Hybrid Precoding Algorithm Research Articles

Energy-Efficient Hybrid Precoding for Massive MIMO mmWave Systems With a Fully-Adaptive-Connected Structure

This paper investigates the hybrid precoding design in millimeter-wave (mmWave) systems with a fully-adaptive-connected precoding structure, where a switch-controlled connection is deployed between every antenna and every radio frequency (RF) chain. To maximally enhance the energy efficiency (EE) of hybrid precoding under this structure, the joint optimization of switch-controlled connections and the hybrid precoders is formulated as a large-scale mixed-integer non-convex problem with high-dimensional power constraints. To efficiently solve such a challenging problem, we first decouple it into a continuous hybrid precoding (CHP) subproblem. Then, with the hybrid precoders obtained from the CHP subproblem, the original problem can be equivalently reformulated as a discrete connection-state (DCS) problem with only 0-1 integer variables. For the CHP subproblem, we propose an alternating hybrid precoding (AHP) algorithm. Then, with the hybrid precoders provided by the AHP algorithm, we develop a matching assisted fully-adaptive hybrid precoding (MA-FAHP) algorithm to solve the DCS problem. It is theoretically shown that the proposed MA-FAHP algorithm always converges to a stable solution with the polynomial complexity. Finally, simulation results demonstrate the superior performance of the proposed MA-FAHP algorithm in terms of EE and beampattern.

Gram–Schmidt orthogonalisation aided hybrid precoding in millimetre‐wave massive MIMO systems

The authors introduce a novel hybrid precoding algorithm based on Gram–Schmidt orthogonalisation (GSO) in millimetre-wave massive MIMO systems. Specifically, the columns of array response matrix orthogonalised by the GSO process are considered as a set of candidate analogue precoders, then traditional orthogonal matching pursuit (OMP) is utilised to find the optimal analogue and digital precoders. Since GSO is a recursive process that depends on the order in which the matrix columns are selected. A heuristic solution to the order of columns selection is suggested according to the array response vector along which the fully-digital precoder has the maximum projection. The proposed algorithm, not only constrained to uniform linear arrays, can avoid the matrix inversion in designing the digital precoder compared to OMP. Simulation results show that the spectral efficiency and bit error rate of the proposed hybrid precoding solutions are close to that obtained with fully digital architectures. Furthermore, the results indicate that the proposed hybrid precoding solutions outperform the orthogonality-based matching pursuit, which uses the columns of the DFT matrix as a set of candidate analogue precoders.

Hybrid precoding based on adaptive RF-chain-to-antenna connection for millimeter wave MIMO systems

Hybrid precoding has recently received significant attentions as a promising alternative to fully digital precoding. The existing hybrid precoding architectures can be classified into two categories: fully-connected (FC) and partially-connected (PC) phase shifter (PS) network structures (FC-PS and PC-PS structures). However, the FC-PS structure involves a large number of PSs which leads to a prohibitive power consumption, and the PC-PS structure suffers from a severe spectral efficiency loss in spite of low power consumption. This paper considers a novel adaptive RF-chain-to-antenna connection based on switch network (AC-S) hybrid precoding architecture, which consists of a digital precoder, an analog switch network and an analog PS network. The advantage of the proposed architecture lies in achieving a satisfactory spectral efficiency while maintaining a relatively low power consumption due to the adaptive connection from a radio frequency (RF) chain to all antennas via a switch network. Based on the aforementioned architecture, an effective hybrid precoding algorithm is presented. In the proposed algorithm, the analog PS precoding matrix, the analog switch precoding matrix and the digital precoding matrix are optimized via a block coordinate descent method, and a stable solution can be obtained by several iterations. Simulation results demonstrate that the proposed algorithm with the AC-S structure not only obtains considerably better spectral efficiency than the PC-PS structure but also offers a lower power consumption than the FC-PS structure.

A Proposed Efficient Hybrid Precoding Algorithm for Millimeter Wave Massive MIMO 5G Networks

Millimeter wave (mmWave) has been regarded as a candidate cellular band for future 5G networks. It exhibits an extension for current cellular bands, where its integrity with massive multiple-input-multiple output (MIMO) and precoding techniques offers a significant capacity improvements. Unfortunately, analog and/or digital precoders are not energy-efficient from mmWave massive MIMO perspectives whereas, one radio frequency (RF) chain per antenna element is required. Accordingly, the hybrid precoding techniques could be introduced as cost-effective solution. It implicates a low dimensional precoding that can be executed in digital domain, followed by a large dimensional analog beam-formers to steer antenna elements. In this paper, we propose a novel low complex and efficient hybrid precoding algorithm to design the analog and digital precoders/combiners for mmWave massive MIMO transceiver. We will show that our proposed precoder approaches the fully digital (unconstrained) precoder with a negligible performance loss that makes it stand as benchmark case. Particularly, we simply design the digital precoding stage based on modified water-filling wherein, the orthogonality criterion among transmitted data streams is guaranteed. Besides, the analog beam-formers are optimally designed via extracting steering angles from an alternative precoder which is derived from a tight and simple upper bound expression. Furthermore, the proposed algorithm will be extended to include the practical analog beam-formers that have limited phase shifter with finite angle resolution. As a result, we will develop a quantization technique, for the analog precoder, with precision up to two bits. Furthermore, we investigate the energy efficiency (EE) performance wherein, EE degradation can be avoided even with one bit of quantization. This will be confirmed through comparing with unconstrained and unquantized precoders. Also, spectral efficiency (SE) performance displays a remarkable gain when it is fairly compared with the state-of-art.

A Spectral Efficient Hybrid Precoding Algorithm for MmWave MIMO Systems

Abstract Millimeter-wave MIMO will use hybrid precoding to improve the spectral efficiency. In this paper, we propose a spectral efficient hybrid precoding algorithm. In order to maximize the projection of hybrid precoding matrix on the optimal precoding matrix, we design the analog precoding matrix by selecting an optimal combination from the candidate matrix. Then, we regard the channel matrix and the obtained analog precoding matrix as an equivalent channel matrix, and use regularized zero-forcing to acquire the digital precoding matrix. Finally, we present simulation results of the proposed hybrid precoding algorithm and show that the algorithm approaches the optimal precoding.

Deep CNN and Equivalent Channel Based Hybrid Precoding for mmWave Massive MIMO Systems

Millimeter wave (mmWave) system tends to have a large number of antenna elements to compensate for the high channel path loss. The immense number of BS antennas incurs high system costs, power, and interconnect bandwidth. To circumvent these obstacles, two-step hybrid precoding algorithms that enable the use of fewer RF chains have been proposed. However, the precoding schemes already in place are either too complex or not performing well enough. In this study, an equivalent channel hybrid precoding was proposed. The part from the transmitter RF chain to the receiver RF chain is regarded as equivalent channel. By reducing the dimension of channel matrix to the level of RF link number, baseband pre-coder is simply calculated from decomposing the equivalent channel matrix H <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">equ</sub> , which greatly reduces the complexity. Based on this novel precoding approach and convolutional neural network (CNN), a novel combiner neural network architecture was also proposed, which can be trained to learn how to optimize the combiner for maximizing the spectral efficiency with hardware limitation and imperfect CSI. Simulation results show that the proposed approaches achieve significant performance improvement.

Statistically-Aided Codebook-Based Hybrid Precoding for Millimeter Wave Channels

In this paper, we propose practical yet effective statistically-aided codebook-based hybrid precoding schemes for massive multiple-input multiple-output systems in millimeter wave bands. Particularly, we develop novel low-overhead hybrid precoding algorithms for selecting the baseband digital and radio frequency analog precoders from statistically skewed DFT-based codebooks. The proposed algorithms aim at maximizing the spectral efficiency based on minimizing the chordal distance between the optimal unconstrained precoder and the hybrid beamformer and maximizing the signal to the interference noise ratio for the single-user and multi-user cases, respectively. We investigate the performance of the proposed algorithms by considering the mutual information of the analog beamforming procedure (the common stage among the proposed algorithms) as a performance evaluation metric. We derive lower and upper bounds on the mutual information of the channel given the proposed algorithms. Moreover, we show that the performance gap between the lower and upper bounds depends heavily on how many DFT columns are aligned to the largest eigenvectors of the transmit antenna array response of the millimeter wave channel or equivalently the transmit channel covariance matrix when only statistical channel knowledge is available at the transmitter. Then, we show that the proposed algorithms are asymptotically optimal as the number of transmit antennas M goes to infinity and the millimeter wave channel has a limited number of paths P, i.e., P <; M. Further, we verify the performance of the proposed algorithms numerically where results illustrate that the spectral efficiency of the proposed algorithms can approach that of the optimal precoder in certain scenarios. Furthermore, these results show that the proposed hybrid precoding schemes have superior spectral efficiency performance while requiring lower (or at most comparable) channel feedback overhead in comparison with the prior art.

Hybrid Precoding Processor for Millimeter Wave MIMO Communications

Millimeter wave (mmWave) multiple-input multiple-output system is one of the most important techniques to increase throughput for 5G communications. To overcome the severe pathloss in the mmWave channel, the hybrid analog/digital precoding technique jointly designs radio frequency (RF) beamforming vectors and a baseband precoding matrix to approach the optimal spectral efficiency with reduced RF chain power and baseband complexity. This brief presents a hybrid precoding algorithm based on multiple orthogonal beamforming codebooks and a local search scheme, which reduces computational complexity by 40% with negligible bit-error-rate performance loss compared with the state-of-the-art algorithms. The proposed hybrid precoding algorithm was also designed and implemented by using TSMC 90-nm CMOS process technology. The fabricated hybrid precoding processor chip achieves 11.1M/10.4M/6.9M/4.3M matrices per second for 1/2/3/4 data streams, respectively. Compared with a previous work, the designed processor increases throughput by 65%/55%/40%/7.5% for 1/2/3/4 data streams with only 28% of the core area.

Hybrid precoding with phase shifter reduction for 5G massive antenna multi‐user systems in millimetre wave

In this study, the performances of commonly used precoding schemes are evaluated based on channel measurements carried out at 28 GHz in a railway station for a massive antenna system configuration. And a hybrid precoding algorithm for a fifth generation (5G) multi-user antenna system is proposed and its performance is evaluated based on real measured channels. Specifically, An upper bound for achievable sum-rate of phased zero forcing (PZF) algorithm is derived and a precoding technique by reduction of phase shifters (PSs) named reduced-PZF (RPZF) is proposed, which can obviously reduce power consumption in hybrid precoding systems. In addition, the authors give the closed-form expression for achievable sum-rate when RPZF is used. There are no requirements in the authors’ proposed scheme with complicated matrix decomposition and optimisation techniques. The simulation results show that it is possible to reduce 30 and 50% of the PSs by using the proposed hybrid precoder with better system performance in the line-of-sight (LoS) and non-LoS scenarios, respectively. In addition, the digital PSs with 3 bits low resolution can achieve the similar performance when using analogue ones.

An Efficient Precoding Algorithm for mmWave Massive MIMO Systems

Symmetrical precoding and algorithms play a vital role in the field of wireless communications and cellular networks. This paper proposed a low-complexity hybrid precoding algorithm for mmWave massive multiple-input multiple-output (MIMO) systems. The traditional orthogonal matching pursuit (OMP) has a large complexity, as it requires matrix inversion and known candidate matrices. Therefore, we propose a bird swarm algorithm (BSA) based matrix-inversion bypass (MIB) OMP (BSAMIBOMP) algorithm which has the feature to quickly search the BSA global optimum value. It only directly finds the array response vector multiplied by the residual inner product, so it does not require the candidate’s matrices. Moreover, it deploys the Banachiewicz–Schur generalized inverse of the partitioned matrix to decompose the high-dimensional matrix into low-dimensional in order to avoid the need for a matrix inversion operation. The simulation results show that the proposed algorithm effectively improves the bit error rate (BER), spectral efficiency (SE), complexity, and energy efficiency of the mmWave massive MIMO system as compared with the existing OMP hybrid and SDRAltMin algorithm without any matrix inversion and known candidate matrix information requirement.

Symbol-Level Hybrid Precoding in mmWave Multiuser MISO Systems

Recently, symbol-level precoding has emerged as a novel efficient solution in multi-user multi-antenna downlink systems, since it can exploit multi-user interference (MUI) and transform it into useful signal. In this correspondence, we attempt to apply symbol-level precoding into the well-known hybrid precoding architecture in multi-user multi-input single-output (MU-MISO) millimeter wave (mmWave) communication systems. Particularly, we aim to design the symbol-varying digital precoder and the analog precoder with low-resolution phase shifters (PSs) to optimize symbol detection performance under the transmit power constraint and the discrete phase constraint. To handle this difficult joint optimization problem, we propose to minimize the Euclidean distance between the optimal fully-digital precoder and the hybrid precoder. An efficient iterative algorithm is developed to solve this problem. Simulation results demonstrate the advantages of symbol-level precoding and validate the effectiveness of our proposed symbol-level hybrid precoding algorithm.

Millimeter-Wave Massive MIMO Systems Relying on Generalized Sub-Array-Connected Hybrid Precoding

In this paper, we consider a generalized sub-array-connected (GSAC) architecture for arbitrary radio frequency (RF) chain and antenna configurations, where the number of RF chains connected to a sub-array and the number of antennas in each sub-array can be arbitrary. Our design objective is to improve the energy-efficiency of the hybrid precoder of millimeter-wave massive multiple input multiple output (MIMO) systems. We firstly propose a successive interference cancellation based hybrid precoding algorithm to maximize the achievable rate for any given RF chain and antenna configuration. This algorithm firstly decomposes the total achievable rate optimization problem into multiple sub-rate optimization problems, then it successively maximizes these sub-rates. Since the number of RF chains is limited, we can afford using an exhaustive search scheme to evaluate all configurations and identify the one having the best energy efficiency. Moreover, to rely on an attractive limited feedback, we also propose a beamsteering codebook for our hybrid precoding aided GSAC architecture. Our simulation results demonstrate that the proposed scheme achieves a similar rate as the corresponding optimal unconstrained precoder. Furthermore, we show that the energy-efficiency of the proposed scheme is better than that of the existing schemes in the fully-connected and sub-array-connected architectures.

Hybrid precoding for millimetre wave MIMO systems based on particle swarm optimisation

Millimetre wave (mmWave) multiple-input multiple-output (MIMO) systems have been proposed to enable Gbps communication for next-generation cellular systems and local area networks. To compensate for the severe propagation loss of the mmWave channel, a cost-effective hybrid precoding architecture, combining a digital precoder and an analogue precoder, is widely used in mmWave MIMO systems. In this study, two hybrid precoding algorithms based on particle swarm optimisation (PSO) algorithm will be proposed for two different hybrid precoding structures, i.e. the fully connected and partially connected structures. First, the authors use the phase of the analogue precoding variable to replace the corresponding variable with the constraints of the unit norm to solve the non-convex constraints skillfully. Then they design analogue precoding by using PSO algorithm and compute the digital precoding based on the least squares solution. Finally, the proposed algorithms are compared with the existing advanced algorithms. Simulation results demonstrate that the proposed algorithms can approach the optimal performance under the corresponding structure.

Two‐stage BFGS‐based hybrid precoding for mmWave multiuser MIMO systems

Millimetre wave (mmWave) communications are the most promising candidate for the future fifth-generation mobile broadband networks, which offer greater available spectrum than current cellular. However, the huge path loss and rain attenuation due to the characteristic of the mmWave channel make it difficult to realise. Thanks to the small wavelength of mmWave signals, massive multi-input-multi-output (MIMO) systems can be leveraged to overcome the path loss. Unfortunately, in contrast to conventional MIMO systems, high-power consumption and hardware cost make fully digital precoding impractical. In this study, the authors study the hybrid precoding structure for multiuser mmWave systems, which compromises the cost and performance. First, an extension algorithm from single user systems, which directly decomposes the optimal fully digital precoder into a baseband precoder and an analogue radio-frequency (RF) precoder, is introduced according to the recent work. Then, the drawback of this kind of algorithm is analysed at high signal-to-noise ratios. Subsequently, a two-stage hybrid precoding algorithm, which is based on the minimum mean-squared error criterion is proposed, where the modified Broyden–Fletcher–Goldfarb–Shanno (BFGS) algorithm is presented to reduce the reconstruction error of computing the analogue RF precoder. Simulation results show that the proposed precoding algorithm can significantly improve the performance of the system sum-rate.

Channel-Statistics-Based Hybrid Precoding for Millimeter-Wave MIMO Systems With Dynamic Subarrays

This paper investigates the hybrid precoding design for millimeter wave (mmWave) multiple-input multiple-output (MIMO) systems with finite-alphabet inputs. The mmWave MIMO system employs partially-connected hybrid precoding architecture with dynamic subarrays, where each radio frequency (RF) chain is connected to a dynamic subset of antennas. We consider the design of analog and digital precoders utilizing statistical and/or mixed channel state information (CSI), which involve solving an extremely difficult problem in theory: First, designing the optimal partition of antennas over RF chains is a combinatorial optimization problem, whose optimal solution requires an exhaustive search over all antenna partitioning solutions; Second, the average mutual information under mmWave MIMO channels lacks closed-form expression and involves prohibitive computational burden; Third, the hybrid precoding problem with given partition of antennas is nonconvex with respect to the analog and digital precoders. To address these issues, this study first presents a simple criterion and the corresponding low complexity algorithm to design the optimal partition of antennas using statistical CSI. Then it derives the lower bound and its approximation for the average mutual information, in which the computational complexity is greatly reduced compared to calculating the average mutual information directly. In addition, it also shows that the lower bound with a constant shift offers a very accurate approximation to the average mutual information. This paper further proposes utilizing the lower bound approximation as a low-complexity and accurate alternative for developing a manifold-based gradient ascent algorithm to find near optimal analog and digital precoders. Several numerical results are provided to show that our proposed algorithm outperforms existing hybrid precoding algorithms.

Doubling Phase Shifters for Efficient Hybrid Precoder Design in Millimeter-Wave Communication Systems

Hybrid precoding is a cost-effective approach to support directional transmissions for millimeter-wave (mmWave) communications, but its precoder design is highly complicated. In this paper, we propose a new hybrid precoder implementation, namely the double phase shifter (DPS) implementation, which enables highly tractable hybrid precoder design. Efficient algorithms are then developed for two popular hybrid precoder structures, i.e., the fully- and partially-connected structures. For the fully-connected one, the RF-only pre-coding and hybrid precoding problems are formulated as a least absolute shrinkage and selection operator problem and a low-rank matrix approximation problem, respectively. In this way, computationally efficient algorithms are provided to approach the performance of the fully digital one with a small number of radio frequency (RF) chains. On the other hand, the hybrid precoder design in the partially-connected structure is identified as an eigenvalue problem. To enhance the performance of this cost-effective structure, dynamic mapping from RF chains to antennas is further proposed, for which a greedy algorithm and a modified K-means algorithm are developed. Simulation results demonstrate the performance gains of the proposed hybrid precoding algorithms over existing ones. It shows that, with the proposed DPS implementation, the fully-connected structure enjoys both satisfactory performance and low design complexity while the partially-connected one serves as an economic solution with low hardware complexity.

Givens rotation based column-wise hybrid precoding for millimeter wave MIMO systems

Hybrid precoding is a promising technique for millimeter wave (mmWave) large-scale multiple-input multiple-output (MIMO) systems. This paper considers a hybrid precoding architecture which is composed of a reductive digital precoder and a phase-only control radio frequency (RF) precoder, and proposes a Givens rotation based column-wise hybrid precoding algorithm. In the proposed algorithm, the digital precoding matrix and the RF precoding matrix are alternatively optimized column by column. For the optimization of the constant modulus RF precoding vector, it is interesting that the optimal solution can be expressed as a product of an arbitrary constant modulus vector and a series of Givens rotation matrices. Accordingly, the original problem is transformed into an unconstrained problem of the Givens rotations, which is easy to be solved. After obtaining the optimal RF precoding vector, the optimal digital precoding vector can be given through the least squares method. Simulation results show that the proposed algorithm can approach the performance of the fully digital precoder effectively and enjoy a higher spectral efficiency than previous works under various channel environments and different system settings.

Energy-Efficient Hybrid Precoding With Low Complexity for mmWave Massive MIMO Systems

Millimeter-wave (mmWave) massive multiple-input multiple-output (MIMO) utilizes large antenna arrays and is considered a promising technology for fifth-generation (5G) and beyond wireless communication systems. However, the high-power consumption of the radio-frequency (RF) chains makes it infeasible. To solve this problem, hybrid precoding is proposed, which is a combination of analog and digital precoding. The fully connected architecture hybrid precoding still requires a large number of phase shifters (PSs). The sub-connected architecture can greatly reduce the required power consumption, and however, it cannot obtain a satisfactory achievable rate. To avoid the high energy consumption and obtain a high resolution, we propose a novel partly connected architecture in this paper. In addition, we propose an energy-efficient successive interference cancelation (SIC) hybrid precoding based on the partly connected architecture, which transforms the problem of maximizing the total achievable rate with non-convex constraints into a series of sub-rate optimization problems. Furthermore, a low-complexity energy-efficient SIC hybrid precoding based on the partly connected architecture is developed, which uses the partial singular value decomposition (SVD) to realize the sub-rate optimization and significantly reduce the complexity. Theoretical analysis demonstrates the superiority of the proposed hybrid precoding in terms of complexity. The simulation results indicate that the proposed hybrid precoding algorithms enjoy better energy efficiency and achievable rate performance than some recently proposed hybrid precoding algorithms.

Machine Learning-Based Spectrum Efficiency Hybrid Precoding With Lens Array and Low-Resolution ADCs

Hybrid precoding is an important issue in millimeter wave (mmWave) massive multi-input and multi-output (MIMO) system. Specially, energy-saving hybrid precoding architectures and efficient hybrid precoding schemes provide ideas for solving this issue. In this paper, we propose a hybrid precoding/combining architecture that is low-cost and easy to implement. Specifically, a hybrid precoding architecture is realized by the lens sub-arrays at the base station (BS). Moreover, a hybrid combining architecture applies the low-resolution analog-to-digital converters (ADCs) at the front end of the radio frequency (RF) chains at the receiving terminal. Based on the hybrid precoding/combining architecture, the hybrid precoder and combiner are jointly optimized to maximize the spectrum efficiency (SE) in the downlink systems, which is a combinatorial optimization problem due to hardware constraints. The cross-entropy (CE) approach in machine learning (ML) is a simple way to solve the combinatorial optimization problem benefiting from its adaptive update procedure. Therefore, we propose an adaptive hybrid precoder/combiner design scheme (AHDS), in which a hybrid precoding algorithm based on the improved CE (ICE) inspired by ML is adopted to design the optimal hybrid precoder, and an approximate optimization method (AOM) is suggested when designing the hybrid combiner. In general, compared with the existing hybrid design schemes, the proposed AHDS is demonstrated to have significant advantage in SE with low computational complexity.

Switch and Inverter Based Hybrid Precoding Algorithm for mmWave Massive MIMO System: Analysis on Sum-Rate and Energy-Efficiency

In millimeter-wave (mmWave)-based massive multiple-input-multiple-output (MIMO) systems, hybrid precoding is considered one of the indispensable techniques in the next generation wireless communication systems (5G) to reduce the number of radio-frequency (RF) chains. However, the existing hybrid precoding techniques often cause performance loss. To solve this problem, the switch and inverter (SI)-based hybrid precoding architecture has been proposed recently as an energy-efficient solution for these challenges. In this paper, a detailed performance analysis on sum-rate as well as energy-efficiency is provided through simulation on the two-stage hybrid precoding, antenna selection (AS)-based hybrid precoding, and adaptive cross-entropy (ACE)-based hybrid precoding. It is aimed to prove that the performance of the ACE-based scheme is much superior to that of the others with the limited ranges of values of all parameters. At last, the suitable parameters are determined and we prove that they can lead to the optimal performance.