Nonlinear Precoding Schemes Research Articles

Symbol-Level Precoding Through the Lens of Zero Forcing and Vector Perturbation

Symbol-level precoding (SLP) has recently emerged as a new paradigm for physical-layer transmit precoding in multiuser multi-input-multi-output (MIMO) channels. It exploits the underlying symbol constellation structure, which the conventional paradigm of linear precoding does not, to enhance symbol-level performance such as symbol error probability (SEP). It also allows the precoder to take a more general form than linear precoding. This paper aims to better understand the relationships between SLP and linear precoding, subsequent design implications, and further connections beyond the existing SLP scope. Focused on the quadrature amplitude modulation (QAM) constellations, our study is built on a basic signal observation, namely, that SLP can be equivalently represented by a zero-forcing (ZF) linear precoding scheme augmented with some appropriately chosen symbol-dependent perturbation terms, and that some extended form of SLP is equivalent to a vector perturbation (VP) nonlinear precoding scheme augmented with the above-noted perturbation terms. We examine how insights arising from this perturbed ZF and VP interpretations can be leveraged to i) substantially simplify the optimization of certain SLP design criteria, namely, total or peak power minimization subject to SEP quality guarantees; and ii) draw connections with some existing SLP designs. We also touch on the analysis side by showing that, under the total power minimization criterion, the basic ZF scheme is a near-optimal SLP scheme when the QAM order is very high -- which gives a vital implication that SLP is more useful for lower-order QAM cases. Numerical results further indicate the merits and limitations of the different SLP designs derived from the perturbed ZF and VP interpretations.

Precoding and Beamforming Techniques in mmWave-Massive MIMO: Performance Assessment

Massive MIMO and mmWave communication are the technologies for achieving 5G design goals. Fortunately, these two technologies share a symbiotic integration. As a result, amalgamating mmWave communications with massive MIMO forms,mmWave-massive MIMO,” which significantly improves spectral and energy efficiency. It also achieves high multiplexing gains and increases mobile network capacity. However, massive MIMO, mmWave communications, and mmWave-massive MIMO systems have been studied independently. Consequently, this article explores the ideas, performances, comparisons, and discussions of these three 5G technologies jointly, considering their precoding and beamforming methods. On the other hand, the complexity of these technologies increases when a large number of antennas and radio frequencies (RFs) are used. Thus, several investigations are going on to search for the appropriate precoding and beamforming strategies with low cost, power, and complexity. Therefore, massive MIMO linear precoding techniques such as zero-forcing, maximum ratio transmission, regularized zero-forcing, truncated polynomial expansion and phased zero forcing are addressed in this work. In addition, the most common non-linear precoding schemes: dirty-paper coding, Tomlinson-Harashima, and vector perturbation, are presented. Furthermore, a detailed discussion of the beamforming techniques called analog, digital, and hybrid analog-digital beamforming schemes is included. We also examine the potential of hybrid analog-digital beamforming with its fully-connected and sub-connected architecture approaches in making mmWave massive MIMO a reality. We evaluate their performance with the parameters: bit error rate, signal to noise ratio, complexity, spectral efficiency, and energy efficiency. According to the analytical and simulation results, the partially-connected hybrid analog/digital beamforming architecture offers better all-over performance for mmWave-Massive MIMO communications by compromising: power consumption, cost, complexity, and performance. Finally, the potential future directions in mmWave-massive MIMO precoding and beamforming challenges are addressed.

Two‐Stage Precoding Based on Overlapping User Grouping Approach in IoT‐Oriented 5G MU‐MIMO Systems

Downlink transmission techniques for multiuser (MU) multiple‐input multiple‐output (MIMO) systems have been comprehensively studied during the last two decades. The well‐known low complexity linear precoding schemes are currently deployed in long‐term evolution (LTE) networks. However, these schemes exhibit serious shortcomings in scenarios when users’ channels are strongly correlated. The nonlinear precoding schemes show better performance, but their complexity is prohibitively high for a real‐time implementation. Two‐stage precoding schemes, proposed in the standardization process for 5G new radio (5G NR), combine these two approaches and present a reasonable trade‐off between computational complexity and performance degradation. Before applying the precoding procedure, users should be properly allocated into beamforming subgroups. Yet, the optimal solution for user selection problem requires an exhaustive search which is infeasible in practical scenarios. Suboptimal user grouping approaches have been mostly focused on capacity maximization through greedy user selection. Recently, overlapping user grouping concept was introduced. It ensures that each user is scheduled in at least one beamforming subgroup. To the best of our knowledge, the existing two‐stage precoding schemes proposed in literature have not considered overlapping user grouping strategy that solves user selection, ordering, and coverage problem simultaneously. In this paper, we present a two‐stage precoding technique for MU‐MIMO based on the overlapping user grouping approach and assess its computational complexity and performance in IoT‐oriented 5G environment. The proposed solution deploys two‐stage precoding in which linear zero forcing (ZF) precoding suppresses interference between the beamforming subgroups and nonlinear Tomlinson‐Harashima precoding (THP) mitigates interuser interference within subgroups. The overlapping user grouping approach enables additional capacity improvement, while ZF‐THP precoding attains balance between the capacity gains and suffered computational complexity. The proposed algorithm achieves up to 45% higher MU‐MIMO system capacity with lower complexity order in comparison with two‐stage precoding schemes based on legacy user grouping strategies.

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.

Transmit Power Minimization for Vector-Perturbation Based NOMA Systems: A Sub-Optimal Beamforming Approach

Non-orthogonal multiple access (NOMA) is one of the potential multiuser supporting techniques in the fifth generation (5G) cellular systems due to its higher spectrum efficiency (SE) and cell-edge throughput. Vector-perturbation (VP) is widely known as one of the nonlinear precoding schemes that achieves near-capacity performance in practical wireless multi-input-multi-output (MIMO) communication systems. In this paper, we propose a hybrid transmission strategy based on VP and NOMA (VP-NOMA) by designing a beamforming matrix with the power allocation strategy to minimize total transmit power for certain quality of service (QoS) requirements. Rather than searching for the optimal beamforming matrix, we propose a more intuitive sub-optimal algorithm, called iteration beamforming for VP-NOMA systems (IBVP-NOMA), to find beamforming vectors. Further, different user clustering strategies are considered and compared to enhance the performance of the VP-NOMA systems. The simulation results demonstrate that the proposed method requires lower transmit power than the NOMA system without VP.

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.

Non-Linear and Non-Iterative Based Transceiver Design for SU-MIMO Systems

This paper considers the design of a low-complexity and high-performance precoder for multiple-input multiple-output (MIMO) systems. The precoder is designed by combining both nonlinear and non-iterative processing strategies. The proposed nonlinear precoding techniques employ a nonlinear constellation precoding technique based on maximum distance separable codes at the transmitter. We propose to reduce the computational complexity in iterative-based precoding algorithms by using less complex non-iterative singular value decomposition-based joint precoder and decoder pair design. The maximum likelihood detection for the linear MIMO channel is considered. The simulation results showed that the proposed nonlinear and non-iterative precoding schemes outperform the conventional linear MIMO precoder design, even when a reduced-complexity suboptimal strategy is adopted, considering the bit error rate performance.

Nonlinear Precoding for Multipair Relay Networks With One-Bit ADCs and DACs

We consider a multipair half-duplex relay communication network, where the relay is deployed with one-analog-to-digital converters and one-bit digital-to-analog converters. To suppress the interpair interference and quantization artifacts, we propose nonlinear precoding schemes to forward the quantized signals at the relay. We first present a technique based on gradient projection, and then show how to refine the solution using ordered quantization and perturbation methods. For the single-user case with BPSK symbols, we obtain a closed-form solution for the optimal transmit vector. Numerical results verify that the proposed precoding design significantly outperforms quantized linear precoding strategies.

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

Block Precoding for Peak-Limited MISO Broadcast VLC: Constellation-Optimal Structure and Addition-Unique Designs

In this paper, we investigate the design of energy-efficient space-time modulation for peak-limited MISO broadcast visible light communication (VLC) systems by cooperatively managing the non-negative multiuser interference. We first characterize a constellation-optimal structure that maximizes the worst-case minimum Euclidean distance of all users for a general space-time modulation design. It turns out that the optimal space-time constellation can be constructed via the spatial repetition of the optimal multidimensional constellation in time dimension over ideal additive white Gaussian noise channels. Then, based on this structure, we specifically design two classes of energy-efficient time-dimensional constellations: 1) for the integer overall bit rate, we design the optimal linear precoded block design, which admits fast maximum likelihood demodulation algorithms. 2) for the non-integer case, we propose a nonlinear precoding scheme called block coded modulation , which sums the code word sets of the optimal linear design and a block channel code. In addition, we show that these two classes of designs are addition-unique, thus, generating an energy-efficient mapping from users’ data to the transmitted constellations. This property enables the efficient demodulation of the sum signal from a noisy received signal as well as the decoding of individual signal from the estimated sum signal. Extensive computer simulations indicate that our addition-unique designs have remarkable performance gains over the currently available zero-forcing, minimum mean square error and time-division multiple access methods for the multiuser multi-input-single-output VLC broadcast systems.

Downlink Massive MIMO Systems: Achievable Sum Rates and Energy Efficiency Perspective for Future 5G Systems

To meet up with the ever increasing subscribers' demand for higher data rates and mobile data traffic growth in the telecommunication industry, the fifth generation (5G) systems is being considered for the next future cellular communication standards. The two principal design requirements being aimed at in 5G are robust data transmission rates in Gigabits and low power consumption systems. Massive multiple input multiple output (M-MIMO) technology is an evolving smart antenna technology which has some key promising potentials to boost 5G networks in meeting the aforementioned requirements. However, there is an emergent concern that increased number of antenna arrays in M-MIMO system could induce high power consumption and poor energy efficiency when deployed at the base stations (BSs). Also, inter-cellular interference which occurs as a result of pilot contamination, fast fading and uncorrelated noise effects in the radio channels are other open issues in M-MIMO system. This work investigates and compare the achievable sum rates and energy efficiency of a downlink single cell M-MIMO systems utilizing linear and nonlinear precoding schemes. First, we have shown how the increasing signal-to-noise ratio and M-antennas impact the achievable sum rates. Furthermore, the energy saving potentials of M-MIMO systems in macro, micro and pico cellular environments when linear and nonlinear precoding schemes are utilized at the BS have been demonstrated. Particularly, by means of power fairness index, the tradeoff among the energy efficiency, sum rate and the system users have also been presented and discussed. Results show that substantial energy efficiency improvements can be achieved in micro and pico cellular environments of downlink M-MIMO systems when non-linear successive interference cancellation precoding is applied compared to linear precoding schemes.

A fast and low-complexity matrix inversion scheme based on CSM method for massive MIMO systems

Massive multiple-input-multiple-output (MIMO), also known as very-large MIMO systems, is an attracting technique in 5G and can provide higher rates and power efficiency than 4G. Linear-precoding schemes are able to achieve the near optimal performance, and thus are more attractive than non-linear precoding schemes. However, conventional linear precoding schemes in massive MIMO systems, such as regularized zero-forcing (RZF) precoding, have near-optimal performance but suffer from high computational complexity due to the required matrix inversion of large size. To solve this problem, we utilize the Cholesky-decomposition and Sherman-Morrison lemma and propose CSM (Cholesky and Sherman-Morrison strategy)-based precoding scheme to the matrix inversion by exploiting the asymptotically orthogonal channel property in massive MIMO systems. Results are evaluated numerically in terms of bit-error-rate (BER)and average sum rate. Comparing with the Neumann series approximation of inversing matrix, it is concluded that, with fewer operations, the performance of CSM-based precoding is better than conventional methods in massive MIMO configurations.

Linear and Nonlinear Precoding Schemes for Centralized Multicell MIMO-OFDM Systems

The aim of this article is to propose and compare linear and nonlinear precoding schemes for multicell multiuser MIMO-OFDM based systems. The considered linear precoder is designed in two phases: first the intercell interference is removed by applying a linear zero-forcing algorithm. Then the system is further optimized by proposing three power allocation algorithms with per base station power constraint and different complexity tradeoffs: one optimal to minimize the average bit-error-rate and two suboptimal. The proposed nonlinear precoding is designed to minimize average bit-error-rate, over the users, conditioned to a channel realization and the transmitted data. In the high SNR regime, this problem simplifies from a constrained quadratic nonlinear optimization to a single quadratic problem with a scaling, allowing to reduce the complexity. The performance of the proposed schemes is evaluated, considering typical pedestrian scenarios based on LTE specifications. Numerical results show that the performance of the nonlinear scheme outperforms the linear ones. The nonlinear algorithm selects and inverts part of the correlation matrix unlike the linear zero-forcing where full inversion is required. This leads to a better performance as the selection allows to get a better conditioned matrix. Also, it is shown that the complexity of the nonlinear scheme is similar to the linear suboptimal closed-form one.

Design and Implementation of a Low-Complexity Multiuser Vector Precoder

Precoding techniques are used in the downlink of multiuser multiple-input multiple-output (MIMO) systems in order to separate the information data streams aimed at scattered user terminals. Vector precoding (VP) is one of the most promising non-linear precoding schemes, which achieves a performance close to the optimum albeit impractical dirty paper coding (DPC) with a feasible complexity. This contribution presents a novel design for the hardware implementation of a high-throughput vector precoder based on the Fixed Sphere Encoder (FSE) algorithm. The proposed fixed-complexity scheme greatly reduces the complexity of the most intricate part of VP, namely the search for the perturbing signal in an infinite lattice. Additionally, an optimized reduced-complexity implementation is presented which considerably reduces the resource usage at the cost of a small performance loss. Provided simulation results show the better performance of the proposed vector precoder in comparison to other fixed-complexity approaches, such as the K-Best precoder, under similar complexity constraints.

비선형 3 User Tomlinson-Harashima 전처리 코딩

본 논문에서는 세 명의 사용자가 존재하는 채널 환경에서 다중 송수신 안테나 시스템의 송신단에서 모든 사용자, 채널에 대한 정보를 완벽하게 알고 있다는 전제하에 목적지 이외의 인접한 채널이나 사용자로부터의 간섭을 먼저 제거하여 목적지로 정보를 송신하여 각 사용자들은 간섭의 영향을 받지 않도록 하는 비선형 전처리 부호화 기법을 소개하고, 이 중 가장 연구가 활발히 진행되고 있는 Tomlinson-Harashima 코딩에 기반하여 전처리 부호화기를 설계하고, 이의 성능을 더티 페이퍼 코딩 기반의 전처리 부호화기의 성능과 비교 분석하였다. In this letter, in order to reduce the inter-channel interference at the transmitted side, we design the precoder based on Tomlinson-Harashima coding, which is well know for one kind of non-linear precoding schemes, for 3-user MIMO wireless systems. And its performance is also analyzed in comparison with that of the Dirty Paper Coding based precoder.

On the achievable rates of multiple antenna broadcast channels with feedback-link capacity constraint

In this paper, we study a MIMO fading broadcast channel where each receiver has perfect channel state information while the channel state information at the transmitter is acquired by explicit channel feedback from each receiver through capacity-constrained feedback links. Two feedback schemes are considered, i.e., the analog and digital feedback. We analyze the achievable ergodic rates of zero-forcing dirty-paper coding (ZF-DPC), which is a nonlinear precoding scheme inherently superior to linear ZF beamforming. Closed-form lower and upper bounds on the achievable ergodic rates of ZF-DPC with Gaussian inputs and uniform power allocation are derived. Based on the closed-form rate bounds, sufficient and necessary conditions on the feedback channels to ensure nonzero and full downlink multiplexing gain are obtained. Specifically, for analog feedback in both AWGN and Rayleigh fading feedback channels, it is sufficient and necessary to scale the average feedback link SNR linearly with the downlink SNR in order to achieve the full multiplexing gain. While for the random vector quantization-based digital feedback with angle distortion measure in an error-free feedback link, it is sufficient and necessary to scale the number of feedback bits B per user as where M is the number of transmit antennas and is the average downlink SNR.

Multiuser TH-precoding for TDD–CDMA over multipath channels

Nonlinear precoding schemes for downlink time-division duplex–CDMA systems over multipath fading channels, are considered. First, the capacity results of a downlink CDMA system with either multiuser detection or precoding, were obtained and compared. It is seen that the two schemes exhibit similar capacity regions for both sum rate and maximum equal rate, which motivates the development of efficient nonlinear transmitter precoding techniques to reduce the receiver complexity at the mobile units without degrading the system performance. We then develop both bit-wise and chip-wise Tomlinson–Harashima (TH) multiuser precoding methods for downlink CDMA with multipath, to remove multi-user interference, inter-chip interference and inter-symbol interference. Efficient algorithms for multiuser power loading and ordering are also developed. Implementation of the proposed TH-precoding schemes in time-varying channels based on channel prediction is addressed as well. Simulations results are provided to demonstrate the effectiveness of the proposed techniques in suppressing interference in downlink CDMA.