Linear Precoding Research Articles

Secure Precoding in MIMO-NOMA: A Deep Learning Approach

A novel signaling design for secure transmission over two-user multiple-input multiple-output non-orthogonal multiple access channel using deep neural networks (DNNs) is proposed. The goal of the DNN is to form the covariance matrix of users' signals such that the message of each user is transmitted reliably while being confidential from its counterpart. The proposed DNN linearly precodes each user's signal before superimposing them and achieves near-optimal performance with significantly lower run time. Simulation results show that the proposed models reach about 98% of the secrecy capacity rates. The spectral efficiency of the DNN precoder is much higher than that of existing analytical linear precoders--e.g., generalized singular value decomposition--and its on-the-fly complexity is several times less than the existing iterative methods.

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.

A Novel Tri-Staged RIA Scheme for Cooperative Cell Edge Users in a Multi-Cellular MIMO IMAC

In the real world of wireless communication systems, one solution to the practical limitation of interference alignment in terms of global channel state information at the transmitter (CSIT) requirement is to consider a linear precoding approach that only uses delayed CSIT known as retrospective interference alignment (RIA). Therefore, in the proposed work, a novel RIA scheme for the cooperative cell edge (CE) users that are more vulnerable to inter-cell interference in a multi-cellular multiple-input multiple-output (MIMO) interference multiple access channels (IMAC) is presented. The core idea of the proposed RIA is characterized by interference refining at the end of the first two stages and interference redirecting at the third stage. The initial stage 1 involves feeding the base station (BS) in cell-1 with the data streams from the cooperative CE users. During stage 2, the BS in cell-2 is fed with data streams from the cooperative CE users in cell-2. In the final stage 3, the overheard equation redirecting is performed. Based on the proposed method, we showed that for a three CE user cooperative multi-cellular MIMO IMAC channel, the achievable degrees of freedom (DoF) is 24/7 and later extended to a general L CE user cooperative multi-cellular MIMO IMAC channel and obtained the desired DoF as 2L(L+1)/2L+1. The simulation result shows that in comparison with the other benchmark schemes considered, the proposed scheme provides a greater DoF and thereby enhances the performance of cooperative CE users.

Globally Optimal Spectrum- and Energy-Efficient Beamforming for Rate Splitting Multiple Access

Rate splitting multiple access (RSMA) is a promising non-orthogonal transmission strategy for next-generation wireless networks. It has been shown to outperform existing multiple access schemes in terms of spectral and energy efficiency when suboptimal beamforming schemes are employed. In this work, we fill the gap between suboptimal and truly optimal beamforming schemes and conclusively establish the superior spectral and energy efficiency of RSMA. To this end, we propose a successive incumbent transcending (SIT) branch and bound (BB) algorithm to find globally optimal beamforming solutions that maximize the weighted sum rate or energy efficiency of RSMA in Gaussian multiple-input single-output (MISO) broadcast channels. Numerical results show that RSMA exhibits an explicit globally optimal spectral and energy efficiency gain over conventional multi-user linear precoding (MU-LP) and power-domain non-orthogonal multiple access (NOMA). Compared to existing globally optimal beamforming algorithms for MU-LP, the proposed SIT BB not only improves the numerical stability but also achieves faster convergence. Moreover, for the first time, we show that the spectral/energy efficiency of RSMA achieved by suboptimal beamforming schemes (including weighted minimum mean squared error (WMMSE) and successive convex approximation) almost coincides with the corresponding globally optimal performance, making it a valid choice for performance comparisons. The globally optimal results provided in this work are imperative to the ongoing research on RSMA as they serve as benchmarks for existing suboptimal beamforming strategies and those to be developed in multi-antenna broadcast channels.

Improved Iterative Inverse Matrix Approximation Algorithm for Zero Forcing Precoding in Large Antenna Arrays

Precoding algorithms are used in massive multiple-input multiple-output (mMIMO) communication systems to ensure effective signal transmission. The zero-forcing (ZF) is one of the most common linear precoding algorithms used in MIMO and mMIMO systems. ZF precoding is complex to implement because it requires direct matrix inversion of the gram matrix. Iterative algorithms have been proposed for approximating matrix inversions. However, iterative algorithms require initial conditions and pre-computations to converge to the optimal transmitted signal vector. This paper proposes a new improved iterative algorithm that guarantees convergence under any circumstances without dependency on any optimized initial parameter or condition. The proposed algorithm is based on a three-step iterative and iterative generalized inverse matrix approximation algorithm. The proposed algorithm was verified using a new correlated channel model that included mutual coupling effects and gain and phase variances caused by radio frequency elements at a base station (BS). The computational complexity of the proposed algorithm was then computed. This study analyzes and compares the bit error rate (BER) performance of the proposed algorithm with that of prominent existing algorithms. Moreover, the sum-rate performance of the proposed algorithm was analyzed. Simulations were performed under both correlated and uncorrelated channel conditions, for comparison and analysis. The simulation results demonstrate that the proposed algorithm outperforms the compared algorithms in terms of the convergence and convergence rates.

Linear Precoding for the Downlink of Cognitive Radio Network

In this paper, a multiple-input–single-output (MISO) overlay cognitive radio (CR) network is considered in which a primary base station (PBS) and a cognitive base station (CBS) share the same spectrum to transmit the information. We consider a novel linear precoding technique to cannel the interferences which is bring about by the CBS’s transmission. Three theorems about the design of the precoding and decoding matrices are put forward. With the linear precoding and decoding, the BER performance of the PBS and CBS are improved significantly. At the same time, the capacity of the PBS and CBS channels are analyzed.

Precise Performance Characterization of Precoded Integer Forcing Applied to Two Parallel Channels

Precoded integer-forcing equalization is a low-complexity transmission and reception scheme, primarily designed for open-loop communication. The data is encoded into independent streams, all using the same linear code, after which linear precoding is applied, while integer-forcing equalization is applied at the receiver side. Previous works have established that this architecture achieves channel capacity up to a finite gap for general multiple-input multiple-output Gaussian channels, as well as obtained tighter bounds for the special case of diagonal (parallel) channels. The present work provides a precise performance characterization when integer-forcing equalization is applied to two parallel channels and where precoding is done using the full-diversity rotation matrix cyclo <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> . It is shown that this scheme achieves capacity up to a gap bounded by <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\log _{2}({\scriptstyle ^{\scriptstyle 9}}\hspace {-0.224em}/\hspace {-0.112em}{\scriptstyle 5})$ </tex-math></inline-formula> bits per complex channel use when the standard integer-forcing receiver is used, and the gap is reduced to <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\log _{2}({\scriptstyle ^{\scriptstyle 5}}\hspace {-0.224em}/\hspace {-0.112em}{\scriptstyle 4})$ </tex-math></inline-formula> bits per complex channel use when its successive decoding variant is applied. In addition, a full characterization of the basis transformation matrices used by the integer-forcing receiver is derived. These turn out to consist only of Fibonacci numbers and are explicitly determined as a function of the condition number. The results obtained are also highly relevant to lattice-reduction detection schemes.

A Low-Complexity Hybrid Linear and Nonlinear Precoder for Line-Of-Sight Massive MIMO With Max-Min Power Control

In line-of-sight (LOS) massive MIMO, there is a nonnegligible probability that the channel vectors of some users become correlated. In these correlated scenarios, nonlinear precoders can be used instead of linear precoders at the cost of high computational complexity. To reduce the complexity of nonlinear precoders, hybrid linear and nonlinear precoders have been suggested in 5G New Radio (NR). In this paper, we find the probability that there is at least one pair of correlated users and we find the average number of correlated users. We propose a hybrid linear and nonlinear precoder (HLNP) with max-min power control for which the served users are divided into two groups. By employing a proposed modified Tomlinson-Harashima Precoding (THP), we design and combine the transmit vectors of the two groups such that inter-group interference is removed. Simulation results show that by employing HLNP instead of zero-forcing, the required transmit power to assure a given average block error rate (BLER) with 95% probability is reduced. For a 64-antennas BS, when modified THP is used for 3 out of 10 users in HLNP, the transmit power is reduced by up to 4.70 dB to assure an average BLER of 10 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">−2</sup> using 16QAM and 64QAM constellations with NR low-density parity-check codes.

Performance Analysis of Linear Precoding in Downlink Based on Polynomial Expansion on Massive MIMO Systems

The performance of linear precoding schemes in downlink Massive MIMO systems is dealt with in this paper. Linear precoding schemes are incorporated with zero-forcing (ZF) and maximum ratio transmission (MRT), truncated polynomial expansion (TPE), regularized zero force (RZF) in Downlink massive MIMO systems. Massive MIMO downlink output is evaluated with linear precoding included. This paper expresses the performance of achievable sum-rate linear precoding with variable signal-to-noise (SNR) ratio and achievable sum rate and several transmitter-receiver antennas, such as imperfect CSI, less complex processing, and inter-user interference. The transmitter has complete state information on the channel. The information narrates how a signal propagates to the receiver from the transmitter and reflects, for example, the cumulative effect of distance scattering, fading, and power decay. They show that the performance analysis of two linear precoding techniques, i.e., Maximum Ratio Transmission (MRT) and Zero Forcing (ZF) for downlink mMIMO output network over a perfect chain. The results show the improved ZF precoding achievable sum rate compared to the MRT precoding schemes and compared the average achievable rate RZF and TPE.

Practical RIS-Aided Coded Systems: Joint Precoding and Passive Beamforming

Reconfigure intelligent surface (RIS) is considered as a promising technology for next generation wireless networks to improve spectrum efficiency or energy efficiency. This letter, for the first time, investigates a practical RIS-aided coded system. Specially, we consider a forward-error-correction (FEC) code and a linear precoder at the transmitter, while a low-complexity iterative receiver is adopted. In addition, the inter-symbol interference (ISI) channels are considered. We aim to jointly optimize the precoding and the passive beamforming of the RIS to minimize the transmission power given the bit error rate (BER). To solve this non-convex optimization problem, we utilize the alternate optimization to iteratively optimize the precoding and passive beamforming, which are respectively a convex problem and a fractional programming problem. Numerical results show that significant performance improvement can be achieved with the proposed optimization scheme.

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.

Knowledge Distillation-Aided End-to-End Learning for Linear Precoding in Multiuser MIMO Downlink Systems With Finite-Rate Feedback

We propose a deep learning-based channel estimation, quantization, feedback, and precoding method for downlink multiuser multiple-input and multiple-output systems. In the proposed system, channel estimation and quantization for limited feedback are handled by a receiver deep neural network (DNN). Precoder selection is handled by a transmitter DNN. To emulate the traditional channel quantization, a binarization layer is adopted at each receiver DNN, and the binarization layer is also used to enable end-to-end learning. However, this can lead to inaccurate gradients, which can trap the receiver DNNs at a poor local minimum during training. To address this, we consider knowledge distillation, in which the existing DNNs are jointly trained with an auxiliary transmitter DNN. The use of an auxiliary DNN as a teacher network allows the receiver DNNs to additionally exploit lossless gradients, which is useful in avoiding a poor local minimum. For the same number of feedback bits, our DNN-based precoding scheme can achieve a higher downlink rate compared to conventional linear precoding with codebook-based limited feedback.

Link and System-Level NOMA Simulator: The Reproducibility of Research

This study focuses on the design of a MATLAB platform for non-orthogonal multiple access (NOMA) based systems with link-level and system-level analyses. Among the different potential candidates for 5G, NOMA is gaining considerable attention owing to the many-fold increase in spectral efficiency as compared to orthogonal multiple access (OMA). In this study, a NOMA simulator is presented for two and more than two users in a single cell for link-level analysis; whereas, for system-level analysis, seven cells and 19 cells scenarios were considered. Long-term evolution (LTE) was used as the baseline for the NOMA simulator, while bit error rate (BER), throughput and spectral efficiency are used as performance metrics to analyze the simulator performance. Moreover, we demonstrated the application of the NOMA simulator for different simulation scenarios through examples. In addition, the performance of multi-carrier NOMA (MC-NOMA) was evaluated in the presence of AWGN, impulse noise, and intercell interference. To circumvent channel impairments, channel coding with linear precoding is suggested to improve the BER performance of the system.

Quantized precoding and companding schemes for PAPR reduction in UFMC‐based massive MIMO downlink systems

AbstractUniversal‐filtered multi‐carrier (UFMC) is a promising waveform technology, which inherits the robustness of FBMC and simplicity of OFDM. In this article, the UFMC waveform is combined with the massive multi‐user multiple‐input and multiple‐output (MU‐MIMO) technology to meet the desired needs of future wireless networks. In order to eliminate MU interference (MUI), the precoding is essential in massive MU‐MIMO downlink. However, the transmitted signals produced by the precoders have high peak‐to‐average power ratio (PAPR), thus resulting in reduction of power efficiency of the system. Hence, this article proposes the quantized MU precoding and companding schemes to increase the power efficiency of UFMC‐based massive MU‐MIMO downlink systems. A nonlinear quantized precoder called squared‐infinity norm Douglas‐Rachford splitting (SQUID), which generates signals with constant envelope, is proposed. The proposed SQUID precoder reduces the power consumption and MUI of UFMC‐based massive MU‐MIMO systems. Moreover, a piecewise linear companding (PLC) scheme, which further reduces the PAPR by employing two threshold values and one companding parameter, is also proposed. The simulation results confirm that the proposed UFMC‐based massive MU‐MIMO with quantized nonlinear SQUID precoding provides better performance than quantized linear precoders. Besides, the proposed system with the PLC scheme offers better PAPR reduction of 4.5 dB when compared with linear nonsymmetrical transform and ‐law schemes.

Cooperative Multiple-Access Channels With Distributed State Information

This paper studies a memoryless state-dependent multiple access channel (MAC) where two transmitters wish to convey a message to a receiver under the assumption of causal and imperfect channel state information at transmitters (CSIT) and imperfect channel state information at receiver (CSIR). In order to emphasize the limitation of transmitter cooperation between physically distributed nodes, we focus on the so-called distributed CSIT assumption, i.e., where each transmitter has its individual channel knowledge, while the message can be assumed to be partially or entirely shared a priori between transmitters by exploiting some on-board memory. Under this setup, the first part of the paper characterizes the common message capacity of the channel at hand for arbitrary CSIT and CSIR structure. The optimal scheme builds on Shannon strategies, i.e., optimal codes are constructed by letting the channel inputs be a function of current CSIT only. For a special case when CSIT is a deterministic function of CSIR, the considered scheme also achieves the capacity region of a common message and two private messages. The second part addresses an important instance of the previous general result in a context of a cooperative multi-antenna Gaussian channel under i.i.d. fading operating in frequency-division duplex mode, such that CSIT is acquired via an explicit feedback of perfect CSIR. The capacity of the channel at hand is achieved by distributed linear precoding applied to Gaussian codes. Surprisingly, we demonstrate that it is suboptimal to send a number of data streams bounded by the number of transmit antennas as typically considered in a centralized CSIT setup. Finally, numerical examples are provided to evaluate the sum capacity of the binary MAC with binary states as well as the Gaussian MAC with i.i.d. fading.

On Linearly Precoded Rate Splitting for Gaussian MIMO Broadcast Channels

In this paper, we consider a general $K$ -user Gaussian multiple-input multiple-output (MIMO) broadcast channel (BC). We assume that the channel state is deterministic and known to all the nodes. While the private-message capacity region is well known to be achievable with dirty paper coding (DPC), we are interested in the simpler linearly precoded transmission schemes. In particular, we focus on linear precoding schemes combined with rate-splitting (RS). First, we derive an achievable rate region with minimum mean square error (MMSE) precoding at the transmitter and joint decoding of the sub-messages at the receivers. Then, we study the achievable sum rate of this scheme and obtain two findings: 1) an analytically tractable upper bound on the sum rate that is shown numerically to be a close approximation, and 2) how to reduce the number of active streams – crucial to the overall complexity – while preserving the sum rate to within a constant loss. The latter results in two practical algorithms: a stream elimination algorithm and a stream ordering algorithm. Finally, we investigate the constant-gap optimality of linearly precoded RS with respect to the capacity. Our result reveals that, while the achievable rate of linear precoding alone can be arbitrarily far from the capacity, the introduction of RS can help achieve the capacity region to within a constant gap in the two-user case. Nevertheless, we prove that the RS scheme’s constant-gap optimality does not extend to the three-user case. Specifically, we show, through a pathological example, that the gap between the sum rate and the sum capacity can be unbounded.

Millimeter Wave Massive MIMO Downlink Per-Group Communications With Hybrid Linear Precoding

We address the problem of analyzing and classifying into groups the downlink channel environment in a dense millimeter-wavelength cell, accounting for path loss, multipath fading, and User Equipment (UE) blocking, by employing a hybrid propagation and multipath fading model, thus using accurate inter-group interference modeling. The base station (BS) employs a large Uniform Planar Array (UPA) to facilitate massive Multiple-Input, Multiple-Output (MIMO) communications with high efficiency. UEs are equipped with a single antenna and are distributed uniformly within the cell. The key problem is analyzing and defining groups toward efficient precoding. Because balanced throughput is desired between groups, up to four separate frequency sub-carriers are employed in an Orthogonal Frequency Division Multiple Access (OFDMA) system. We show that by employing three or four OFDMA subcarriers, depending on the number of UEs in the cell and the cell range, the UEs can be efficiently separated into <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">high-throughput</i> groups, with each group employing Virtual Channel Model Beams (VCMB) based inner precoding, followed by efficient Multi-User Multiple-Input Multiple-Output (MU-MIMO) outer precoders. For each group, we study two different sub-grouping methods offering different advantages. We show that the improvement offered by Zero-Forcing Per-Group Precoding (ZF-PGP) over Matched Filter Precoding (MFP) and Zero-Forcing Precoding (ZFP) is very high when finite-alphabet inputs are used. We also show ZF-PGP with finite-alphabet inputs significantly outperforms MFP with Gaussian inputs in certain realistic setups. Finally, a new technique for power allocation among different UEs is proposed, called Optimized Per-Group Power Allocation (OPGPA), which achieves much higher power efficiency jointly with equal throughput among all UEs in each group.

Promising Gains of 5G Networks with Enhancing Energy Efficiency Using Improved Linear Precoding Schemes

Promising Gains of 5G Networks with Enhancing Energy Efficiency Using Improved Linear Precoding Schemes

Diversity Enhancement of MIMO System with GA Optimized Linear Precoding of Orthogonal Space-Time Block Codes

The MIMO (Multiple-Input Multiple-Output) systems in the field of digital communications make it possible to improve data transmission according to two main parameters which are often antagonistic: the information rate and the transmission reliability estimated in average binary error probability (BEP) term. With such systems, CSI (Channel State Information) on transmission is a key point for reducing the BEP thanks to different power allocation strategies. Thus, a linear precoder on transmission associated with a linear decoder on reception can optimize a particular criterion thanks to this information. This paper proposes a MIMO system with precoded orthogonal space-time block codes (OSTBC) optimized by Genetic Algorithm with ZF and MMSE equalization. The performance evaluation is achieved by BER vs. SNR graphs.

Deep-learning based linear precoding for MIMO channels with finite-alphabet signaling

This paper studies the problem of linear precoding for multiple-input multiple-output (MIMO) communication channels employing finite-alphabet signaling. Existing solutions typically suffer from high computational complexity due to costly computations of the constellation-constrained mutual information. In contrast to existing works, this paper takes a different path of tackling the MIMO precoding problem. Namely, a data-driven approach, based on deep learning, is proposed. In the offline training phase, a deep neural network learns the optimal solution on a set of MIMO channel matrices. This allows the reduction of the computational complexity of the precoder optimization in the online inference phase. Numerical results demonstrate the efficiency of the proposed solution vis-à-vis existing precoding algorithms in terms of significantly reduced complexity and close-to-optimal performance.