Wave Massive Massive Multiple-input Multiple-output Research Articles

Optimized CNN and adaptive RBFNN for channel estimation and hybrid precoding approaches for multi user millimeter wave massive MIMO

ABSTRACT The millimetre-wave (mmWave) communication satisfies the demand for high data rates due to the characteristic of wide bandwidth. Using massive multiple-input multiple-output (MIMO) technology, a significant propagation loss of mmWave communication is effectively compensated. However, it is challenging to provide a specialised radio frequency chain for each antenna due to the constrained physical area with closely spaced antennas and prohibitive power consumption in mmWave massive MIMO systems. This paper presents novel approaches for effective channel estimation and hybrid precoding in mmWave communication systems. To address the challenges of channel estimation, a convolutional neural network (CNN) is utilised, and network parameters are optimised using enhanced whale optimization algorithm (EWOA). The proposed CNN-based channel estimation method aims to accurately estimate the channel in mmWave systems with enhanced efficiency and reduced complexity. By training CNN using EWOA optimisation algorithm, the network parameters are fine-tuned to improve accuracy and generalisation capability of channel estimation process. Furthermore, hybrid precoding is achieved using adaptive radial-basis function neural networks (adaptive RBFNNs) which enables efficient precoding while minimising complexity. Moreover, the adaptive RBFNN approach determines the optimal precoding weights based on channel state information, resulting in a improved performance and a reduced computational overhead. The performance analysis is validated using the MATLAB/Simulink software and offers to provide effectual and reliable mmWave communication systems, facilitating the realisation of high-speed and high-capacity wireless networks.

Deep Learning for Beam Training in Millimeter Wave Massive MIMO Systems

This paper investigates deep learning for beam training in millimeter wave (mmWave) massive multiple-input multiple-output (MIMO) systems. Different from the existing work, we explore how the deep learning can be applied for beam training. In particular, a deep neural network (DNN) is used to deal with the nonlinear and nonmonotonic properties of channel power leakage in mmWave communications. Accordingly, we propose two DNN-based beam training (DBT) schemes. The first scheme, named original DBT (ODBT), uses a DNN to predict the beam combination best matching the strongest channel path of the mmWave channel based on the probability vector. The other scheme, named enhanced DBT (EDBT), performs additional beam training tests after obtaining the probability vector. Simulation results show that the proposed schemes can achieve satisfactory performance in terms of successful rate and achievable rate with substantially reduced beam training overhead and improved signal coverage.

Learned-SBL-GAMP based hybrid precoders/combiners in millimeter wave massive MIMO systems.

In Millimeter-Wave (mm-Wave) massive Multiple-Input Multiple-Output (MIMO) systems, hybrid precoders/combiners must be designed to improve antenna gain and reduce hardware complexity. Sparse Bayesian learning via Expectation Maximization (SBL-EM) algorithm is not practically feasible for high signal dimensions because estimating sparse signals and designing optimal hybrid precoders/combiners using SBL-EM still provide high computational complexity for higher signal dimensions. To overcome the issues of high computational complexity along with making it suitable for larger data sets, in this paper, we propose Learned-Sparse Bayesian Learning with Generalized Approximate Message Passing algorithm (L-SBL-GAMP) algorithm for designing optimal hybrid precoders/combiners suitable for mmWave Massive MIMO systems. The L-SBL-GAMP algorithm is an extension of the SBL-GAMP algorithm that incorporates a Deep Neural Network (DNN) to improve the system performance. Based on the nature of the training data, the L-SBL-GAMP can design the optimal Hybrid precoders/combiners, which enhances the spectral efficiency of mmWave massive MIMO systems. The proposed L-SBL-GAMP algorithm reduces the iterations, training overhead, and computational complexity compared to the SBL-EM algorithm. The simulation results unveil that the proposed L-SBL-GAMP provides higher achievable rates, better accuracy, and low computational complexity compared to the existing algorithm, such as Orthogonal Matching Pursuit (OMP), Simultaneous Orthogonal Matching Pursuit (SOMP), SBL-EM and SBL-GAMP for mmWave massive MIMO architectures.

Interference Alignment in Channel Estimation Using Hybrid Deep Neural Network with Multi-user Propagation Model for 5G in MM Wave Massive MIMO

Massive Multiple Input Multiple Output (MIMO) technologies, as well as higher frequencies utilization, such as MilliMeter Wave (MM Wave) frequencies, should be utilized in the 5G wireless network. This massive transmission will require a higher frequency band and in cellular massive MIMO, frequencies re-use leads to interference in channel estimation. Interference Alignment (IA) is a transmission strategy of the channel with higher capacities of signal-to-noise ratio. This interference needs to be aligned before the transmission of signal, so this research proposes a novel technique in IA by hybridization of deep learning techniques for Heterogeneous Networks (HetNets). The aim of this work is to develop a new interference alignment scheme based on multi-user with a neural network which can be efficient in mitigation of interference of the networks. The model that is proposed properly exploits the interference alignment concept by developing a multi-user group of small cells assisted by various BSs in the heterogeneous networks for MM Wave. The paper focuses on channel estimation by IA for a 5G network that transmits MMWave using neural networks. The neural network is utilized for learning the mapping functions between the received mmWave channels with negligible overhead. Here Hybrid Deep Neural Network is used with Multi-User Propagation (HDNN-MUP) model for IA and demonstrates a practical upper bound for MIMO array sizes that balance throughput and estimation overhead. The experimental analysis is done by utilizing the parameters namely Signal-to-noise ratio (SNR), Bit Error Rate (BER), computational time, energy efficiency, and spectral efficiency.

IUG‐based beam selection for wideband millimetre wave massive MIMO systems

AbstractBeam selection aims to select beams with large power and little inter‐user interference (IUI). In wireless communication scenarios, the levels of IUI are usually different, but, most existing beam selection methods apply the same beam selection criteria for all users, which is detrimental to maintain an attractive trade‐off between computational complexity and system performance. Considering the discrepancy of IUI comprehensively, this paper proposes a beam selection method based on interfering user grouping (IUG) for wideband millimetre‐wave massive multiple‐input multiple‐output (MIMO) systems. Firstly, a candidate beam set (CBS) is constructed in light of the sparsity and power distribution of the beamspace channel. Based on the CBS, all users are classified into non‐interfering users (NIUs), low‐interference users (LIUs) and high‐interference users (HIUs). For NIUs, the beams with large power are selected from CBS under the magnitude maximization (MM) criterion; for LIUs, a novel MM criterion with a tabu list is designed, which can effectively tackle the drawback of assigning shared beams in traditional MM; for HIUs, the incremental algorithm based on the sum‐rate maximization criterion is developed to find the optimal beams from CBS. Simulation results validate that the proposed IUG‐based method can obtain a good performance with lower computational complexity compared with the existing methods.

CSI Feedback With Model-Driven Deep Learning of Massive MIMO Systems

In order to achieve reliable communication with a high data rate of massive multiple-input multiple-output (MIMO) systems in frequency division duplex (FDD) mode, the estimated channel state information (CSI) at the receiver needs to be fed back to the transmitter. However, the feedback overhead becomes exorbitant with the increasing number of antennas. In this letter, a two stages low rank (TSLR) CSI feedback scheme for millimeter wave (mmWave) massive MIMO systems is proposed to reduce the feedback overhead based on model-driven deep learning. Besides, we design a deep iterative neural network, named FISTA-Net, by unfolding the fast iterative shrinkage thresholding algorithm (FISTA) to achieve more efficient CSI feedback. Moreover, a shrinkage thresholding network (ST-Net) is designed in FISTA-Net based on the attention mechanism, which can choose the threshold adaptively. Simulation results show that the proposed TSLR CSI feedback scheme and FISTA-Net outperform the existing algorithms in various scenarios.

Beam division multiple access for millimeter wave massive MIMO: Hybrid zero-forcing beamforming with user selection

<p>Massive multiple-input multiple-output (MIMO) systems are considered a promising solution to minimize multiuser interference (MUI) based on simple precoding techniques with a massive antenna array at a base station (BS). This paper presents a novel approach of beam division multiple access (BDMA) which BS transmit signals to multiusers at the same time via different beams based on hybrid beamforming and user-beam schedule. With the selection of users whose steering vectors are orthogonal to each other, interference between users is significantly improved. While, the efficiency spectrum of proposed scheme reaches to the performance of fully digital solutions, the multiuser interference is considerably reduced.</p>

An Efficient Machine Learning Based Precoding Algorithm for Millimeter-Wave Massive MIMO

Millimeter wave communication works in the 30–300 GHz frequency range, and can obtain a very high bandwidth, which greatly improves the transmission rate of the communication system and becomes one of the key technologies of fifth-generation (5G). The smaller wavelength of the millimeter wave makes it possible to assemble a large number of antennas in a small aperture. The resulting array gain can compensate for the path loss of the millimeter wave. Utilizing this feature, the millimeter wave massive multiple-input multiple-output (MIMO) system uses a large antenna array at the base station. It enables the transmission of multiple data streams, making the system have a higher data transmission rate. In the millimeter wave massive MIMO system, the precoding technology uses the state information of the channel to adjust the transmission strategy at the transmitting end, and the receiving end performs equalization, so that users can better obtain the antenna multiplexing gain and improve the system capacity. This paper proposes an efficient algorithm based on machine learning (ML) for effective system performance in mmwave massive MIMO systems. The main idea is to optimize the adaptive connection structure to maximize the received signal power of each user and correlate the RF chain and base station antenna. Simulation results show that, the proposed algorithm effectively improved the system performance in terms of spectral efficiency and complexity as compared with existing algorithms.

Distributed Detection for Centralized and Decentralized Millimeter Wave Massive MIMO Sensor Networks

Multi-sensor millimeter wave (mmWave) massive multiple-input multiple-output (MIMO) wireless sensor networks (WSNs) relying on both distributed (D-MIMO) and centralized (C-MIMO) configurations are conceived. Hybrid combining based low complexity fusion rules are constructed for the fusion center (FC) for both D-MIMO and C-MIMO systems employing a partially connected structure (PCS) and a fully connected structure (FCS), respectively. The decision rules are based on the transmission of local binary sensor decisions and also take into account the accuracy of local detection at the individual sensors. Closed-form analytical expressions are derived for the probabilities of false alarm and correct detection to analyze the system's performance. Furthermore, the asymptotic distributed detection (DD) performance corresponding to both antenna architectures is analyzed in the large-scale antenna regime along with the pertinent power scaling laws. Additionally, digital signaling matrices are designed for enhancing the system performance. Our simulation results quantify the performance gains of the proposed architectures, which closely match the analytical results.

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.

Principle of Computation Power Optimization in Millimeter Wave Massive MIMO Systems

The computation power of baseband units (BBUs) is a major source of power consumption in millimeter wave (mmWave) massive multiple-input multiple-output (MIMO) systems with a large number of users due to complex signal processing. The effective reduction of computation power is critical for improving system energy efficiency. In this paper, the principle of reducing the computation power of BBUs is first investigated in mmWave massive MIMO systems with a hybrid precoding structure. A recursive constraint in decomposing the baseband precoding matrix is derived for reducing the computation power of hybrid precoding systems. Furthermore, the optimal number of sub-matrices minimizing the maximum error in decomposing the baseband precoding matrix is obtained. Based on the proposed principle, consisting of the recursive constraint and the optimal number of sub-matrices, a fast Monte Carlo baseband precoding (FMCBP) algorithm is developed to reduce the computation power of BBUs and improve system energy efficiency. Simulation results show that the total transmission rate and energy efficiency of mmWave systems are coupled with the computation power of BBUs, based on the FMCBP algorithm. Moreover, the FMCBP algorithm maximally improves the energy efficiency of multi-user mmWave massive MIMO communication systems by 124 percent, compared with the conventional equivalent zero-forcing algorithm.

Performance evaluation of wireless data traffic in Mm wave massive MIMO communication

&lt;span&gt;Due to the evaluation of mobile devices and applications in the current decade, a new direction for wireless networks has emerged. The general consensus about the future 5G network is that the following should be taken into account; the purpose of thousand-fold system capacity, hundredfold energy efficiency, lower latency, and smooth connectivity. The massive multiple-input multiple-output (MIMO), as well as the Millimeter wave (mm Wave) have been considered in the ultra-dense cellular network (UDN), because they are viewed as the emergent solution for the next generations of communication. This article focuses on evaluating and discussing the performance of mm Wave massive MIMO for ultra-dense network, which is one of the major technologies for the 5G wireless network. More so, the energy efficiencies of two kinds of architectures for wireless backhaul networks were investigated and compared in this article. The results of the simulation revealed some points that should be considered during the deployment of small cells in the two architectures UDN with backhaul network capacity and backhaul energy efficiency, that the changing the frequency bands in Distribution approach gives the same energy efficiency reached to 600 Mb/s at 15 nodes while the Conventional approach results reached less than 100 Mb/s at the same number of nodes.&lt;/span&gt;

Power saving and optimal hybrid precoding in millimeter wave massive MIMO systems for 5G

The proliferation of wireless services emerging from use cases offifth-generation(5G) technology is posing many challenges on cellular communicationinfrastructure. They demand to connect a massive number of devices withenhanced data rates. The massive multiple-input multiple-output (MIMO)technology at millimeter-wave (mmWave) in combination with hybrid precodingemerges as a concrete tool to address the requirements of 5G networkdevelopments. But Massive MIMO systems consume significant power fornetwork operations. Hence the prior role is to improve the energy efficiency byreducing the power consumption. This paper presents the power optimizationmodels for massive MIMO systems considering perfect channel state information(CSI) and imperfect CSI. Further, this work proposes an optimal hybrid precodingsolution named extended simultaneous orthogonal matchingpursuit (ESOMP).Simulation results reveal that a constant sum-rate can be achieved in massiveMIMO systems while significantly reducing the power consumption. Theproposed extended SOMPhybrid precoder performsclose to the conventionaldigital beamforming method. Further, modulation schemes compatible withmassive MIMO systems are outlined and their bit error rate (BER) performance isinvestigated

Guest Editorial Special Issue on Multiple Antenna Technologies for Beyond 5G-Part II

Recently, the first version of the fifth-generation (5G) new radio (NR) standard with massive multiple-input multiple-output (MIMO) has been finished by the 3rd Generation Partnership Project (3GPP), with initial deployments occurring in 2018. Despite the major advances in 5G, there are still many challenges remaining. 6G and beyond will require even higher data rates, lower latencies, better energy efficiency, and improved robustness. <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Multiple antenna technologies,</i> which have played important roles in nearly all recent wireless standards, will be key to addressing these challenges. MIMO research continues to evolve, and new MIMO research topics such as enhanced massive MIMO techniques and array architectures hold much potential for 6G and beyond. Cell-free massive MIMO utilize a large number of distributed access points (APs) that jointly serve users in a coordinated fashion, using only local channel state information at each AP. While the performance of cell-free massive MIMO can be analyzed using a similar methodology as in cellular massive MIMO, the fundamental limits, signal processing, and resource allocation are substantially different. In order to reduce the hardware cost and energy consumption in millimeter wave (mmWave) massive MIMO systems, beamspace MIMO has been proposed to significantly reduce the number of required radio-frequency (RF) chains by using lens antenna arrays or phase shifters. Alternatively, the intelligent reflecting surface (IRS) concept involves electromagnetically controllable surfaces that can be integrated into large-scale infrastructure such as building walls, airports, and stadiums. There are active and partially passive forms of large intelligent surface (LIS), and variants with either large antenna spacing or continuous aperture. There are also some substantial differences between the new multiple antenna technologies and traditional MIMO systems, such as transceiver design and propagation models. This special issue aims to highlight recent research on multiple antenna technologies.

Guest Editorial Special Issue on Multiple Antenna Technologies for Beyond 5G-Part—I

Recently, the first version of the fifth-generation (5G) new radio (NR) standard with massive multiple-input multiple-output (MIMO) has been finished by the 3rd Generation Partnership Project (3GPP), with initial deployments occurring in 2018. Despite the major advances in 5G, there are still many challenges remaining. 6G and beyond will require even higher data rates, lower latencies, better energy efficiency, and improved robustness. <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Multiple antenna technologies,</i> which have played important roles in nearly all recent wireless standards, will be key to addressing these challenges. MIMO research continues to evolve, and new MIMO research topics such as enhanced massive MIMO techniques and array architectures hold much potential for 6G and beyond. Cell-free massive MIMO utilize a large number of distributed access points (APs) that jointly serve users in a coordinated fashion, using only local channel state information at each AP. While the performance of cell-free massive MIMO can be analyzed using a similar methodology as in cellular massive MIMO, the fundamental limits, signal processing, and resource allocation are substantially different. In order to reduce the hardware cost and energy consumption in millimeter wave (mmWave) massive MIMO systems, beamspace MIMO has been proposed to significantly reduce the number of required radio-frequency (RF) chains by using lens antenna arrays or phase shifters. Alternatively, the intelligent reflecting surface (IRS) concept involves electromagnetically controllable surfaces that can be integrated into large-scale infrastructure such as building walls, airports, and stadiums. There are active and partially passive forms of large intelligent surface (LIS), and variants with either large antenna spacing or continuous aperture. There are also some substantial differences between the new multiple antenna technologies and traditional MIMO systems, such as transceiver design and propagation models. This special issue aims to highlight recent research on multiple antenna technologies.

Alternate hybrid precoding algorithm for wideband millimetre wave massive MIMO systems

Hybrid precoding, combining the digital and analogue precoding, is a key enabler to reach a compromise between system performance and hardware complexity in millimetre wave (mmWave) massive multiple-input multiple-output (MIMO) systems. Most previous studies on hybrid precoding considered narrowband channels. However, mmWave systems are expected to operate on wideband channels with frequency selectivity. In this study, the authors focus on the hybrid precoding design in mmWave massive MIMO systems using orthogonal frequency division multiplexing (OFDM). By transforming the hybrid precoding problem into a series of sub-problems, they propose a low-complexity algorithm to design the digital precoder and analogue precoder alternately. In particular, a phase pursuit method is introduced to seek this solution of analogue precoding matrix with the constant amplitude constraint. Simulation results and complexity evaluations reveal that the proposed algorithm can obtain better performance and lower complexity than some existing solutions in mmWave OFDM systems.

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.

On the Energy Efficiency of Millimeter Wave Massive MIMO Based on Hybrid Architecture

Millimeter Wave (mmWave) Massive Multiple Input Multiple Output (MIMO) has been a promising candidate for the current and next generation of cellular networks. The hybrid analogue/digital precoding will be a crucial ingredient in the mmWave cellular systems to reduce the number of Radio Frequency (RF) chains along with the corresponding energy and power consumption of the systems. In this paper, we aim to improve the energy efficiency of mmWave Massive MIMO by using a combination of high dimension analogue precoder and low dimension digital precoder. The spectral efficiency and the corresponding transmitted and consumed power of the mmWave Massive MIMO is formulated by taking all the consumed power from the transmitting side to receiving end into account. We propose the Power Controlled Energy Maximization (PCEM) algorithm in this paper, and the proposed algorithm works by controlling the transmission power to balance the improved radiated energy efficiency and the increased power consumption for a given number of transceiver chains. The simulation and analytical results show that the proposed algorithm performs better than the reference algorithms by maximizing the overall energy efficiency of the system without much complexity.

A multi-user linear equalizer for uplink broadband millimeter wave massive MIMO

Most previous work on hybrid beamforming millimeter wave (mmWave) communications and massive multiple input multiple output (MIMO) systems focused on narrowband channels. However, it is expected that the mmWave channels will be wideband, and for that reason, it is important to design solutions for frequency-selective channels. Therefore, in this paper, we consider the design of a hybrid analog/digital multiuser linear equalizer for broadband mmWave massive MIMO systems, optimized using the bit error rate (BER) as a metric. For the digital part, a closed-form solution is obtained by showing that the minimum mean square error (MMSE) and minimum BER solutions are identical. The analog part, which is assumed to be the same for all subcarriers, is computed iteratively over the radio frequency (RF) chains, and it is shown that the solution obtained in a previous iteration may be updated inexpensively to obtain a solution for the current iteration. The simulation results show that the performance gap between the proposed hybrid broadband multiuser equalizer and full digital equalizer decreases monotonically and exponentially with the number of RF chains until reaching zero. Moreover, the gap decay rate is faster for sparser mmWave channels, where fewer RF chains are required to achieve the same performance of the full digital architecture.

Energy-Efficient Hybrid Precoding Scheme Based on Antenna Selection Technology in Massive Multiple-Input Multiple-Output Systems

Hybrid precoding is a promising technology for massive multiple-input multiple-output (MIMO) systems. It can reduce the number of radio frequency (RF) chains. However, the power consumption is still very high owing to the large-scale antenna array. In this paper, we propose an energy-efficient precoding scheme based on antenna selection technology. The precoding scheme greatly increases the energy efficiency (EE) of the system. In the first step, we derive an exact closed-form expression of EE. Meanwhile, we further study the relationship between the number of transmit antennas and EE on the basis of the exact closed-form expression of EE. We prove that there exists an optimal value. When the number of transmit antennas equals to the value, the EE of the system can reach the maximum by a proper hybrid precoding scheme. Then, we propose an antenna selection algorithm to select antennas from the transmit antennas. And the number of selected antennas equals to the optimal value. Subsequently, we design the analog precoder based on a codebook to maximize the equivalent channel gain. At last, we further improve the EE by baseband digital precoding. The precoding algorithm we proposed offers a compromise between spectral efficiency (SE) and EE in millimeter wave (mmWave) massive MIMO systems. Finally, simulation results validate our theoretical analysis and show that a substantial EE gain can be obtained over the precoding scheme we proposed without large performance loss.