Hybrid Precoding Algorithm Research Articles

Optical TTD compensation network-based phase precoding for THz massive MIMO systems

In sixth generation (6G) communications, terahertz (THz) communication is one of the most important technologies in the future due to its ultra-bandwidth, where hybrid beamforming has been widely used to solve the severe transmission attenuation in the THz band. However, the use of frequency-flat phase shifters in hybrid beamforming leads to the beam split effect. To solve the beam split influence, we propose a novel optical true time delay compensation network (OTTDCN)-based phase precoding structure with low power consumption. In the proposed scheme, the OTTDCN pre-generates multiple beam compensation modes to achieve phase compensation for different frequencies. As a result, the compensated beams can be reoriented toward the target direction at different frequencies. Moreover, a low-complexity beam compensation mode-based hybrid precoding algorithm is proposed, where the selection of the optimal beam compensation modes used for all radio-frequency (RF) chains with finite beam compensation modes is considered. The results show that the OTTDCN-based phase precoding scheme can effectively alleviate the beam split effect with low power consumption and achieve near-optimal performance.

JCNN-Based DD Hybrid Precoding Algorithm With TPSAS Structure for FD-MIMO Systems

JCNN-Based DD Hybrid Precoding Algorithm With TPSAS Structure for FD-MIMO Systems

DL-PC algorithm for partially-connected hybrid precoding in massive MIMO systems

In hybrid precoding, a partially-connected (PC) architecture has aroused significant attention for its low hardware complexity. Unfortunately, the hybrid precoding with the PC architecture may suffer from a severe spectral efficiency loss. To overcome the loss, a deep learning-based hybrid precoding algorithm for the PC architecture is proposed in this paper. Firstly, the optimization problem of hybrid precoding is transformed into a neural network prediction problem. Furthermore, a convolutional neural network(CNN) is designed to predict the hybrid precoder, where the channel matrix is used as input. Especially, to meet the constraints of the hybrid precoder, two lambda layers are introduced into the CNN architecture. Specifically, a lambda1 layer is constructed to address the constant modulus constraint of the analog precoding matrix and the block diagonal constraint. Then, a lambda2 layer is constructed to optimize the digital precoding matrix and address the transmit power constraint. Finally, the vectorized hybrid precoding matrix is output by the well-trained network. Simulation results show that the proposed algorithm can enhance spectral efficiency and energy efficiency with lower computation time.

Low‐complexity unsupervised learning‐based hybrid precoding for massive MIMO systems

AbstractHybrid precoding can significantly reduce the number of required radio frequency (RF) chains in massive MIMO systems. However, due to the large number of antennas and the high‐dimensional channel, the existing hybrid precoding algorithms usually require very high complexity. In this paper, we propose a convolutional neural network (CNN)‐based hybrid precoding scheme by utilizing unsupervised learning to reduce both the computational complexity and space complexity. Specifically, we first design a low‐complexity CNN structure to achieve the analog precoder, where the size of the convolution kernel and the number of channels are reduced by the further improved inception network. Then, we obtain the digital precoder by the classical zero‐forcing (ZF) algorithm. Simulation results show that, the proposed CNN‐based hybrid precoding can approach the sum‐rate performance of the classical two‐stage hybrid precoding but has much lower complexity.

Digital Joint Equivalent Channel Hybrid Precoding for Millimeter Wave Massive MIMO Systems

Aiming at the problem that the spectral efficiency of hybrid precoding (HP) is too low in the current millimeter-wave (mmWave) massive multiple input multiple output (MIMO) system, this paper proposes a digital joint equivalent channel hybrid precoding algorithm. Based on the introduction of digital encoding matrix iteration. First, the objective function is expanded to obtain the relation equation, and the pseudo-inverse iterative function of the analog encoder is derived by using the pseudo-inverse method, which solves the problem of greatly increasing the amount of computation caused by the lack of rank of the digital encoding matrix, and reduces the overall complexity of hybrid precoding. Secondly, the analog coding matrix and the millimeter-wave sparse channel matrix are combined into an equivalent channel, and then the equivalent channel is subjected to Singular Value Decomposition (SVD) to obtain a digital coding matrix, and then the derived pseudo-inverse iterative function is used to iteratively regenerates the simulated encoding matrix. The simulation results show that the proposed algorithm improves the system spectral efficiency by 10–20% compared with other algorithms, and the stability is also improved.

Joint hybrid-precoding design for MU-MISO systems with a subconnected architecture

In this study, we propose a joint hybrid-precoding algorithm for multiuser multiple-input single-output downlink systems. Specifically, we consider that the base station employs an energy-efficient hybrid-precoding subconnected (SC) architecture with fixed equal subarrays (FESA) (SC-FESA). Optimizing the analog precoding matrix in an SC-FESA architecture is challenging due to its unique constraint structure. In this study, to maximize system sum rate, we propose an efficient method to transform the system’s sum-rate optimization problem into a continuous and differentiable objective function wherein only the nonzero elements of the analog precoding matrix are optimized. For the formulated problem, we develop an alternating optimization (AO) approach to jointly optimize the digital and analog precoders in succession by maximizing the system’s sum rate. Specifically, in the proposed AO method, when the digital precoder is fixed, we employ the Riemannian conjugate gradient algorithm to generate the analog precoder. Furthermore, when the analog precoder is fixed, we use the minimum mean squared error method to obtain the digital precoder. Numerical simulation results show that the proposed AO algorithm improves the sum rate and energy efficiency of the SC-FESA architecture compared to existing algorithms.

Improved SIC-SVD Hybrid Precoding Algorithm for Indoor Sub-THz Systems

Improved SIC-SVD Hybrid Precoding Algorithm for Indoor Sub-THz Systems

Deep learning-driven MIMO: Data encoding and processing mechanism

Large-scale Multiple-Input Multiple Output (MIMO) is the key technology of 5G communication. However, dealing with physical channels is a complex process. Machine learning techniques have not been utilized commercially because of the limited learning capabilities of traditional machine learning algorithms. We design a deep learning hybrid precoding scheme based on the attention mechanism. The method mainly includes channel modeling and deep learning encoding two modules. The channel modeling module mainly describes the problem formally, which is convenient for the subsequent method design and processing. The model design module introduces the design framework, details, and main training process of the model. We utilize the attention layer to extract the eigenvalues of the interference between multiple users through the output attention distribution matrix. Then, according to the characteristics of inter-user interference, the loss minimization function is used to study the optimal precoder to achieve the maximum reachable rate of the system. Under the same condition, we compare our proposed method with the traditional unsupervised learning-based hybrid precoding algorithm, the TTD-based (True-Time-Delay, TTD) phase correction hybrid precoding algorithm, and the deep learning-based method. Additionally, we verify the role of attention mechanism in the model. Extensive simulation results demonstrate the effectiveness of the proposed method. The results of this research prove that deep learning technology can play a driving role in the encoding and processing of MIMO with its unique feature extraction and modeling capabilities. In addition, this research also provides a good reference for the application of deep learning in MIMO data processing problems.

Hybrid precoding design forMmWavemulti‐user massiveMIMOsystems under high mobility

AbstractStudying hybrid precoding in a high mobility scenario is challenging task. Because the channel changes quickly with time and becomes double selective fading in the spatial domain. As a result, there is a difficulty to achieve perfect channel state information or estimate the channel under high mobility. In this paper, an applicable hybrid precoding based on amplitude and phase excitation beams for millimeter wave (mmWave) massive multiple input multiple output (MIMO) systems is proposed under high speed railway. The proposed hybrid precoding uses the data from the locations of the mobile stations to build the amplitude and phase beam matrix. The proposed precoders and decoders are designed to maximize the mobile service. An optimization problem of mobile service maximization is formulated for designing hybrid precoders and decoders. To solve the optimization problem, a heuristic technique under power constraint is provided. The proposed hybrid precoding algorithm is compared with analog only beam steering algorithm, partially connected hybrid precoding algorithm and fully connected hybrid precoding algorithm. Results illustrated that the proposed precoding scheme outperforms the other precoding algorithms and handover success probability is enhanced under high mobility.

Adaptive Hybrid Precoding With High Energy Efficiency for Millimeter Wave Communication Systems

Conventional hybrid precoding architectures for millimeter wave systems can be classified into two categories: fully-connected (FC) and subconnected (SC). However, due to the large number of phase shifters (PSs), the conventional hybrid precoding architectures often suffer from high power consumptions. To this end, two novel energy-efficient architectures are proposed, which are, respectively, named as adaptive FC (AFC) architecture and adaptive SC (ASC) architecture. The proposed architectures can adapt the connections between the radio frequency chains and antenna elements according to the channel environment, so that the hardware overhead can be reduced remarkably compared with the conventional counterparts. Afterwards, two novel hybrid precoding algorithms are proposed based on the AFC and ASC architectures. Particularly, in the proposed algorithm, a subspace projection-based branch-and-bound method is developed to derive the switch precoding matrix, thereby the computational burden can be reduced by more than two orders of magnitude in comparison to the traditional branch-and-bound method. Additionally, the problem of PS precoding matrix is reformulated as a positive semidefinite quadratic form via an elegant diagonal loading factor, so that the PS precoding matrix can be obtained easily. Simulation results verify that the proposed architectures and algorithms can offer both high energy efficiencies and spectral efficiencies.

CNN Based Hybrid Precoding for MmWave MIMO Systems With Adaptive Switching Module and Phase Modulation Array

Hybrid precoding is considered as a promising candidate to balance between the sum rate and the power and cost in the mmWave MIMO systems. However, it still suffers from huge power consumption due to considerable radio frequency links and phase shifters. In this study, an energy-efficient adaptive switching module (ASM) and phase modulation array (PMA) assisted hybrid precoding scheme is proposed, in which ASM is introduced to enhance the energy efficiency while PMA is employed to implement analog precoding to reduce power consumption. The ASM-PMA hybrid precoder design problem related to three matrix variables is formulated. Besides, the joint ASM-PMA hybrid precoder/combiner design at both transmitter and receiver is also investigated. Owing to the tough task of joint optimization of matrix variables, we can divide it into two sub-problems. Correspondingly, alternating optimization hybrid precoding (AOHP) algorithm is suggested to solve the PMA. Then, matching theory and convolutional neural network (CNN) based algorithms are respectively proposed to seek the optimal ASM. For the CNN based scheme, relaxed adaptive switching CNN (RAS-CNN) is designed to solve the binary integer problem in the offline train stage, while in the online deployment stage, ideal adaptive switching CNN (IAS-CNN) is adopted. Furthermore, CNN accepts estimated channel as input to yield robust precoding performance and lower computational complexity. Simulation results verify that, the proposed hybrid precoding can outperform other schemes in energy efficiency with satisfactory spectral efficiency.

Spectral efficiency analysis of distributed millimeter wave massive MIMO system using spatial point processes

This paper considers a downlink distributed millimeter wave massive multi-input multi-output (D-mmMIMO) system, consisting of multiple randomly distributed radio access units (RAUs), the distribution of which is modeled as either a Poisson point process (PPP) or a Matérn hard-core point process (MHCPP). Compared with the PPP model where RAUs are randomly distributed without restriction, the MHCPP model constructed from a PPP by dependently thinning is more realistic, since it imposes a minimum distance between two RAUs so that they are not too close to each other. When a hybrid precoding algorithm based on antenna array response vectors is adopted, the upper bounds on average spectral efficiencies of the UEs for both the PPP D-mmMIMO system and MHCPP D-mmMIMO system are derived. Finally, simulation results are provided to demonstrate the validity of the developed analysis. The presented results also show that, when the MHCPP is generated from the PPP used in the PPP D-mmMIMO system, the MHCPP D-mmMIMO system with a low hard-core distance achieves a quite close performance to the PPP D-mmMIMO system, and increasing hard-core distance has a negative impact on spectral efficiency. In contrast, when the MHCPP is constructed from a different PPP, which system performs better depends on the intensities of two PPPs as well as hard core distance.

A review on Precoding Techniques For mm-Wave Massive MIMO Wireless Systems

The growing demands for high data rate wireless connectivity shed lights on the fact that appropriate spectrum regions need to be investigated so that the expected future needs will be satisfied. With this in mind, the research community has shown considerable interest in millimeter-wave (mm-wave) communication. Generally, hybrid transceivers combining the analog phase shifter and the RF chains with digital signal processing (DSP) systems are used for MIMO communication in the fifth generation (5G) wireless networks. This paper presents a survey for different precoding or beamforming techniques that have been proposed in the literature. These beamforming techniques are mainly classified based on their hardware structure into analog and digital beamforming. To reduce the hardware complexity and power consumption, the hybrid precoding techniques that combine analog and digital beamforming can be implemented for mm-wave massive MIMO wireless systems. The performance of the most common hybrid precoding algorithms has been investigated in this paper.

Weighted Sum Rate Maximization of the mmWave Cell-Free MIMO Downlink Relying on Hybrid Precoding

The cell-free MIMO concept relying on hybrid precoding constitutes an innovative technique capable of dramatically increasing the network capacity of millimeter-wave (mmWave) communication systems. It dispenses with the cell boundary of conventional multi-cell MIMO systems, while drastically reducing the power consumption by limiting the number of radio frequency (RF) chains at the access points (APs). In this paper, we aim for maximizing the weighted sum rate (WSR) of mmWave cell-free MIMO systems by conceiving a low-complexity hybrid precoding algorithm. We formulate the WSR optimization problem subject to the transmit power constraint for each AP and the constant-modulus constraint for the phase shifters of the analog precoders. A block coordinate descent (BCD) algorithm is proposed for iteratively solving the problem. In each iteration, the classic Lagrangian multiplier method and the penalty dual decomposition (PDD) method are combined for obtaining near-optimal hybrid analog/digital precoding matrices. Furthermore, we extend our proposed algorithm for deriving closed-form expressions for the precoders of fully digital cell-free MIMO systems. Moreover, we present the convergency analysis and complexity analysis of our proposed method. Finally, our simulation results demonstrate the superiority of the algorithms proposed for both fully digital and hybrid precoding matrices.

Low-complexity OTFS-based hybrid precoding in mmWave high mobility systems

The integration of aircraft into air-to-ground (A2G) communications with a variety of applications has attracted much attention, and it is critical to establish reliable communication links in A2G systems. However, suffering from the multipath effects and high Doppler frequency shifts, the quality of the transmission links is severely degraded in high mobility scenarios. To overcome the performance degradation caused by the double selective channel, a new modulation technique called orthogonal time-frequency-space (OTFS) is proposed recently. Moreover, millimeter wave (mmWave) massive multiple-input-multiple-output (MIMO) precoding is a simple and effective method to improve the system performance. Unfortunately, most of the existing MIMO-OTFS studies are implemented on the full-digital architecture, which will lead to high power consumption and high hardware cost. Besides, with the assumption of the practical waveforms in OTFS systems, it is complicated to work out the precoding algorithm. The objective of this paper is to develop a low-complexity OTFS-based hybrid precoding algorithm with rectangular waveforms for mmWave A2G communications. We first establish the delay-Doppler (DD) domain signal transmission process in hybrid precoding and derive the equivalent baseband DD domain channel matrix. Next, a two-stage hybrid precoding algorithm is proposed, in which the analog precoder based on steering vector is designed, and the recursive digital precoding algorithm is explored. Then a matrix approximation-based strategy is discussed to further reduce complexity. Furthermore, the computational complexity of the proposed algorithm is analyzed. Finally, the numerical results show the lower complexity and superior bit error rate performance of the proposed algorithm compared with the existing OTFS algorithms in high mobility scenarios.

HP‐SPC algorithm with dynamic partially connected structure for mmWave MIMO systems

AbstractThis article proposes a low complexity hybrid precoding algorithm for the switch network‐based dynamic partially connected (SPC) structure, that is, named as HP‐SPC algorithm. First, via a new defined effective optimal precoding matrix, the analog switch precoding matrix optimization problem is transformed into a sparse representation problem. Thus, invoking that the key characteristic of only one nonzero entry in each row of the analog dynamic switch precoding matrix, the analog dynamic switch precoding matrix can be accurately and effectively solved. Second, the digital precoding matrix optimization problem is modeled as a dictionary update problem by the defined effective optimal precoding matrix and the combining matrix. Further, the digital precoding matrix is easily optimized based on the defined effective optimal precoding matrix, since the measurement vectors are sparsely represented by a single dictionary atom. Third, the analog phase shifter precoding matrix is given by the phase rotation method. Finally, the precoding matrices are alternant updated until convergence, a near optimal solution of the precoding matrix is obtained. Compared with the previous works, the proposed HP‐SPC algorithm provides better hybrid precoding performance, for examples: (1) it avoids complexity computation such as matrix inversion and singular value decomposition, so that it presents a low computational complexity; (2) it has a favorable property of convergence since a stable point can be reached with about 10 loop iterations. Based on the simulation results, the effectiveness of HP‐SPC algorithm is further demonstrated.

Energy and Spectral-Efficient Lens Antenna Subarray Design in MmWave MIMO Systems

Lens antenna subarray (LAS) is one of the recently introduced technologies for future wireless networks that significantly improves the energy efficiency of multiple-input multiple-output (MIMO) systems while achieving higher spectral efficiency compared to single-lens MIMO systems. However, a control mechanism for the design of LAS-MIMO is considered a challenging task to efficiently manage the network resources and serve multiple users in the system. Therefore, a sub-grouped LAS-MIMO architecture along with a hybrid precoding algorithm are proposed in this paper to reduce the cost and hardware overhead of traditional hybrid MIMO systems. Specifically, the LAS structure is divided into sub-groups to serve multiple users with different requirements, and an optimization problem based on the achievable sum-rate is formulated to maximize the spectral efficiency of the system. By splitting the sum-rate problem into sub-rate optimization problems, we develop a low-complexity hybrid precoding algorithm to effectively control the proposed architecture and maximize the achievable sum-rate of each subgroup. The proposed precoding algorithm selects the beam of each lens from a predefined set within a subgroup that maximizes the subgroup sum-rate, while the phase shifters and digital precoders in each subgroup are computed independently. The link between subgroups is updated based on successive interference cancelation to minimize interference between users of different subgroups. Our analysis and simulation results show that the proposed precoding algorithm of the sub-grouped LAS-MIMO architecture performs almost as well as traditional fully-connected hybrid MIMO systems in terms of spectral efficiency at low and high signal-to-noise ratio (SNR). It also outperforms traditional fully-connected and sub-connected hybrid MIMO systems in terms of energy efficiency, even when a large number of lenses are used.

A Sparse Optimization Approach for Beyond 5G mmWave Massive MIMO Networks

Millimeter-Wave (mmWave) Massive MIMO is one of the most effective technology for the fifth-generation (5G) wireless networks. It improves both the spectral and energy efficiency by utilizing the 30–300 GHz millimeter-wave bandwidth and a large number of antennas at the base station. However, increasing the number of antennas requires a large number of radio frequency (RF) chains which results in high power consumption. In order to reduce the RF chain's energy, cost and provide desirable quality-of-service (QoS) to the subscribers, this paper proposes an energy-efficient hybrid precoding algorithm for mmWave massive MIMO networks based on the idea of RF chains selection. The sparse digital precoding problem is generated by utilizing the analog precoding codebook. Then, it is jointly solved through iterative fractional programming and successive convex optimization (SCA) techniques. Simulation results show that the proposed scheme outperforms the existing schemes and effectively improves the system performance under different operating conditions.

Low-Complexity Hybrid Precoding for Subarray Architecture mmWave MIMO Systems

Hybrid precoding for millimeter wave (mmWave) multiple-input multiple-output (MIMO) systems has attracted much attention in recent years for subarray architecture compared to array architecture because of its low cost and low power consumption. This is due to the small number of required phase shifters in the subarray architecture. In this paper, we investigate the issue of hybrid precoding for the subarray architecture in narrowband mmWave MIMO systems. First, we derive the spectral efficiency of the subarray architecture with hybrid precoding and discuss the problem formulation. Then, we propose two low-complexity hybrid precoding algorithms for the subarray architecture for narrowband mmWave MIMO systems. In the first algorithm, the hybrid precoding matrix is divided into subarrays submatrices and each subarray submatrix is then divided into vectors. The analog precoding of each subarray is determined from the first vector of the subarray submatrix, which is then used to determine the elements of the digital precoder from all vectors in the subarray submatrix (vector by vector) using a simple maximum ratio combining (MRC) method. The proposed algorithm is called vector-by-vector (VBV) hybrid precoding. Finally, to further enhance the system performance, the proposed VBV precoding in the first algorithm is also combined with an iterative solution, and the resulting algorithm is called iterative VBV precoder. Simulation results verify that the proposed precoding algorithms outperform that of the successive interference cancellation-based subarray precoding and has a performance that is close to that obtained by the fully-connected spatially sparse precoding in various system settings, with lower complexity.

Two-Stage Hybrid Precoding for Minimizing Residuals Using Convolutional Neural Network

This letter presents a two-stage (Ts) hybrid precoding algorithm based on convolutional neural network (CNN) with minimum hybrid precoding residual, named as Ts-CNN algorithm. Firstly, using the optimal precoding matrix as a label, a new CNN architecture is constructed, which can be trained to learn how to predict the vectorized hybrid precoder. Furthermore, a two-stage hybrid precoding scheme is proposed. In the first stage, the proposed CNN learns how to minimize the residual between the hybrid precoder and the optimal precoder when it only has the estimated channel as its input. Specifically, two special network layers are designed to satisfy the constraint conditions of the output. In the second stage, the estimated channel is fed into the well-trained CNN, correspondingly, the analog precoding matrix and the digital precoding matrix are output. Simulation results and complexity analysis show that under certain conditions, the proposed method offers better spectral efficiency than the other related methods with acceptable complexity.