Nonlinear Precoding Research Articles

XOR Physical Layer Network Coding with Non-Linear Precoding for Quadrature Amplitude Modulations in Bi-Directional MIMO Relay Systems

XOR Physical Layer Network Coding with Non-Linear Precoding for Quadrature Amplitude Modulations in Bi-Directional MIMO Relay Systems

Linear Precoding with User and Transmit Antenna Selection

The major challenge in the current scenario of wireless system is increasing number of users and hence increased co-channel interference within the limited spectrum available for communication. The compromise in terms of user quality and reliability of communication system is evitable from increased number of call drops and busy channels during mobile voice calls. The above mentioned challenge is attributed for increase in the number of users accommodated in the defined spectrum. The paper presents a novel user selection and transmit antenna selection based approach for enhanced reliability in multi-user multiple input multiple output system, which is next generation wireless system. In contrast to existing technique for multiple antennas and which is evolution of regular channel inversion with block diagonalization, the proposed technique considers systematic and optimum deployment of user selection in the system to enhance sum rate or the system capacity. The comparison of algorithms viz. random, norm based and capacity based user selection is presented with its implementation with precoding techniques which is used to minimize co-channel interference. The analysis proposes that, for each selected user if the transmit antennas are chosen with presented algorithm, the sum rate is improved by 17%. Also, the bit error rate performance of linear precoding with user selection is equivalent to non-linear precoding without user selection.

Hybrid MU-MIMO Precoding Based on K-Means User Clustering

Multi-User (MU) Multiple-Input-Multiple-Output (MIMO) systems have been extensively investigated over the last few years from both theoretical and practical perspectives. The low complexity Linear Precoding (LP) schemes for MU-MIMO are already deployed in Long-Term Evolution (LTE) networks; however, they do not work well for users with strongly-correlated channels. Alternatives to those schemes, like Non-Linear Precoding (NLP), and hybrid precoding schemes were proposed in the standardization phase for the Third-Generation Partnership Project (3GPP) 5G New Radio (NR). NLP schemes have better performance, but their complexity is prohibitively high. Hybrid schemes, which combine LP schemes to serve users with separable channels and NLP schemes for users with strongly-correlated channels, can help reduce the computational burden, while limiting the performance degradation. Finding the optimum set of users that can be co-scheduled through LP schemes could require an exhaustive search and, thus, may not be affordable for practical systems. The purpose of this paper is to present a new semi-orthogonal user selection algorithm based on the statistical K-means clustering and to assess its performance in MU-MIMO systems employing hybrid precoding schemes.

A Novel Nonlinear and Non-iterative Precoding Technique for Single and Multi User MIMO Systems

A modification of the well known linear and iterative based precoder intended for both single and multi-user multiple-input multiple-output (MIMO) has been proposed. The proposed precoder uses the nonlinear and non-iterative processing strategies to obtain more efficient and less complexity designs. The non-linearity in the precoder is introduced by using the nonlinear constellation precoding technique based on maximum distance separable codes. Also, the computation complexity in iterative based precoder design is avoided by using a singular value decomposition method. The maximum likelihood detection for the linear MIMO channel is considered. The simulation results are provided in-terms of bit error rate versus signal-to-noise ratio to show that the proposed combined non-linear and non-iterative precoding schemes outperform the conventional linear and iterative based MIMO precoder designs.

Heterogeneous Multi-Tier Networks: Improper Signaling for Joint Rate-Energy Optimization

Wireless nodes in future communication systems need to overcome three barriers when compared to their transitional counterparts, namely, to support significantly higher data rates, have long-lasting energy supplies, and remain fully operational in interference-limited heterogeneous networks. This could be partially achieved by providing three promising features, which are radio frequency (RF) energy harvesting, improper Gaussian signaling, and operating in full-duplex communication mode, i.e., transmit and receive at the same time within the same frequency band. In this paper, we consider these aspects jointly in a multi-antenna heterogeneous two-tier network. In this network, the users in the femtocell share the scarce resources with the cellular users in the macro-cell and have to cope with the interference from the macro-cell base station as well as the transmitter noise and residual self-interference due to imperfect full-duplex operation. Interestingly enough, while these impairments are detrimental from the achievable rate perspective, they are beneficial from the energy harvesting aspect, as they carry RF energy. In this paper, we consider this natural tradeoff jointly and propose appropriate optimization problems for beamforming and optimal resource allocation. Moreover, various receiver structures are employed for both information detection and energy harvesting (EH) capabilities. This paper aims at characterizing the tradeoff between the achievable rates and harvested energies. Rate and energy maximization problems are thoroughly investigated. Interestingly, with sufficiently high EH demands, we observe the convergence of the rate region obtained by non-linear precoding to the rate region achieved by widely linear precoding at the base station.

Low Complexity Iterative-QR (IQR) Precoder Design Based on Structure Blocks for Massive MIMO System

Massive multiple-input multiple-output (MIMO) technology is a promising technique having a high spectral efficiency for future wireless systems. Counterintuitively, the practical issues of transmitted signals are being attenuated by fading, propagation limitations, and implement non-linear precoding are solved by enlarging system dimensions. However, the computational complexity of precoding grows with the system dimensions. The existence block diagonalization (BD) precoding, which completely pre-cancels the multiuser interference is very complicated to implement with the use of a large number of BS antennas, since it considers full multiplexing order. Motivated by the high performance of the BD and generalized for the case when the users have multiple antennas, we propose a structure blocks based on iterative QR decompositions (IQRDs) to compute the precoding scheme. The proposed BLIQR-based precoder designed partitioned the channel matrix into capable square-wise blocks matrix and the IQRDs are applied to the blocks channel matrix. The channel matrix is partitioned such that it can fulfill the multiplexing order for the use in Massive MIMO. The computational complexity of the proposed design is effectively reduced and the sum-rate performance is improved, especially in large number of BS antennas. The performance of the proposed scheme achieves a good trade-off between throughput and computational complexity.

Non-Linear Precoding Scheme Using MMSE Based Successive Inter-User Interference Pre-Cancellation and Perturbation Vector Search for Downlink MU-MIMO Systems

Non-Linear Precoding Scheme Using MMSE Based Successive Inter-User Interference Pre-Cancellation and Perturbation Vector Search for Downlink MU-MIMO Systems

Quantized Precoding for Massive MU-MIMO

Massive multiuser (MU) multiple-input multiple-output (MIMO) is foreseen to be one of the key technologies in fifth-generation wireless communication systems. In this paper, we investigate the problem of downlink precoding for a narrowband massive MU-MIMO system with low-resolution digital-to-analog converters (DACs) at the base station (BS). We analyze the performance of linear precoders, such as maximal-ratio transmission and zero-forcing, subject to coarse quantization. Using Bussgang’s theorem, we derive a closed-form approximation on the rate achievable under such coarse quantization. Our results reveal that the performance attainable with infinite-resolution DACs can be approached using DACs having only 3–4 bits of resolution, depending on the number of BS antennas and the number of user equipments (UEs). For the case of 1-bit DACs, we also propose novel nonlinear precoding algorithms that significantly outperform linear precoders at the cost of an increased computational complexity. Specifically, we show that nonlinear precoding incurs only a 3 dB penalty compared with the infinite-resolution case for an uncoded bit-error rate of 10−3, in a system with 128 BS antennas that uses 1-bit DACs and serves 16 single-antenna UEs. In contrast, the penalty for linear precoders is about 8 dB.

Performance Evaluation of NL-BMD Precoding over Analog-Digital Hybrid Beamforming for High SHF Wide-Band Massive MIMO in 5G

Massive multiple-input multiple-output (MIMO) technology is a key enabler in 5G. A configuration combining analog beamforming and digital MIMO signal processing for multi-beam multiplexing, i.e. analog-digital hybrid beamforming, is one of the promising approaches of massive MIMO. With the configuration, we can mitigate the problems of complexity and power consumption, which are serious in higher super high frequency and extremely high frequency bands. In this paper, we evaluate the performance of nonlinear block multi-diagonalization (NL-BMD) precoding, an intermediate solution between the conventional linear precoder (LP) and nonlinear precoder (NLP), over an analog-digital hybrid beamforming constitution. Through numerical evaluation assuming indoor hotspot scenarios, it is clarified that, NL-BMD yields up to 18.8% improvement and 5.1 dB gain in average sum-rate spectral efficiency performance, compared with block diagonalization (BD), which is one of the typical schemes of conventional LP, while reducing the complexity to 1/2 of the conventional NLP. In addition, even under a dynamic fading condition, NL-BMD shows tolerance for channel transitions and still better performance than BD: NL-BMD suppresses performance loss in sum-rate spectral efficiency due to channel transitions to 18.3%, whereas BD shows over 20% loss.

Linear and Nonlinear Precoding Based Dynamic Spectrum Management for Downstream Vectored G.fast Transmission

In the G.fast digital subscriber line frequency range (up to 106 or 212 MHz), where crosstalk channels may even become larger than direct channels, linear zero-forcing (ZF) precoding is no longer near-optimal for downstream (DS) vectored transmission. To improve performance, we develop a novel low-complexity algorithm for both linear and nonlinear precoding-based dynamic spectrum management that maximizes the weighted sum-rate under realistic per-line total power and per-tone spectral mask constraints. It applies to DS scenarios with a single copper line at each customer site [i.e., broadcast channel (BC) scenarios], as well as to DS scenarios with multiple copper lines at some or all customer sites (i.e., the so-called multiple-input-multiple-output-BC scenarios). The algorithm alternates between precoder and equalizer optimization, where the former relies on a Lagrange multiplier based transformation of the DS dual decomposition approach formulation into its dual upstream (US) formulation, together with a low-complexity iterative fixed-point formula to solve the resulting US problem. Simulations with measured G.fast channel data of a very high crosstalk cable binder are provided revealing a significantly improved performance of this algorithm over ZF techniques for various scenarios, and in addition, a faster convergence rate compared with the state-of-the-art WMMSE algorithm.

Nonlinear Precoding for XOR Physical Layer Network Coding in Bi-Directional MIMO Relay Systems

Nonlinear Precoding for XOR Physical Layer Network Coding in Bi-Directional MIMO Relay Systems

Joint energy efficiency optimization with nonlinear precoding in multi-cell broadcast systems

In this paper, we focus on maximizing weighted sum energy efficiency (EE) for a multi-cell multi-user channel. In order to solve this non-convex problem, we first decompose the original problem into a sequence of parallel subproblems which can optimized separately. For each subproblem, a base station employs dirty paper coding to maximize the EE for users within a cell while regulating interference induced to other cells. Since each sub-problem can be transformed to a convex multiple-access channel problem, the proposed method provides a closed-form solution for power allocation. Then, based on the derived optimal covariance matrix for each subproblem, a local optimal solution is obtained to maximize the sum EE. Finally, simulation results show that our algorithm based on non-linear precoding achieves about 20 percent performance gains over the conventional linear precoding method.

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.

Linear precoding based on polynomial expansion: reducing complexity in massive MIMO.

Massive multiple-input multiple-output (MIMO) techniques have the potential to bring tremendous improvements in spectral efficiency to future communication systems. Counterintuitively, the practical issues of having uncertain channel knowledge, high propagation losses, and implementing optimal non-linear precoding are solved more or less automatically by enlarging system dimensions. However, the computational precoding complexity grows with the system dimensions. For example, the close-to-optimal and relatively “antenna-efficient” regularized zero-forcing (RZF) precoding is very complicated to implement in practice, since it requires fast inversions of large matrices in every coherence period. Motivated by the high performance of RZF, we propose to replace the matrix inversion and multiplication by a truncated polynomial expansion (TPE), thereby obtaining the new TPE precoding scheme which is more suitable for real-time hardware implementation and significantly reduces the delay to the first transmitted symbol. The degree of the matrix polynomial can be adapted to the available hardware resources and enables smooth transition between simple maximum ratio transmission and more advanced RZF.By deriving new random matrix results, we obtain a deterministic expression for the asymptotic signal-to-interference-and-noise ratio (SINR) achieved by TPE precoding in massive MIMO systems. Furthermore, we provide a closed-form expression for the polynomial coefficients that maximizes this SINR. To maintain a fixed per-user rate loss as compared to RZF, the polynomial degree does not need to scale with the system, but it should be increased with the quality of the channel knowledge and the signal-to-noise ratio.

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.

Joint Transceiver, Data Streams, and User Ordering Optimization for Nonlinear Multiuser MIMO Systems

We consider nonlinear signal processing algorithms for downlink multiple-input multiple-output (MIMO) systems with multiple-antenna users. The design goal is to improve bit error rate (BER) performance by jointly optimizing the transceiver, data streams, and user ordering, under given total transmit power. We consider a general global objective function, whose elements are Schur-convex functions of the mean square error (MSE) of each user. With nonlinear Tomlinson-Harashima precoding combined with block successive zero-forcing precoding at the transmitter, we show that the optimal nonlinear transceiver leads to favorable diagonal and parallel structures for all users with the general global performance metric. The number of data streams of each user is allowed to be an arbitrary number no more than the rank of the effective channel. We then provide closed-form expressions of the transceiver matrices and optimal power allocation of each user, and analytically characterize the optimal number of data streams of each user for the minimax and average BER metrics. The user ordering is also optimized to further improve the system performance. We also analytically investigate the impact of channel spatial correlation on the performance of our scheme and illustrate why our proposed adaptive strategy can mitigate the performance degradation caused by channel spatial correlation. The superiority of our proposed framework is demonstrated through numerical results.

OFDM Techniques for MIMO-OFDM System: A Review

MIMO-OFDM technology converts frequency selective MIMO channel into number of parallel flat fading MIMO channel.It fundamentally simplifies the baseband receiver processing by eliminating the need of complex MIMO equalizer. In this paper every one of the strategies that provide increased BER performance for OFDM has been discussed. Linear Constellation Precoding (LCP) with subcarrier grouping technique has been introduced to overcome the multipath fading that result from conventional OFDM. Later on Nonlinear Constellation Precoding (NCP) without subcarrier grouping is introduced to replace the LCP technique. NCP strategy is adaptable to diversity channels and diversity order irrespective of their number which is not in case of LCP scheme. At end Nonlinear Constellation Precoding (NCP) with subcarrier grouping is introduced. As a conclusion, in future if the same procedures are implemented in the OFDM part of MIMO-OFDM system it will provide improved BER than conventional MIMO-OFDM system.

Nonlinear joint transmit-receive processing for coordinated multi-cell systems: centralized and decentralized

This paper proposes a nonlinear joint transmit-receive (tx-rx) processing scheme for downlink-coordinated multi-cell systems with multi-stream multi-antenna users. The nonlinear joint tx-rx processing is formulated as an optimization problem to maximize the minimum signal-to-interference noise ratio (SINR) of streams to guarantee the fairness among streams of each user. Nonlinear Tomlinson-Harashima precoding (THP) is applied at transmitters, and linear receive processing is applied at receivers, to eliminate the inter-user interference and inter-stream interference. We consider multi-cell systems under two coordinated modes: centralized and decentralized, corresponding to systems with high- and low-capacity backhaul links, respectively. For the centralized coordinated mode, transmit and receive processing matrices are jointly determined by the central processing unit based on the global channel state information (CSI) shared by base stations (BSs). For the decentralized coordinated mode, transmit and receive processing matrices are computed independently based on the local CSI at each BS. In correspondence, we propose both a centralized and a decentralized algorithm to solve the optimization problem under the two modes, respectively. Feasibility and computational complexity of the proposed algorithms are also analyzed. Simulation results prove that the proposed nonlinear joint tx-rx processing scheme can achieve user fairness by equalizing the bit error rate (BER) among streams of each user and the proposed scheme outperforms the existing linear joint tx-rx processing. Moreover, consistent with previous research results, performance of the proposed centralized nonlinear joint tx-rx processing scheme is proved to be better than that of the decentralized nonlinear joint tx-rx processing.

Constant Envelope Precoding for Single-User Large-Scale MISO Channels: Efficient Precoding and Optimal Designs

Constant envelope (CE) precoding is a very recently developed transmission approach for large antenna array systems, where each antenna is restricted to transmit CE signals and only phases are used to shape desired information signals at the receiver. CE precoding is proposed as a solution for circumventing the high peak-to-average power ratio (PAPR) problem arising in non-CE transmission approaches, which becomes a difficult hardware implementation issue in large antenna array systems. While CE precoding is a nonlinear precoding approach and introduces challenges not seen in the widely-used non-CE linear precoding approach, the former has been shown to hold great potential in large-scale single-user MISO channels from an information rate analysis viewpoint. The present paper considers single-user MISO CE precoding from a transceiver realization viewpoint. We first solve the noise-free receive signal region characterization problem. From the characterization proof, we derive a simple and efficient CE precoder algorithm whose complexity is linear in the number of antennas. Then, we consider optimal CE precoding designs when the system can perform either antenna-subset selection or unequal per-antenna power allocation-both aiming at maximizing the system performance under transmission power constraints. Polynomial-time exact algorithms for the proposed design, via simple search or convex optimization, are developed. Simulation results demonstrate that for large antenna array systems, the proposed CE precoding schemes can yield symbol error probability performance comparable to that of the non-CE maximum ratio transmission scheme.

Distributed Transmitter Optimization for the Wyner-Type Downlink via Belief Propagation

We study a Wyner-type downlink network, where any two adjacent base stations (BSs) can communicate with each other and cooperate on transmission of discrete data symbols to their intended mobile stations (MSs) situated along a circular array. With focus on the binary case, we take the symbol detection point of view and formulate a novel non-linear precoding optimization problem by imposing minimum Symbol Error Probabilities as Quality-of-Service constraints at MSs. We then cast the problem into a factor graph and propose a belief propagation (BP) framework to solve the problem in a distributed manner based on only local communication between adjacent BSs. Numerical results confirm the convergence of the distributed algorithm and demonstrate the transmit power saving from the proposed precoder over two state-of-the-art linear precoders. To the best of our knowledge, this is the first work that leverages the BP method for non-linear precoding.