Low-Complexity Hybrid Precoding Research Articles

Near-Optimal Low-Complexity Hybrid Precoding for THz Massive MIMO Systems

Near-Optimal Low-Complexity Hybrid Precoding for THz Massive MIMO Systems

Low-complexity hybrid precoding for sub-connected millimeter wave massive MIMO systems

Hybrid analog-digital precoding architectures facilitate practical implementation of millimeter wave (mmW) massive multiple-input multiple-output (mmW-mMIMO) systems by reducing the number of radio frequency chains required. The spectral efficiency (SE) and energy efficiency (EE) optimization problems of these systems are typically non-convex and NP-hard, as the joint optimization that involves the analog and digital precoding functions along with the constant modulus constraints required by analog phase shifters, results in highly non-linear problems. To address such problems, we propose a decoupled two-stage design. More specifically, in the first stage, a closed-form approximation of the effective channel is proposed, and thus the SE maximization problem can be transformed to an effective channel gain maximization problem. Then, the analog precoding matrices can be generated to facilitate the second stage, where the digital precoding matrix is devised for maximizing the system’s EE. In addition, the circuit power consumption statistics of the system modules are exploited and a sub-connected mmW-mMIMO architecture is adopted during EE optimization. Finally, simulation results are provided to validate the effectiveness of our proposed mmW-mMIMO scheme with hybrid precoding.

Low-Complexity Hybrid Precoding Based on PAST for Millimeter Wave Massive MIMO System

Low-Complexity Hybrid Precoding Based on PAST for Millimeter Wave Massive MIMO System

Spectral-efficient hybrid precoding for multi-antenna multi-user mmWave massive MIMO systems with low complexity

Millimeter-wave (mmWave) massive multiple-input multiple-output (MIMO) systems allow for a data transmission rate of gigabits per second owing to the large bandwidth available in the mmWave spectrum and the antenna gains provided by the massive MIMO system. However, hybrid precoding with high complexity and low spectral efficiency cannot address the challenge of high cost and power consumption of RF chains of multi-user systems. In this paper, we propose a low-complexity hybrid precoding scheme for downlink multi-antenna multi-user mmWave massive MIMO systems, aiming to enhance the sum spectral efficiency (SSE) performance. We first extend the dimension of the analog precoding matrix into a square matrix and find the optimal analog combiner by selecting some of the discrete Fourier transform (DFT) bases, which enhances the equivalent baseband channel matrix gain. Then, we directly aggregate the channel gain through the equal gain transmission (EGT) method to ensure the frequency efficiency performance. Finally, we propose an improved BD scheme to design the digital precoder and combiner to reduce the inter-user interference. We consider both the mmWave channel and the Rayleigh channel to evaluate the performance of the proposed algorithm. The simulation results verify that the proposed scheme enjoys near-optimal achievable sum spectrum efficiency and BER performance in both the mmWave channel and Rayleigh channel and performs even better in Rayleigh channel than in the mmWave channel.

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.

System-Level Assessment of Low Complexity Hybrid Precoding Designs for Massive MIMO Downlink Transmissions in Beyond 5G Networks

The fast growth experienced by the telecommunications field during the last few decades has been motivating the academy and the industry to invest in the design, testing and deployment of new evolutions of wireless communication systems. Terahertz (THz) communication represents one of the possible technologies to explore in order to achieve the desired achievable rates above 100 Gbps and the extremely low latency required in many envisioned applications. Despite the potentialities, it requires proper system design, since working in the THz band brings a set of challenges, such as the reflection and scattering losses through the transmission path, the high dependency with distance and the severe hardware constraints. One key approach for overcoming some of these challenges relies on the use of massive/ultramassive antenna arrays combined with hybrid precoders based on fully connected phase-shifter architectures or partially connected architectures, such as arrays of subarrays (AoSAs) or dynamic AoSAs (DAoSAs). Through this strategy, it is possible to obtain very high-performance gains while drastically simplifying the practical implementation and reducing the overall power consumption of the system when compared to a fully digital approach. Although these types of solutions have been previously proposed to address some of the limitations of mmWave/THz communications, a lack between link-level and system-level analysis is commonly verified. In this paper, we present a thorough system-level assessment of a cloud radio access network (C-RAN) for beyond 5G (B5G) systems where the access points (APs) operate in the mmWave/THz bands, supporting multi-user MIMO (MU-MIMO) transmission with massive/ultra-massive antenna arrays combined with low-complexity hybrid precoding architectures. Results showed that the C-RAN deployments in two indoor office scenarios for the THz were capable of achieving good throughput and coverage performances, with only a small compromise in terms of gains when adopting reduced complexity hybrid precoders. Furthermore, we observed that the indoor-mixed office scenario can provide higher throughput and coverage performances independently of the cluster size when compared to the indoor-open office scenario.

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.

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.

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.

Robust Efficient Hybrid Pre-Coding Scheme for mmWave Cell-Free and User-Centric Massive MIMO Communications

Millimeter-wave cell-free and user-centric massive multiple input multiple output (MIMO) systems are promising, due to the reliable ultra-high data rate services. Thus, it is a significant issue to design low-complexity hybrid precoders. In this paper, a simplified sum-mean-square-error (SMSE) is used to design hybrid precoders, based on the array gain and spatial macro-diversity. Then, a heuristic hybrid pre-coding scheme is proposed, with two analog design algorithms that are with or without the knowledge of statistical information. The influence of the imperfect state information of beams is theoretically analyzed, from the instantaneous and ergodic aspects, verifying the robustness of the proposed scheme. Simulation results show that our proposed low-complexity hybrid precoder can be easily realized with acceptable bit error rate (BER) and sum-rate performances, especially when the total transmit power is small.

Radio Frequency Link and User Selection Algorithm for 5G Mobile Communication System

Based on the millimetre-wave time-domain channel detector, this paper conducts channel measurement and modelling for different scenarios and antenna types in typical frequency bands and thus carries out a study on the propagation characteristics of millimetre-wave channels in typical frequency bands and scenarios for 5G. The time-varying characteristics and modelling methods of millimetre-wave clusters are studied, and the time-varying channel simulation strategy and linear regression fitting method are used to establish the time-varying generation and extinction model of clusters by combining the measured data of 26 GHz large-scale antenna channels. The algorithm is based on the correlation dictionary and achieves the efficient and optimal selection of large-scale antenna arrays in the millimetre-wave band. A low-complexity multiuser hybrid precoding design scheme is proposed based on the wideband millimetre-wave large-scale Multiple-Input Multiple-Output (MIMO) system. The scheme aims to maximize the system spectral efficiency and introduces the net spectral efficiency as a bridge to decouple the analogy precoding design from the digital precoding design, thus significantly reducing the computational complexity. In the analogy precoding stage, a Hungarian algorithm-based beam assignment method is proposed to avoid beam conflicts and maximize the net spectral efficiency of the system; in the digital precoding stage, the equivalent channel matrix of each subcarrier is diagonalized to eliminate multiuser interference. Finally, the effectiveness of the scheme is verified by simulation. In this paper, we focus on the radio frequency (RF) link and user selection algorithm of 5G mobile communication system. Through the study of these two aspects, the RF link of our communication system has high stability and reliability, and through the study of the algorithm used for selection, our results also have a strong practical value.

Low-complexity non-iterative hybrid precoding scheme for millimeter wave massive MIMO systems

ABSTRACT Conventional multiple-input multiple-output (MIMO) systems operating at sub-6 GHz frequencies generally employ fully digital precoding which requires dedicated radio frequency (RF) chain for each antenna element. However, this architecture is infeasible for the millimetre wave (mmWave) massive MIMO systems due to excessive power consumption and space constraints posed by large number of RF chains. Hence, hybrid precoding architecture, which utilises small size digital precoder followed by large size analog precoder, is employed for such systems. Due to the constant-magnitude hardware constraint on the phase shifter elements of analog precoder, efficient design of hybrid precoders is a challenge. In this paper, a low-complexity non-iterative hybrid precoder/combiner design is proposed for a single-user mmWave massive MIMO system. The analog RF precoder vectors are selected non-iteratively from the set of transmit array response vectors such that they are ‘aligned’ with the optimal precoder of the channel. Then, for the fixed analog precoder, the digital baseband precoder is evaluated using least square solution. Matrix operations like singular value decomposition, correlation and inversion are required only once. A similar approach is adopted for the design of hybrid combiners of the receiver. Simulation results show effectiveness of the proposed method in terms of spectral efficiency maximisation.

Initial Value Acceleration-Based Alternating Minimization Algorithm for Dynamic Sub-Connected Hybrid Precoding in Millimeter Wave MIMO Systems

Symmetry-based sub-connected hybrid precoding is an energy-friendly structure in wireless communications. Most of the prior work set a diagonal constraint on the analog precoder and used a randomly set matrix as the initial analog precoder, which did not match the optimal channel conditions, leading to a decrease in spectral efficiency, and some had huge complexity when calculating the digital precoder. Aiming to solve these problems, this paper proposed a low-complexity hybrid precoding algorithm based on Initial value Acceleration-based Alternating Minimization (IAAM). Leveraging the special structure of analog precoder in sub-connected scheme, we design the analog precoder through low-complexity quadratic programming and use the least square method to obtain the digital precoder. Moreover, we design a heuristic algorithm with the objective function of maximizing the effective channel gain to calculate the initial analog precoder as the starting point for alternating minimization. The simulation results show that the spectral efficiency of this algorithm is at least 17.5% higher than the existing two traditional sub-connected algorithms. Additionally, it increases energy efficiency by at least 12.8% compa with the Orthogonal Matching Pursuit (OMP) algorithm. Its algorithm convergence speed is fast, which increases with the number of RF chains.

Low-Complexity Hybrid Precoding Algorithm Based on Log-Det Expansion for GenSM-Aided MmWave MIMO System

Generalized spatial modulation (GenSM) aided millimeter wave (mmWave) multiple-input multiple-output (MIMO) system has been recently considered as a new efficient technique due to the combination of numerous antennas and reduced number of radio frequency (RF) chains. However, the present hybrid precoding schemes for GenSM-aided system are still troubled by high computational complexity and performance loss in spectral efficiency (SE). In this paper we propose low-complexity hybrid precoding schemes based on Martin's expansion for logarithmic determinant (log-det) form in analytical SE lower bound. Digital and analog precoders are herein optimized separately, which means complicated alternating minimization iteration is omitted. Besides, we can adjust algorithmic complexity adaptively corresponding to different demand levels for users. Finally the numerical simulations show that the proposed methods outperform other GenSM-aided mmWave MIMO schemes and can achieve a better tradeoff between complexity and SE.

Low Complexity Hybrid Precoding and Combining for Millimeter Wave Systems

In millimeter-wave (mmWave) systems, hybrid precoding/combining architectures are an attractive low-complexity alternative to the use of fully digital precoding. This is because of the reduction in the number of Radio-Frequency (RF) and mixed-signal hardware components. Hybrid precoding/combining design involves a combination of analog and digital processing that enables both beamforming and spatial multiplexing gains in mmWave systems. This paper presents an algorithm for hybrid precoding and combining designs in mmWave systems. The proposed design does not depend on the antenna array geometry, unlike the orthogonal matching pursuit (OMP) hybrid precoding/combining approach. Moreover, this algorithm allows hybrid precoders/combiners to perform close to the known optimal performance of unconstrained digital precoders and combiners. Simulation results verify that the proposed hybrid precoding/combining scheme outperforms the previous methods in the literature in terms of bit error rate (BER) and achievable spectral efficiency with lower complexity.

The Configurable Hybrid Precoding Processor for Bit-Stream-Based mmWave MIMO Systems

Beamforming technology plays an essential role in the promising millimeter wave (mmWave) massive multiple-input and multiple-output (MIMO) communications for fifth generation (5G) new radio system. Specifically, hybrid analog beamforming and digital precoding scheme can be employed to reduce the excessive radio frequency (RF) chains and data converters in the massive MIMO transceiver while still maintaining optimal spectral efficiency. However, traditional hybrid precoding architecture cannot be configured to support different system specifications, such as the number of bit streams or transmit antennas, leading to the limitation to hardware flexibility and efficiency. This article presents a configurable and low-complexity hybrid precoder based on the parallel data-stream processing in respect of system, algorithm, and architecture. The proposed algorithm was designed to avoid signal dependence between data streams so as to realize configurable precoding architecture. The performance and complexity of the proposed algorithm were also simulated and analyzed in detail in this article. Moreover, the hybrid precoding processor chip was designed and implemented based on the proposed algorithm. A novel data-processing flow was designed in the precoder so as to increase the hardware efficiency and configurability. The designed hybrid precoding chip can be configured to support one to four data streams for 16 × 16 mmWave MIMO systems. The designed precoder was implemented by using TSMC 40-nm CMOS technology. The normalized throughput achieved 11.1 M channel-matrices per second at a maximum clock frequency of 300 MHz. The area complexity is 263.5 kGE, and power consumption is 119.1 mW.

Two-Step Multiuser Equalization for Hybrid mmWave Massive MIMO GFDM Systems

Although millimeter-wave (mmWave) and massive multiple input multiple output (mMIMO) can be considered as promising technologies for future mobile communications (beyond 5G or 6G), some hardware limitations limit their applicability. The hybrid analog-digital architecture has been introduced as a possible solution to avoid such issues. In this paper, we propose a two-step hybrid multi-user (MU) equalizer combined with low complexity hybrid precoder for wideband mmWave mMIMO systems, as well as a semi-analytical approach to evaluate its performance. The new digital non-orthogonal multi carrier modulation scheme generalized frequency division multiplexing (GFDM) is considered owing to its efficient performance in terms of achieving higher spectral efficiency, better control of out-of-band (OOB) emissions, and lower peak to average power ratio (PAPR) when compared with the orthogonal frequency division multiplexing (OFDM) access technique. First, a low complexity analog precoder is applied on the transmitter side. Then, at the base station (BS), the analog coefficients of the hybrid equalizer are obtained by minimizing the mean square error (MSE) between the hybrid approach and the full digital counterpart. For the digital part, zero-forcing (ZF) is used to cancel the MU interference not mitigated by the analog part. The performance results show that the performance gap of the proposed hybrid scheme to the full digital counterpart reduces as the number of radio frequency (RF) chains increases. Moreover, the theoretical curves almost overlap with the simulated ones, which show that the semi-analytical approach is quite accurate.

Energy-Efficient Power Allocation with Hybrid Beamforming for Millimetre-Wave 5G Massive MIMO System

Massive multiple-input and multiple-output systems combined with hybrid beamforming technique is a key approach to achieve high data rate and extended cell coverage in the fifth generation (5G) cellular networks . Specifically, the precoding for analog/digital hybrid beamforming technique is absolutely essential for millimeter-wave (mm-wave) frequency based transmission for 5G, simply because the technique reduces hardware complexity and energy consumption for high-frequency design. In order to prove the aforementioned advantages, the present paper will investigate the energy efficiency (EE) and optimization of low complexity hybrid precoding (EELCHP) algorithm to enable the reduction of radio frequency (RF) chains within the base station (BS). The proposed solution will also incorporate high-resolution phase shifters (HRPS) specifically for downlink multi-user mm-wave system. The intelligence within the EELCHP algorithm for hybrid beamforming is based on the fully complex zero-forcing (ZF) precoding mechanism that allowed the maximization of energy efficiency by reducing the RF chains, without affecting the potentially increasing number of antennas. In addition, maximum EE is possible by eliminating the nonlinear concave fractional issue based on the Lagrange duality method. During the simulation process of the proposed method, we further realized that hardware complexity and power consumption can be reduced by allowing the RF chains to select only one beam per switch within the beamforming solution. Furthermore, with the implementation of EELCHP algorithm, more energy is saved due to low complexity system by reducing the required RF chain.

Alternating Optimization Based Low Complexity Hybrid Precoding in Millimeter Wave MIMO Systems

Hybrid precoding is an effective solution to reduce the cost of millimeter wave systems. In recent years, joint optimization has begun to attract the attention of researchers due to its excellent performance. In this letter, we adopt the alternating optimization method to design a low complexity hybrid precoding. In particular, the spectral efficiency optimization problems are simplified to sub-optimization problems under certain constraints. For each sub-optimization problem, we alternatively optimize the columns of the analog precoding matrix and combining matrix by using the projected gradient method. Then, the digital domain matrices are derived from the equivalent channel. Simulation results and complexity analyses show that the performance of the proposed hybrid precoding based on alternating optimization is close to the unconstrained optimal precoder and the algorithm has lower complexity.

Low-Complexity Hybrid Precoding for Multi-User MmWave Systems With Low-Resolution Phase Shifters

Large-scale antennas systems have been attracted significant attention to provide considerable array gains for millimeter wave (mmWave) communications systems. However, huge hardware complexity and power consumptions make the conventional precoding architectures impractical to realize. Recently, hybrid precoding structures for mmWave communications systems are widely investigated to save the cost and achieve satisfactory performance. Unfortunately, most existing precoder designs lie in the assumption of infinite or high-resolution phase shifters (PSs), which are also difficult to realize in real-world. Motivated by this fact, a low complexity hybrid precoder and combiner design for multi-user systems with two-bit resolution PSs is proposed in this paper, which provides an appropriate trade-off between energy efficiency and system sum-rate. Specifically, the candidate sets for analog beamforming are constructed by introducing the auxiliary variables, in which the number of elements is the same as that of antennas. Accordingly, the computational complexity of searching optimal beamformer is significantly reduced over proposed codebooks. Then, to avoid high complexity singular value decomposition (SVD) of channel matrix, we propose a rank-1 approximate decomposition algorithm based-on principal component analysis technique. At last, the user scheduling algorithm is presented to further improve the performance in multiuser-scenario. Simulation results verified the effectiveness of the proposed algorithms, the performance of which is close to the optimal unquantized precoder.