise Ratio(SSLNR) 환경에서의 ZF(Zero-Forcing)에 적용하여 누출 전력을 제거한다. 또 IUI 제거 알고리즘을 사용했을 시 문제가 되는 원하는 신호 전력(Desired signal power)의 크기를 크게 보장할 수 없다는 점을 보완하기 위해 적절한 채널 열 순열(Channel ordering)을 수행하여 원하는 신호의 전력을 높인다. IUI 제거 알고리즘 사용과 적절한 채널 열 순열을 통해 기존의 SSLNR-Zero-Forcing Tomlinson Harashima precoding(ZF-THP) 기법보다 더 나은 비트오류확률(Bit Error Rate : BER)성능을 낼 수 있다. In this paper, Inter user interference elimination algorithm based on Block Diagonal Geometric Mean Decomposition(BD-GMD) for eliminating inter user interference apply to Zero-Forcing in the Successive Signal to Leakage plus Noise Ratio(SSLNR) in Coordinated Multi-Point Coordinated Beamforming system(CoMP CB). As a result, the leakage power is eliminated. The inter user interference elimination algorithm, however, cannot guarantee the enough desired signal power therefore we perform the channel ordering to overcome this disadvantage and increase the desired signal power. The simulation results show that the proposed scheme provides the improved Bit Error Rate(BER) performance compared with existing SSLNR-Zero-Forcing-Tomlinson Harashima precoding(SSLNR-ZF-THP).

Joint Tomlinson-Harashima source and linear relay precoder design in amplify-and-forward multiple-input multiple-output two-way relay systems

Existing minimum-mean-squared-error (MMSE) transceiver designs in amplified-and-forward (AF) multiple-input multiple-output (MIMO) two-way relay systems all assume a linear precoder at the sources. Nonlinear source precoders in such a system have not been considered yet. In this paper, we study the joint design of source Tomlinson-Harashima precoders (THPs), relay linear precoder and MMSE receivers in two-way relay systems. This joint design problem is a highly nonconvex optimization problem. By dividing the original problem into three sub-problems, we propose an iterative algorithm to optimize precoders and receivers. The convergence of the algorithm is ensured since the updated solution is optimal to each sub-problem. Numerical simulation results show that the proposed iterative algorithm outperforms other algorithms in the high signal-to-noise ratio (SNR) region.

Robust Non-linear Precoder for Multiuser MISO Systems Based on Delay and Channel Quantization

In multiuser multiple-input single-output (MISO) systems, non-linear precoder is able to achieve the theoretical sum capacity of downlink channel with perfect channel state information (CSI). However, the perfect CSI is not available at the transmitter in practical system, especially in frequency division duplex (FDD) system where the imperfect CSI is the delayed, quantized channel direction information relayed back from the receiver through a dedicated feedback channel. So the performance of conventional non-linear precoder degrades significantly. In this paper, a robust non-linear Tomlinson---Harashima precoding (THP) based on sum mean squared error (SMSE) minimization for the downlink of multiuser MISO FDD systems is proposed. The proposed precoder is robust to the channel uncertainties arising from channel delay and quantization error. Furthermore, an improved non-linear THP with channel magnitude information (CMI) consideration is introduced to compensate the instantaneous CMI shortage at the transmitter. Additionally, the computational complexity of both proposed precoders can be reduced remarkably by Cholesky factorization with symmetric permutation. Simulation results demonstrate the improvement in bit error ratio performance and illustrate the SMSE performance of the proposed algorithms compared with conventional THP with perfect CSI in the literature.

Quantized CSI-Based Tomlinson-Harashima Precoding in Multiuser MIMO Systems

This paper considers the implementation of Tomlinson-Harashima (TH) precoding for multiuser MIMO systems based on quantized channel state information (CSI) at the transmitter side. Compared with the results in [1], our scheme applies to more general system setting where the number of users in the system can be less than or equal to the number of transmit antennas. We also study the achievable average sum rate of the proposed quantized CSI-based TH precoding scheme. The expressions of the upper bounds on both the average sum rate of the systems with quantized CSI and the mean loss in average sum rate due to CSI quantization are derived. We also present some numerical results. The results show that the nonlinear TH precoding can achieve much better performance than that of linear zero-forcing precoding for both perfect CSI and quantized CSI cases. In addition, our derived upper bound on the mean rate loss for TH precoding converges to the true rate loss faster than that of zero-forcing precoding obtained in [2] as the number of feedback bits becomes large. Both the analytical and numerical results show that nonlinear precoding suffers from imperfect CSI more than linear precoding does.

Multi-dimensional Constellation Tilting for Reducing the Power Loss of Tomlinson-Harashima Precoder

We propose a multi-dimensional extension of the constellation tilting (CT) method for reducing the power loss of Tomlinson-Harashima precoding. By the extension, constellations for multiple signal streams are simultaneously rotated at a proper angle so that the number of available tilting angles is rapidly increased. Then, this growth of the available angles improves the performance of CT and computer simulations show that the proposed extension obtains the enhanced power reduction effect.

Outage-based design of robust Tomlinson–Harashima transceivers for the MISO downlink with QoS requirements

We consider a broadcast channel in which the base station is equipped with multiple antennas and each user has a single antenna, and we study the design of transceivers based on Tomlinson–Harashima precoders with probabilistic quality of service (QoS) requirements for each user, in scenarios with uncertain channel state information (CSI) at the transmitter. Each user's QoS requirement is specified as a constraint on the maximum allowed outage probability of the receiver's mean square error (MSE) with respect to a specified target MSE, and we demonstrate that these outage constraints are associated with constraints on the outage of the received signal-to-interference-plus-noise-ratio (SINR). We consider four different stochastic models for the channel uncertainty, and we design the downlink transceiver so as to minimize the total transmitted power subject to the satisfaction of the probabilistic QoS constraints. We present three conservative approaches to solving the resulting chance constrained optimization problems. These approaches are based on efficiently solvable deterministic convex design formulations that guarantee the satisfaction of the probabilistic QoS constraints. We also demonstrate how to apply these approaches in order to obtain computationally efficient solutions to some related design problems. Our simulations indicate that the proposed methods can significantly expand the range of QoS requirements that can be satisfied in the presence of uncertainty in the CSI.

A VLSI Design of a Tomlinson-Harashima Precoder for MU-MIMO Systems Using Arrayed Pipelined Processing

SUMMARY This paper presents a VLSI design of a TomlinsonHarashima (TH) precoder for multi-user MIMO (MU-MIMO) systems. The TH precoder consists of LQ decomposition (LQD), interference cancellation (IC), and weight coefficient multiplication (WCM) units. The LQ decomposition unit is based on an application specific instruction-set processor (ASIP) architecture with floating-point arithmetic for high accuracy operations. In the IC and WCM units with fixed-point arithmetic, the proposed architecture uses an arrayed pipeline structure to shorten a circuit critical path delay. The implementation result shows that the proposed architecture reduces circuit area and power consumption by 11% and 15%,

Power Optimization of Tilted Tomlinson-Harashima Precoder in MIMO Channels with Imperfect Channel State Information

This paper concentrates on the designing of a robust Tomlinson-Harashima Precoder (THP) over multiple-input multiple-output (MIMO) channels in wireless communication systems with assumption of imperfect channel state information (CSI) at the transmitter side. With the assumption that the covariance matrix of channel estimation error is available at the transmitter side, we design a THP that presents robustness against channel uncertainties. In the proposed robust THP, the transmit power is further minimized by using the Tilted constellation concept. This power minimization reduces the interchannel Interference (ICI) between subchannels and, furthermore, recovers some part of the THP's power loss. The bit error rate (BER) of the proposed system is further improved by using a power loading technique. Finally, the simulation results compare the performance of our proposed robust THP with a conventional MIMO-THP.

Novel THP Scheme with Minimum Noise Enhancement for Multi-User MIMO Systems

In this paper, we propose a modified Tomlinson Harashima precoding (THP) method with less increase of computational complexity for the multi-user MIMO downlink system. The proposed THP scheme minimizes the influence of noise enhancement at the receivers by placing the diagonal weighted filters at both transmitter side and receiver side with square root. Compared to previously proposed non-linear precoding methods including vector perturbation (VP), the proposed THP achieves high BER performance. Furthermore, we show that the proposed THP method is implemented with lower computational complexity than that of existing modified THP and VP in literature.

Diversity Fairness in Tomlinson–Harashima Precoded Multiuser MIMO Through Retransmission

We study the diversity unfairness associated with the conventional Tomlinson–Harashima precoding (THP) in multiuser multiple-input multiple-output downlink transmission. A single-retransmission scheme that combines two THP signals at each user with a complementary multi-user suppression order is investigated. For a system with <formula formulatype="inline" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex Notation="TeX">$M$</tex></formula> antennas at the transmitter and a single antenna at each user, the proposed scheme provides a diversity order <formula formulatype="inline" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex Notation="TeX">$M+1$</tex></formula> for all users and ensures diversity fairness. We study two retransmission policies, where the users either consider only the current received codeword or combine both codewords for decoding. An asymptotic analysis of the outage probability for both THP retransmission schemes is provided. In addition, a power allocation policy that minimizes the outage probability and accommodates the same coding gain at each user is discussed by formulating a geometric optimization problem.

A Low Complexity Precoding Transceiver Design for Double STBC System

A precoding design for double space-time block coding (STBC) system is investigated in this paper, i.e., the joint processing of STBC and dirty paper coding (DPC) techniques. These techniques are used for avoiding dual spatial streams interference and improving the transmitter diversity. The DPC system is interference free on multi-user or multi-antenna. The STBC transceiver can provide the transmit diversity. Due to the benefits about the STBC and DPC system, we propose a new scheme called STBC-DPC system. The transceiver design involves the following procedures. First, the ordering QR decomposition of channel matrix and the maximum likelihood (ML) one-dimensional searching algorithm are proposed to acquire a reliable performance. Next, the channel on/off assignment using water filling algorithm is proposed to overcome the deep fading channel problem. Finally, the STBC-DPC system with the modulus operation to limit the transmit signal level, i.e., Tomlinson-Harashima precoding (THP) scheme, is proposed to retain low peak-to-average power ratio (PAPR) performance. Simulation results confirm that the proposed STBC-DPC/THP with water filling ML algorithm can provide the low PAPR and excellent bit error rate (BER) performances.

Vectored DSL: Potential, Implementation Issues and Challenges

This paper investigates specific techniques suitable for Vectored DSL, their performance, complexity and practical implementation. More specifically, various Vectored DSL techniques for both upstream and downstream transmission are discussed, including the Tomlinson-Harashima Pre-coder (THP), Diagonalizing Pre-coder (DP), Zero-Forcing (ZF) canceller, and Decision-Feedback (DF) canceller. A thorough discussion on some of the practical implementation aspects of Vectored DSL is provided. In particular, various implementation challenges are discussed, including computational load, memory storage, line management, partial crosstalk cancellation, and the effect of imperfect channel knowledge. As well, the potential gains and challenges of combining Phantom DSL and Vectored DSL are also discussed. Illustrative examples are provided based on both measured data and channel models to compare the various Vectored DSL techniques and their practical implementation challenges.