Harashima Precoding Research Articles

A low‐complexity transmit combining method for downlink of massive multiuser multiple input multiple output systems

AbstractMultiuser multiple input multiple output (MU‐MIMO) systems can provide high spectral efficiency (SE) that is achieved with transmit/receive combining schemes at the base station (BS) for downlink (DL) and uplink (UL). So far, various combining schemes for DL were proposed, with the regularized zero forcing (RZF) and Tomlinson–Harashima precoding (THP) being usually considered. In a case of massive MU‐MIMO systems, with a large number of antennas, the matrix inversion operation used in the RZF and THP schemes causes high computational complexity that significantly aggravates implementation and raises its costs. The authors propose a low‐complexity transmit combining scheme for the massive MU‐MIMO systems with time division duplex (TDD), devised in a similar manner as the THP scheme, based on the gram‐Schmidt orthogonalization, and show that it achieves slightly better SE than the THP scheme for the estimated channel state information (CSI), but with a much lower complexity than the THP and RZF schemes.

Mitigating pilot contamination in Rician faded massive MIMO 5G systems using enhanced zero forcing precoding and ring partitioning

In this paper, pilot contamination, in massive multiple-input multiple-output (MIMO) system is reduced to a significant extent by using base station (BS) rotation, user (UE) scheduling and enhanced Zero Forcing (e-ZF) precoding. Cellular network is divided, based on the angle, and partitioned into rings for grouping mobile UEs. Grouping is done by creating specifically designed policies using three significant network parameters. Neural network is used for scheduling grouped UEs and then UEs are assigned with optimal pilots. Hybrid particle swarm optimization with fuzzy (PSOF) logic detects optimal pilot in accordance to channel quality and additive white gaussian noise (AWGN). Simulations are performed in MATLAB-R2017b and performance is experimentally evaluated in terms of achievable rate, noise ratio and spectral efficiency in Rician Fading environment. Comparative results are evaluated with respect to conventional precoding techniques as dirty paper coding (DPC), block diagonalization (BD), matched filter (MF) and Tomlinson Harashima (TH) precoding.

Improved Tomlinson–Harashima Precoding for Ultra Reliable Communication in Intelligent Transportation Systems

Cyber-physical systems (CPSs) are characterized by integrating computation and physical processes. To cope with the challenges of the application of the CPSs in all kinds of environments, especially the cellular vehicle-to-everything (C-V2X) which needs high quality end-to-end communication, the robustness and reliability for CPSs are very crucial. Aiming at the technical challenges of information transmission caused by the fading effect and the fast time-varying characteristics of the channel for C-V2X communication, an improved Tomlinson–Harashima precoding (THP) algorithm for multiple input multiple output (MIMO) systems is proposed. Channel state information (CSI) and correlation are exploited to compensate instantaneous CSI, which could reflect current real-time channel status exactly. Further, the iterative water filling power allocation algorithm and the multiuser scheduling algorithm based on the greedy algorithm are jointly optimized and applied to the THP, which could improve the system performance. Simulation results show that the proposed algorithm can be efficiently applied to high-speed mobility scenarios and improve bit error ratio (BER) performance as well as spectrum utilization.

BD-UCD-Based Nonlinear Hybrid Precoding for Millimeter Wave Massive Multiuser MIMO Systems

In this letter, we investigate the downlink hybrid precoding design for time-division duplexing (TDD) millimeter wave (mmWave) massive multiuser MIMO (MU-MIMO) systems, aiming to enhance both the sum spectral efficiency (SSE) and the bit error rate (BER) performance. First, we propose a joint analog precoding and combining design via Gram-Schmidt orthogonalization to maximize the beamforming gain while mitigating the inter-user interference. Then, by exploiting the uplink-downlink duality, we propose a block diagonal uniform channel decomposition (BD-UCD) based digital precoding and combining scheme to further improve the SSE and BER performance. Furthermore, Tomlinson–Harashima precoding (THP) is utilized to eliminate both the inter-user interference and the inter-stream interference. Simulation results demonstrate that the proposed BD-UCD-based nonlinear hybrid precoding scheme performs close to the fully-digital BD-UCD scheme and outperforms the other existing hybrid precoding schemes in terms of SSE and BER performance.

16QAM spectral efficiency frequency division multiplexing transmission with Tomlinson–Harashima precoding for intensity modulation and direct detection optical links

In the spectral efficient frequency division multiplexing (SEFDM) system, in order to minimize mutual interference between subcarriers, a detector should be introduced at the receiver to handle the interference, but increases the complexity of system. In this paper, we propose a simplified precoding algorithm at transmitter instead of receiver, which can first implement higher 16QAM SEFDM transmission over standard single mode fiber (SSMF). The technique is based on interference information from non-orthogonality between subcarriers and uses nonlinear matrix operations to improve system performance with low complexity. The numerical results show that the precoding scheme achieves SSMF transmission of intensity modulation and direct detection (IM/DD) 16QAM SEFDM system under the premise of achieving higher spectral efficiency, and obtains good bit error rate performance.

Robust Tomlinson-Harashima Precoding for Two-Way Relaying

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

Experimental Demonstration of 600 Gb/s Net Rate PAM4 Transmissions over 2 km and 10 km with a 4-λ CWDM TOSA

We propose to introduce a controlled amount of inter-symbol interference (ISI) during pulse shaping in a high symbol rate intensity modulation direct detection (IM/DD) system to increase the alternating current (AC) power of the received electrical signal after photo-detection and transimpedance amplification. We experimentally demonstrate high-speed 4-level pulse amplitude modulation (PAM4) transmissions with a 4-λ coarse wavelength division multiplexing (CWDM) transmitter optical sub-assembly (TOSA) using the proposed scheme. The intentionally introduced ISI is mitigated using either transmitter-side Tomlinson Harashima precoding (THP) or receiver-side feed forward equalization (FFE) aided with a 2-tap post filter and maximum likelihood sequence estimation (MLSE). Both methods enable 4 × 81 Gbaud PAM4 transmission over 2 km of single mode fiber (SMF), with a bit error rate (BER) below the 7% overhead hard-decision forward error correction (HD-FEC) threshold of 3.8 × 10−3, which corresponds to a net rate of >600 Gb/s. We also explore the limit of our system at 10 km. The result shows that an aggregated net rate of 600 Gb/s excluding the HD-FEC overhead can still be achieved by loading different symbol rates onto different wavelength channels.

A Modulo-FIR Equalizer for Wireline Communications

This paper presents a transmit-side modulo-FIR equalizer (MFE) that is suitable for future high-throughput links. In a proposed PAM transceiver architecture, forward error correction (FEC) is employed to mitigate the BER degradation by the reduced SNR. Because of the poor compatibility of a decision-feedback equalizer with the FEC system, we propose to use the MFE on the transmitter side instead, thereby avoiding a problem of error propagation. The MFE has several advantages over the conventional transmit-side equalization technique, Tomlinson–Harashima precoding (THP). The MFE predicts a modulo bit before the FIR equalizer whereas the THP equalizer calculates a modulo bit within the IIR equalizer. Hence, the overall calculation complexity is much relaxed in the MFE case, improving the operating speed. Moreover, the performance of the FIR equalizer is better than that of the IIR equalizer for handling a multiple-pole channel. By employing the MFE, the maximally achievable eye opening is improved by 30 % for PAM4 signaling, compared to the THP case.

An Improved Dropping Algorithm for Line-of-Sight Massive MIMO With Tomlinson–Harashima Precoding

One of the problems in line-of-sight massive MIMO is that a few users can have correlated channel vectors. To alleviate this problem, a dropping algorithm has been proposed in the literature, which drops some of the correlated users to make the spatial correlation among the remaining users be less than a certain threshold. Thresholds were found by running a large number of simulations. In this letter, the same dropping algorithm is analyzed for a known nonlinear precoder: Tomlinson-Harashima precoder. Instead of simulation-based thresholds, closed-form analytical expressions are derived in this letter for two power allocation schemes: max-min and equal received power control schemes. It is shown that the derived thresholds are optimal in terms of achievable sum-rate when there is only one correlated pair of users. For channels with multiple pairs of correlated users, simulation results show that using the derived thresholds improves the 5th percentile sum-rate. Due to the fairness criterion of max-min, the improvement for max-min power control is much higher than equal received power control.

IM/DD Beyond Bandwidth Limitation for Data Center Optical Interconnects

Intensity modulation with direct detection (IM/DD) provides a low-cost solution for data center optical interconnects. To achieve higher data rate, Tomlinson–Harashima precoding (THP) is adopted to increase the operating symbol rate beyond the Nyquist rate defined by the system bandwidth. By applying THP, the signal is precoded by a feedback filter at the transmitter for the mitigation of the intersymbol interference caused by the faster-than-Nyquist signaling and the spectral power fading induced by the interaction of chromatic dispersion and direct detection. In this paper, high-performance THP-based IM/DD transmission is demonstrated, increasing the achievable data rate using a limited system bandwidth. In the experimental demonstration, we achieve a net bit rate of 185 Gb/s for up to 2-km fiber link, transmitting 74 GBd precoded eight-level pulse amplitude modulation (PAM-8) using an IM/DD system with 33 GHz brick-wall electrical bandwidth limitation.

Artificial-Noise-Aided Nonlinear Secure Transmission for Multiuser Multi-Antenna Systems With Finite-Rate Feedback

We consider a low-complexity transceiver design for secure communications of a multiuser multi-antenna system with an external multi-antenna eavesdropper. We propose to employ Tomlinson–Harashima precoder (THP) to simultaneously transmit message-bearing signals and artificial noise (AN) according to the quantized channel state information (CSI). Based on random vector quantization of the channel vectors, we obtain analytical approximations of the ergodic secrecy rate (ESR) of each legitimate receiver (LR) and the ergodic secrecy sum rate of the system with arbitrary system parameters. Based on the obtained analytical results, the near-optimal power allocation to the information signals and AN can be obtained using a numerical method. We show using an information-theoretical method that, besides the advantage in the ESR over the linear precoding scheme, THP can reduce the supported rate of the eavesdropper’s channel by preventing the eavesdropper from obtaining the legitimate channels’ (quantized) CSI. The ESR loss of each LR compared with the perfect CSI case will increase without bound for a fixed number of feedback bits. We also derive a feedback bit scaling law to solve this problem. Finally, numerical results are provided to verify our analytical results and also the advantage of the proposed secure nonlinear transceiver over the corresponding linear scheme.

Tomlinson–Harashima precoding for transmitter‐side inter‐symbol interference cancellation in PSK modulation

Dirty paper coding (DPC) is a non-linear transmit scheme in presence of known interference, which is capacity achieving. Unfortunately, the implementation complexity of DPC is usually prohibitive. A sub-optimal yet practical method to implement DPC in inter-symbol interference channels is Tomlinson–Harashima precoding (THP). However, THP is not applicable to the constant-envelope phase shift keying (PSK) modulation. In this study, a modified Tomlinson–Harashima precoder is proposed to implement DPC for PSK modulation. The technique involves design of decision region at the receiver side and an algorithm to select the phase of transmitted symbol optimally at the transmitter side accordingly. Various patterns, namely, striped, checked, hexagonal, and radial are proposed and examined. Simulation results show that by using the proposed equaliser, the error floor is eliminated and significantly smaller bit-error rate is achieved. Numerical and simulation results show that the striped pattern outperforms other decision region designs. Moreover, its implementation and computational complexities is almost the same as the Tomlinson–Harashima precoder.

Near Optimum User Selection for Minimum Mean Square Error Based Tomlinson Harashima Precoding

This paper proposes novel user selection techniques for the Tomlinson-Harashima precoding (THP) based on the minimum mean square error (MMSE) criterion. These techniques utilize a part of the intermediate values in the derivation of the THP weight, which makes it possible to implement the techniques with lower computational complexity. For further complexity reduction, we propose successive user selection techniques based on the techniques proposed above where user terminals are selected one by one. It is confirmed by computer simulations that the proposed techniques outperform conventional selection techniques. The computational complexity of the successive selection techniques is about 1/20 as small as that of the original selection techniques when 4 user terminals are selected out of 10 terminals.

Nonlinear-Precoded Multiuser Secure Transmission With Cooperative Jamming and Adaptive Limited Feedback

This paper studies secure transceiver design for multiuser multiantenna systems with an external passive eavesdropper and a cooperative jamming helper. Due to the finite-rate constraint of feedback channels, only quantized channel state information (CSI) of the legitimate users is available at the transmitter and the helper. A nonlinear-precoded secure transmission strategy is proposed using Tomlinson–Harashima precoding at the transmitter and null-space beamforming at the helper based on the quantized CSI. The accurate closed-form expression of an approximation for the ergodic rate of each legitimate user is obtained using quantization cell approximation for random vector quantization of the channels. Assuming the quantized CSI of the legitimate channels and the helper's channel at the eavesdropper, closed-form expression of an upper bound of the ergodic rate of each user's message at the eavesdropper is also derived. Then, a closed-form expression of an approximation for the worst-case ergodic secrecy sum rate follows. We also theoretically show that, besides the advantage in ergodic rate over the linear precoding scheme, when the quantized CSI is not available at the eavesdropper, Tomlinson–Harashima precoding is also more effective in degrading the received signal quality at the eavesdropper, and, thus, is more capable to enhance the secrecy of the systems compared with the linear precoding scheme. Given the total bandwidth constraint of CSI-feedback channels, an adaptive feedback bit allocation algorithm is proposed for each legitimate user to optimize the ergodic secrecy rate performance. Numerical results illustrate that the proposed nonlinear-precoded secure transmission strategy outperforms the corresponding linear precoding scheme, and significant advantage can be achieved by adaptively allocating the total available feedback bits.

A Hybrid Tomlinson–Harashima Transceiver Design for Multiuser mmWave MIMO Systems

This letter presents a new hybrid transceiver design for multiuser millimeter wave (mmWave) multiple-input–multiple-output downlink systems. To achieve improved sum-rate and error-rate performances, the proposed hybrid system is based on a combination of the Tomlinson–Harashima precoding and the block-diagonal geometric mean decomposition. With some novel observations and design choices, we showed that a closed-form solution can be obtained similarly for the hybrid design. Simulation shows the proposed design performs very close to its fully digital counterpart, and substantially outperforms the existing linear precoder-based hybrid transceivers.

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

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

Approximate Perturbation Aided Lattice Encoding (APPLE) for G.fast and Beyond

G.fast suffers from strong far-end crosstalk at high frequencies in cable binders containing a large number of twisted copper pairs. For the 212-MHz G.fast spectrum, the power penalty incurred by the conventional zero-forcing precoding-based linear vectoring (LV) scheme is far more substantial than it was over the 30-MHz VDSL2 spectrum. In this paper, we propose a novel non-LV (NLV) scheme based on Babai’s nearest plane approximation of the closest lattice point problem on the reduced lattice basis. Similar to the conventional Tomlinson–Harashima precoding (THP)-based NLV, the proposed approximate perturbation aided lattice encoding (APPLE) scheme closely approaches the dirty paper coding capacity which provided that the system employs a fully rate-adaptive power allocation policy per tone per pair. However, if the system employs a scalar power policy that is only rate-adaptive with respect to each tone, APPLE becomes capable of achieving a higher throughput per binder than THP. APPLE’s transmitter complexity is considerably lower than that of the conventional lattice encoding schemes (e.g., vector perturbation) and comparable to that of THP.

Tomlinson–Harashima Precoding For Dispersion Uncompensated PAM-4 Transmission With Direct-Detection

Combating the destructive effects of power-fading in fiber-optic systems using direct-detection is the key for increasing the transmission rates and/or reach. Some of the solutions used in the past include additional components, e.g., a dispersion-compensating fiber or an IQ-modulator, which increase the costs of the entire system. Another solution, the compensation of the channel distortions using decision-feedback equalization, is limited to its error-propagation effect. In this paper, we introduce Tomlinson–Harashima precoding for the compensation of power-fading, which allows us to use the efficiency of feedback equalization for channels with spectral zeros without the disadvantage of error propagation. In an experimental investigation with different scenarios, including transmission over 25 km up to 100 km of standard single-mode fiber with gross data rates ranging from 56 to 560 Gb/s, we show that Tomlinson–Harashima precoding significantly outperforms decision-feedback equalization in all cases. Using Tomlinson–Harashima precoding, power-fading can be efficiently compensated for using digital signal processing only, keeping the system flexible and at the same time cost-effective.

An Interference Cancellation Technique for Distributed MIMO Systems

This study proposes an uncooperative-multi-cell-multiple-input–multiple-output system to increase the throughput of an ill-conditioned wireless MIMO downlink system. The proposed algorithm suppresses the inter-cell interference at each mobile station using a set of adaptive receive beamformers, but handles the intra-cell interference at each base station using a Tomlinson Harashima precoder. Using the singular vectors of channel matrices, the receive beamformers can be designed based on a linear-constrained-minimum-variance criterion. On the other hand, to obtain high enough degree of freedoms for cancelling the intra-cell interference at each base station, the precoder is applied to the re-assembled downlink virtual channel formed by the simplified channel state information. Using the proposed interference suppression techniques, a multi-cell downlink system with multiple uncooperative base stations can be decomposed into a set of parallel subchannels. The resulting system has better performance in channel capacity than conventional MIMO systems. Computer simulations support the validity of the proposed approach.

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.