Regularized Zero-forcing Research Articles

Asymptotic Analysis of RLS-Based Digital Precoder With Limited PAPR in Massive MIMO

This paper focuses on the performance analysis of a class of limited peak-to-average power ratio (PAPR) precoders for downlink multi-user massive multiple-input multiple-output (MIMO) systems. Contrary to conventional precoding approaches based on simple linear precoders such as maximum ratio transmission (MRT) and regularized zero-forcing (RZF), the precoders in this paper are obtained by solving a convex optimization problem. To be specific, these precoders are designed so that the power of each precoded symbol entry is restricted, and the PAPR at each antenna is tunable. By using the Convex Gaussian Min-max Theorem (CGMT), we analytically characterize the empirical distribution of the precoded vector and the joint empirical distribution between the distortion and the intended symbol vector. This allows us to study the performance of these precoders in terms of per-antenna power, per-user distortion power, signal-to-noise and distortion ratio (SINAD), and bit error probability. We show that for this class of precoders, there is an optimal transmit per-antenna power that maximizes the system performance in terms of SINAD and bit error probability.

New generalized zero forcing beamforming for serving more users in energy-harvesting enabled networks

This paper considers a multi-user wireless communication network supported by a multiple-antenna base station (BS), where the users who are located sufficiently close to the BS employ wireless energy harvesting (EH) to replenish their energy needs. The objective of this work is to design an efficient beamforming to maximize the minimum throughput among all the information users (IUs), subject to EH constraints. In this regard, transmit time-switching approach is employed, where energy and information are transmitted over different fractions of a time-slot. To achieve efficient EH, a conjugate beamforming (matched filtering) is applied. To design efficient information beamforming for max–min throughput optimization, conventional zero-forcing (ZF) beamforming can be adopted, however, it will not suppress multi-user interference if the number of users is greater than the number of antennas at the BS. To this end, different from the existing works which employ regularized zero-forcing (RZF) beamforming, this work proposes a new generalized zero-forcing (GZF) beamforming, which promises better max–min throughput compared to that achieved by the RZF beamforming. A new path-following algorithm is developed to achieve max–min throughput optimization by GZF beamforming, which is based on a simple convex quadratic program over each iteration.

Iterative Generalized Eigenvector Precoder With Deterministic Equivalents for 3D Massive MIMO

In this paper, we propose an iterative generalized eigenvector (GE) precoder design for three dimensional (3D) massive multi-input multi-output (MIMO) downlink with uniform planar array (UPA) and imperfect channel state information (CSI). We use a posterior beam based statistical channel model which includes the channel aging and the spatial correlation. We consider the problem of maximizing the expected sum-rate under a total power constraint. By replacing the expected sum-rate with their deterministic equivalents, we obtain the structure of the optimal linear precoders. The columns of the optimal precoding matrices are the generalized eigen-vectors of two matrices. One of the two matrices is related to the transmitted signal of the intended user, and the other is related to the power constraint and the leakage to other users. Furthermore, the two matrices are also functions of the precoders, thus iterative updates of the precoder are needed. Then, we investigate the power allocation and the computation of the Lagrangian multiplier, and propose an iterative algorithm based on the structure of the optimal precoders. Simulation results show that the proposed precoders can achieve significantly performance gain than the widely used regularized zero forcing (RZF) precoder and signal to leakage plus noise ratio (SLNR) precoder.

Impacts of Asynchronous Reception on Cell-Free Distributed Massive MIMO Systems

Multiple remote antenna units (RAUs) cooperate to serve a certain user in cell-free distributed massive multiple-input multiple-output (MIMO) systems. Due to the different distances between each RAU and the user, asynchronous reception effects will occur. This paper studies the impacts of asynchronous reception effects on cell-free distributed massive MIMO systems. We first derive the minimum-mean-square error (MMSE) channel estimation under the asynchronous reception effects. Given the estimated channel state information, we derive the closed-form expressions of the user achievable rates with maximum ratio transmission (MRT) and regularized zero-forcing (RZF) precoders, which are further used to analyze the impacts of asynchronous reception effects. The accuracy of the closed-form expressions are verified. Simulation results demonstrate that asynchronous reception effects cause a non-negligible drop on the system spectral efficiency. Moreover, the performance degradation is proportional to the subcarrier sequence number and even more serious with the increasing of signal-to-noise ratio (SNR) or the number of antennas per RAU.

The Role of Correlation in the Performance of Massive MIMO Systems

Massive multiple-input multiple-output (m-MIMO) is considered as an essential technique to meet the high data rate requirements of future sixth generation (6G) wireless communications networks. The vast majority of m-MIMO research has assumed that the channels are uncorrelated. However, this assumption seems highly idealistic. Therefore, this study investigates the m-MIMO performance when the channels are correlated and the base station employs different antenna array topologies, namely the uniform linear array (ULA) and uniform rectangular array (URA). In addition, this study develops analyses of the mean square error (MSE) and the regularized zero-forcing (RZF) precoder under imperfect channel state information (CSI) and a realistic physical channel model. To this end, the MSE minimization and the spectral efficiency (SE) maximization are investigated. The results show that the SE is significantly degraded using the URA topology even when the RZF precoder is used. This is because the level of interference is significantly increased in the highly correlated channels even though the MSE is considerably minimized. This implies that using a URA topology with relatively high channel correlations would not be beneficial to the SE unless an interference management scheme is exploited.

Low‐complexity linear precoding for low‐PAPR massive MU‐MIMO‐OFDM downlink systems

SummaryTo design new revolutionary wireless communication systems, orthogonal frequency‐division multiplexing (OFDM)‐based massive multiuser (MU) multiple‐input multiple‐output (MIMO) has been shown to be the most promising technology to significantly enhance the spectral, energy, and hardware efficiencies. However, massive MU‐MIMO‐OFDM transmitters exhibit signal with high peak‐to‐average power ratio (PAPR). Accordingly, the nonlinearity of the radio frequency (RF) power amplifier (PA), which causes the most severe hardware impairment, is expected to be a low‐cost and energy‐efficient component to enable cost‐ and energy‐efficient massive MU‐MIMO‐OFDM BS deployments, generating harmful in‐band distortion and out‐of‐band (OOB) emissions. In this paper, we develop a PAPR‐aware downlink transmission scheme in an OFDM‐based large‐scale MU‐MIMO. Linear precoding of data and peak‐canceling signals (PCSs) are employed to reduce the PAPRs of the transmitted signals by exploiting the excess degrees of freedom (DoFs) provided by equipping the base station (BS) by a large number of transmit antennas. Specifically, we design PCSs to be added to the frequency‐domain precoded data signals, with the goal of reducing the PAPRs of their time‐domain counterpart signals. Most importantly, the added PCSs have to lie in the null spaces of their associated MIMO channel matrices such that they do not cause any MU interference (MUI) and OOB radiation. In this regard, an efficient algorithm is developed, which is based on different data and PCSs precoders, and the corresponding achievable PAPR reduction and bit error rate (BER) performance are analyzed. Moreover, to optimize a tradeoff between performance and complexity, linear precoders based on matrix polynomials (M‐POLYs) and gradient‐iterative approaches are studied for both data and PCSs precoding. Simulation results reveal that these latter provide similar performance as the regularized zero‐forcing (RZF) and orthogonal projection null space (OPNS)‐based data and PCSs precoders, while they need much lower computational complexity. The substantial PAPR reduction provided by the proposed algorithm offers interesting insights for the design of energy‐efficient massive MU‐MIMO‐OFDM systems.

Precoding With Received-Interference Power Control for Multibeam Satellite Communication Systems

Zero-Forcing (ZF) and Regularized Zero-Forcing (RZF) precoding are low-complexity sub-optimal solutions widely accepted in the satellite communications community to mitigate the resulting co-channel interference caused by aggressive frequency reuse. However, both are sensitive to the conditioning of the channel matrix, which can greatly reduce the achievable gains. This paper brings the attention to the benefits of a design that allows some residual received interference power at the co-channel users. The motivation behind this approach is to relax the dependence on the matrix inversion procedure involved in conventional precoding schemes. In particular, the proposed scheme aims to be less sensitive to the user scheduling, which is one of the key limiting factors for the practical implementation of precoding. Furthermore, the proposed technique can also cope with more users than satellite beams. In fact, the proposed precoder can be tuned to control the interference towards the co-channel beams, which is a desirable feature that is not met by the existing RZF solutions. The design is formulated as a non-convex optimization and we study various algorithms in order to obtain a practical solution. Supporting results based on numerical simulations show that the proposed precoding implementations are able to outperform the conventional ZF and RZF schemes.

Accelerated Randomized Methods for Receiver Design in Extra-Large Scale MIMO Arrays

Massive multiple-input-multiple-output (M-MIMO) features a capability for spatial multiplexing of large number of users. This number becomes even more extreme in extra-large (XL-MIMO), a variant of M-MIMO where the antenna array is of very large size. Yet, the problem of signal processing complexity in M-MIMO is further exacerbated by the XL size of the array. The basic processing problem boils down to a sparse system of linear equations that can be addressed by the randomized Kaczmarz (RK) algorithm. This algorithm has recently been applied to devise low-complexity M-MIMO receivers; however, it is limited by the fact that certain configurations of the linear equations may significantly deteriorate the performance of the RK algorithm. In this paper, we embrace the interest in accelerated RK algorithms and introduce three new RK-based low-complexity receiver designs. In our experiments, our methods are not only able to overcome the previous scheme, but they are more robust against inter-user interference (IUI) and sparse channel matrices arising in the XL-MIMO regime. In addition, we show that the RK-based schemes use a mechanism similar to that used by successive interference cancellation (SIC) receivers to approximate the regularized zero-forcing (RZF) scheme.

Optimal Per-Antenna ADC Bit Allocation in Correlated and Cell-Free Massive MIMO

In Massive MIMO base stations (BSs), the hardware design needs to balance high spectral efficiency (SE) with low complexity. The level of hardware impairments (HWIs) indicates how strong the signal distortion introduced by hardware imperfections is. In particular, the analog-to-digital converters (ADCs) have an important impact on signal distortion and power consumption. This article addresses the fundamental problem of selecting the optimal hardware quality in the Massive MIMO space. In particular, we examine the optimal HWI and ADC bit allocation per BS antenna to maximize the SE. The results show that in co-located arrays with low channel gain variations across antennas, equal ADC bit allocation is optimal. In contrast, cell-free Massive MIMO systems benefit the most from optimizing the ADC bit allocation achieving improvements in the order of 2 [bit-per-channel-use] per user equipment when using regularized zero-forcing (RZF). In addition, when including the impact of power consumption in cell-free Massive MIMO with RZF, allocating low values of mixed ADC bit resolutions across the BS antennas can increase the energy efficiency up to 30% compared to equal ADC bit allocation.

Energy-Efficient MU-Massive-MIMO Hybrid Precoder Design: Low-Resolution Phase Shifters and Digital-to-Analog Converters for 2D Antenna Array Structures

This paper investigates a multi-user massive multiple-input multiple-output (MU-mMIMO) hybrid precoding (HP) scheme using low-resolution phase shifters (PSs) and digital-to-analog converters (DACs). The proposed HP approach involves two stages: RF beamforming based on the slowly time-varying channel second-order correlation matrix, and baseband MU precoding based on the instantaneous effective baseband channel to mitigate MU-interference by a regularized zero-forcing (RZF) technique. We consider three HP design architectures: (i) HP using full-resolution PSs and DACs, with a baseband transfer block for constant-modulus RF beamformer, (ii) HP using $b$ -bit PSs and full-resolution DACs, with an orthogonal matching pursuit (OMP) based algorithm that can approach the optimal unconstrained RF beamformer, and (iii) HP using $b$ -bit PSs and $q$ -bit DACs, taking into account also DAC quantization noise. Illustrative results show that the proposed HP schemes with low-resolution PSs can approach the sum-rate of full-resolution PSs by using only 2-bit PSs, while offering higher energy efficiency. Furthermore, a study of sum-rate results for various PS and DAC quantization levels reveals that HP can achieve near-optimal performance with only 2-bit PSs and 5-bit DACs. Moreover, a comparison of the different array configurations, namely, uniform linear array (ULA), uniform circular array (UCA), uniform rectangular array (URA), and concentric circular array (CCA), indicates that URA and CCA outperform UCA and ULA in terms of spectral and energy efficiencies.

Large-Scale Beamforming for Massive MIMO via Randomized Sketching

Massive MIMO system yields significant improvements in spectral and energy efficiency for future wireless communication systems. The regularized zero-forcing (RZF) beamforming is able to provide good performance with the capability of achieving numerical stability and robustness to the channel uncertainty. However, in massive MIMO systems, the matrix inversion operation in RZF beamforming becomes computationally expensive. To address this computational issue, we shall propose a novel randomized sketching based RZF beamforming approach with low computational complexity. This is achieved by solving a linear system via randomized sketching based on the preconditioned Richard iteration, which guarantees high quality approximations to the optimal solution. We theoretically prove that the sequence of approximations obtained iteratively converges to the exact RZF beamforming matrix linearly fast as the number of iterations increases. Also, it turns out that the system sum-rate for such sequence of approximations converges to the exact one at a linear convergence rate. Our simulation results verify our theoretical findings.

Low Complexity High-Performance Precoding Algorithms for mm-Wave MU-MIMO Communication System

In this paper, linear precoding (LP) algorithm has been studied to improve the bit error rate (BER) performance of large scale multiple input multiple output (MIMO) system. A new technique of enhancing the BER performance of linear precoding algorithm without complexity in hardware and mathematical calculations is proposed and it is used on a traditional LP algorithms like a Maximum Ratio Transmission (MRT), a Zero-Forcing (ZF), a Regularized Zero-Forcing (RZF), and a Minimum Mean Square Error (MMSE) for Millimeter wave MU-MIMO communication system. A new technique is also used to mitigate the BER gab problem between (ZF, MMSE) and (RZF, MMSE) linear precoding algorithms. The result shows that with using the new technique, the BER performance of modified LP significantly outperform their traditional LP by 10−5 when using 4 element of BS antenna, 10−6 when using 16 element of BS antenna and mitigate the BER gab problem at different signal to noise ratio (SNR).

Large System Analysis of Downlink MISO-NOMA System via Regularized Zero-Forcing Precoding With Imperfect CSIT

This letter studies the multiple-input single-output (MISO) non-orthogonal multiple-access (NOMA) downlink using regularized zero-forcing (RZF) precoding with imperfect channel state information (CSI). We first propose a new user scheduling scheme based on imperfect CSI and a model to characterize the channel correlation between the weak and strong users. Then we derive an approximate expression of the ergodic sum-rate using large-system random matrix theory. This approximation permits us to derive the optimal power allocation scheme that satisfies the rate requirement of the weak users. Simulation results are presented to confirm the accuracy of the approximation and reveal the relationships between the ergodic sum-rate, the channel correlation, and other system parameters.

Spectral Efficient Precoding Design for Multi-cell Large MU-MIMO System

Large scale multiuser multi-input multi-output (MU-MIMO) system is an emerging wireless technology, which can impart huge spectral efficiency, enhanced link reliability, and serves several users simultaneously in the same frequency–time resource. Pilot contamination (PC) is the major bottleneck in achieving the optimum performance of a multi-cell large MU-MIMO system. We propose a new multi-cell block diagonalization-QR-minimum mean square error (M-BD-QR-MMSE) precoding scheme to diminish the effects of pilot contamination in a multi-cell MIMO system. The reduced effects of Pilot contamination result in the enhancement of spectral efficiency for the multi-cell MU-MIMO system. The design of the proposed scheme utilizes block diagonalization (BD) in combination with MMSE precoding that obtains large null space using QR decomposition operation to reduce intercell and intracell interference much efficiently than conventional precoding schemes. The gain in spectral efficiency with the proposed scheme is enhanced through non-universal pilot reuse in contrast to single-cell schemes. Furthermore, the downlink spectral efficiency expression has been derived for a large scale MIMO system, and the same is computed using Monte Carlo simulations to analyze the results. The numerical results depict that the proposed M-BD-QR-MMSE provides a significant improvement in the spectral efficiency in comparison with traditional single-cell MMSE (S-MMSE), regularized zero-forcing (R-ZF), ZF, Maximum ratio transmission (MRT) and multi-cell MMSE (M-MMSE) schemes. The proposed precoding design provides the spectral enhancements of 32.19 and 50.13 bit/s/Hz/cell in comparison to conventional multi-cell MMSE and single-cell MMSE precoding schemes respectively.

Efficient Kalman Filter-Based Precoder Tracking for Time-Varying Massive MIMO-OFDM Systems

The inaccuracy of channel state information (CSI) and high computational complexity for pseudo-inverse calculation in time-varying massive multiple-input multiple-output (MIMO) systems can hinder the widespread utility of regularized zero-forcing (RZF) precoding. In this letter, a novel framework is proposed for directly tracking the RZF coefficients using a Kalman filter to improve the underlying precoding performance. Specifically, a temporal autocorrelation function (ACF) of RZF coefficients is derived for the proposed tracking. Simulation results show that our proposed algorithm can almost reach the performance of the existing benchmark involving pseudo-inverse computation and thus, significantly reduces the underlying complexity by more than 32%.

Local Partial Zero-Forcing Precoding for Cell-Free Massive MIMO

Cell-free Massive MIMO (multiple-input multiple-output) is a promising distributed network architecture for 5G-and-beyond systems. It guarantees ubiquitous coverage at high spectral efficiency (SE) by leveraging signal co-processing at multiple access points (APs), aggressive spatial user multiplexing and extraordinary macro-diversity gain. In this study, we propose two distributed precoding schemes, referred to as \textit{local partial zero-forcing} (PZF) and \textit{local protective partial zero-forcing} (PPZF), that further improve the spectral efficiency by providing an adaptable trade-off between interference cancelation and boosting of the desired signal, with no additional front-hauling overhead, and implementable by APs with very few antennas. We derive closed-form expressions for the achievable SE under the assumption of independent Rayleigh fading channel, channel estimation error and pilot contamination. PZF and PPZF can substantially outperform maximum ratio transmission and zero-forcing, and their performance is comparable to that achieved by regularized zero-forcing (RZF), which is a benchmark in the downlink. Importantly, these closed-form expressions can be employed to devise optimal (long-term) power control strategies that are also suitable for RZF, whose closed-form expression for the SE is not available.

Investigation of LS-MIMO systems with channel aging effects

Recently in many works, it has been identified that large-scale multiple-input-multiple-output (LS-MIMO) is one of the key technologies for achieving extraordinary gains of energy and spectral efficiencies in wireless communication systems. This technology employs low cost hardware which enlightens its significance. The efficiency of single-cell or multi-cell LS-MIMO systems is affected by various factors such as hardware impairments, energy consumption, bandwidth allocation and outdated channel. In this paper LS-MIMO systems have been analyzed with the effects of channel aging or often called outdated channel. New expression for minimum-mean-square error (MMSE) estimate has been derived for LS-MIMO system in downlink (DL). We use three precoding schemes and results show that regularized zero-forcing (RZF) gives better performance than zero-forcing (ZF) and maximum ratio combining (MRT). We also show that how Doppler’s shift in combination of outdated channel affects the performance of the system with all the above mentioned precoding schemes.

Robust Regularized ZF in Cooperative Broadcast Channel Under Distributed CSIT

In this work, we consider the sum rate performance of joint processing coordinated multi-point transmission network (JP-CoMP, a.k.a Network MIMO) in a so-called distributed channel state information (D-CSI) setting. In the D-CSI setting, the various transmitters (TXs) acquire a local, TX-dependent, estimate of the global multi-user channel state matrix obtained via terminal feedback and limited backhauling. The CSI noise across TXs can be independent or correlated, so as to reflect the degree to which TXs can exchange information over the backhaul, hence allowing to model a range of situations bridging fully distributed and fully centralized CSI settings. In this context we aim to study the price of CSI distributiveness in terms of sum rate at finite SNR when compared with conventional centralized scenarios. We consider the family of JP-CoMP precoders known as regularized zero-forcing (RZF). We conduct our study in the large scale antenna regime, as it is currently envisioned to be used in real 5G deployments. It is then possible to obtain accurate approximations on so-called deterministic equivalents of the signal to interference and noise ratios. Guided by the obtained deterministic equivalents, we propose an approach to derive a RZF scheme that is robust to the distributed aspect of the CSI, whereby the key idea lies in the optimization of a TX-dependent power level and regularization factor. Our analysis confirms the improved robustness of the proposed scheme with respect to CSI inconsistency at different TXs, even with moderate number of antennas and receivers (RXs).

Performance of Network-Assisted Full-Duplex for Cell-Free Massive MIMO

Network assisted full-duplex (NAFD) is a spatial-division duplex technique for future wireless networks with cell-free massive multiple-input multiple-output (CF massive MIMO) network, where a large number of remote antenna units (RAUs), either using half-duplex or full-duplex, jointly support truly flexible duplex including time-division duplex, frequency-division duplex and full duplex on demand of uplink and downlink traffic by using network MIMO methods. With NAFD, bi-directional data rates of the wireless network could be increased and end-to-end delay could be reduced. In this paper, the spectral efficiency of NAFD communications in CF massive MIMO network with imperfect channel state information (CSI) is investigated under spatial correlated channels. Based on large dimensional random matrix theory, the deterministic equivalents for the uplink sum-rate with minimum-mean-square-error (MMSE) receiver as well as the downlink sum-rate with zero-forcing (ZF) and regularized zero-forcing (RZF) beamforming are derived. Numerical results show that under various environmental settings, the deterministic equivalents are accurate in both a large-scale system and system with a finite number of antennas. It is also shown that with the downlink-to-uplink interference cancellation, the uplink spectral efficiency of CF massive MIMO with NAFD could be improved. The spectral efficiencies of NAFD with different duplex configurations such as in-band full-duplex, and half-duplex are compared. With the same total numbers of transmit and receive antennas, NAFD with half-duplex RAUs offers a higher spectral efficiency. To alleviate the uplink-to-downlink interference, a novel genetic algorithm based user scheduling strategy (GAS) is proposed. Simulation results show that the achievable downlink sum-rate by using the GAS is greatly improved compared to that by using the random user scheduling.

Non-Iterative Downlink Training Sequence Design Based on Sum Rate Maximization in FDD Massive MIMO Systems

This paper considers the problem of downlink (DL) training sequence design with limited coherence time for frequency division duplex (FDD) massive MIMO systems in a general scenario of single-stage precoding and distinct spatial correlations between users. To this end, a computationally feasible solution for designing the DL training sequences is proposed using the principle of linear superposition of sequences constructed from the users' channel covariance matrices. Based on the non-iterative superposition training structure and the P-degrees of freedom (P-DoF) channel model, a novel closed-form solution for the optimum training sequence length that maximizes the DL achievable sum rate is provided for the eigenbeamforming (BF) precoder. Additionally, a simplified analysis that characterizes the sum rate performance of the BF and regularized zero forcing (RZF) precoders in closed-form is developed based on the method of random matrix theory and the P-DoF channel model. The results show that the superposition training sequences achieve almost the same rate performances as state-of-the-art training sequence designs. The analysis of the complexity results demonstrates that more than four orders-of-magnitude reduction in the computational complexity is achieved using the superposition training design, which signifies the feasibility of this approach for practical implementations compared with state-of-the-art iterative algorithms for DL training designs. Importantly, the results indicate that the analytical solution for the optimum training sequence length with the P-DoF channel model can be effectively used with high accuracy to predict the sum rate performance in the more realistic one ring (OR) channel model, and thus, near optimal solutions can be readily obtained without resorting to computationally intensive optimization techniques.