Millimeter-wave Massive Multiple-input Multiple-output Systems Research Articles

Joint Transceiver and Intelligent Reflecting Surface Design for mmWave Massive MIMO Systems

This article aims to maximize the spectral efficiency of an intelligent reflecting surface (IRS)-assisted hybrid millimeter-wave massive multiple-input–multiple-output system by jointly optimizing the hybrid precoding at the base station, hybrid combining at the user equipment, and reflecting beamforming at the IRS, where the reflecting beamforming and analog precoding/combining are implemented with finite-resolution phase shifters. This joint design problem can be decoupled into reflecting beamforming and hybrid precoding/combining design problems. However, such a decoupled approach experiences difficulties in solving the reflecting beamforming design problem. A known solution further reformulates the reflecting beamforming design problem into a more tractable problem addressed by a Riemannian manifold optimization (RMO)-based algorithm. However, the application of the RMO-based algorithm to solve the reformulated problem may lead to performance degradation given that the reformulated problem differs from the original one. Moreover, the RMO-based algorithm is tailored for the IRS with infinite-resolution phase shifters rather than practical finite-resolution phase shifters. Furthermore, the complexity of the RMO-based algorithm remains high. Therefore, we propose two coordinate descent method-based algorithms to tackle these issues. Simulation results demonstrate the effectiveness of the proposed algorithms compared with the state-of-the-art RMO-based algorithm.

A Family of Deep Learning Architectures for Channel Estimation and Hybrid Beamforming in Multi-Carrier mm-Wave Massive MIMO

Hybrid analog and digital beamforming transceivers are instrumental in addressing the challenge of expensive hardware and high training overheads in the next generation millimeter-wave (mm-Wave) massive MIMO (multiple-input multiple-output) systems. However, lack of fully digital beamforming in hybrid architectures and short coherence times at mm-Wave impose additional constraints on the channel estimation. Prior works on addressing these challenges have focused largely on narrowband channels wherein optimization-based or greedy algorithms were employed to derive hybrid beamformers. In this paper, we introduce a deep learning (DL) approach for channel estimation and hybrid beamforming for frequency-selective, wideband mm-Wave systems. In particular, we consider a massive MIMO Orthogonal Frequency Division Multiplexing (MIMO-OFDM) system and propose three different DL frameworks comprising convolutional neural networks (CNNs), which accept the raw data of received signal as input and yield channel estimates and the hybrid beamformers at the output. We also introduce both offline and online prediction schemes. Numerical experiments demonstrate that, compared to the current state-of-the-art optimization and DL methods, our approach provides higher spectral efficiency, lesser computational cost and fewer number of pilot signals, and higher tolerance against the deviations in the received pilot data, corrupted channel matrix, and propagation environment.

Residual Learning and Multi-Path Feature Fusion-Based Channel Estimation for Millimeter-Wave Massive MIMO System.

Channel estimation is a challenging task in a millimeter-wave (mm Wave) massive multiple-input multiple-output (MIMO) system. The existing deep learning scheme, which learns the mapping from the input to the target channel, has great difficulty in estimating the exact channel state information (CSI). In this paper, we consider the quantized received measurements as a low-resolution image, and we adopt the deep learning-based image super-resolution technique to reconstruct the mm Wave channel. Specifically, we exploit a state-of-the-art channel estimation framework based on residual learning and multi-path feature fusion (RL-MFF-Net). Firstly, residual learning makes the channel estimator focus on learning high-frequency residual information between the quantized received measurements and the mm Wave channel, while abundant low-frequency information is bypassed through skip connections. Moreover, to address the estimator’s gradient dispersion problem, a dense connection is added to the residual blocks to ensure the maximum information flow between the layers. Furthermore, the underlying mm Wave channel local features extracted from different residual blocks are preserved by multi-path feature fusion. The simulation results demonstrate that the proposed scheme outperforms traditional methods as well as existing deep learning methods, especially in the low signal-to-noise-ration (SNR) region.

Optimal hybrid precoder design for millimeter-wave massive MIMO systems

Millimeter-waves (mmWave) have emerged as a promising candidate for next-generation communication systems. However, they have severe degradation issues that can be overcome by multiple-input multiple-output (MIMO) technology. Still, high-power consumption and budget issues are associated with multiple antennas. Therefore, hybrid precoders are exploited to combat these inevitable issues. The prime objective of this manuscript is to develop a hybrid precoder for massive MIMO systems that can provide better performance than the existing ones in terms of bit error rate (BER) versus signal-to-noise ratio (SNR). In this context, we exploit iterative geometric mean decomposition (IGMD) method that presents asymptotically optimum performance not only in traditional MIMO systems but also in massive MIMO systems. Later, the outcomes of the proposed scheme are compared with a recent design exploiting generalized triangular decomposition (GTD) scheme. The simulation studies show that the proposed method provides more than 7 dB improvement according to other designs.

Manifold Discriminative Learning Inspired Hybrid Beamforming for Millimeter-Wave Massive MIMO Systems

Millimeter-wave (mmWave) massive MIMO (multiple-input multiple-output) is a promising technology as it provides significant beamforming gains and interference reduction capabilities due to the large number of antennas. However, mmWave massive MIMO is computationally demanding, as the high antenna count results in high-dimensional matrix operations when conventional MIMO processing is applied. Hybrid precoding is an effective solution for the mmWave massive MIMO systems to significantly decrease the number of radio frequency (RF) chains without an apparent sum-rate loss. In this paper, we propose user clustering hybrid precoding to enable efficient and low-complexity operation in high-dimensional mmWave massive MIMO, where a large number of antennas are used in low-dimensional manifolds. By modeling each user set as a manifold, we formulate the problem as clustering-oriented multi-manifolds learning. The manifold discriminative learning seek to learn the embedding low-dimensional manifolds, where manifolds with different user cluster labels are better separated, and the local spatial correlation of the high-dimensional channels within each manifold is enhanced. Most of the high-dimensional channels are embedded in the low-dimensional manifolds by manifold discriminative learning, while retaining the potential spatial correlation of the high-dimensional channels. The nonlinearity of high-dimensional channel is transformed into global and local nonlinearity to achieve dimensionality reduction. Through proper user clustering, the hybrid precoding is investigated for the sum-rate maximization problem by manifold quasi conjugate gradient methods. The high signal to interference plus noise ratio (SINR) is achieved and the computational complexity is reduced by avoiding the conventional schemes to deal with high-dimensional channel parameters. Performance evaluations show that the proposed scheme can obtain near-optimal sum-rate and considerably higher spectral efficiency than some existing solutions

Novel Convolutional Restricted Boltzmann Machine manifold learning inspired dynamic user clustering hybrid precoding for millimeter-wave massive multiple-input multiple-output systems

Millimeter-wave massive multiple-input multiple-output is a key technology in 5G communication system. In particular, the hybrid precoding method has the advantages of being power efficient and less expensive than the full-digital precoding method, so it has attracted more and more attention. The effectiveness of this method in simple systems has been well verified, but its performance is still unknown due to many problems in real communication such as interference from other users and base stations, and users are constantly on the move. In this article, we propose a dynamic user clustering hybrid precoding method in the high-dimensional millimeter-wave multiple-input multiple-output system, which uses low-dimensional manifolds to avoid complicated calculations when there are many antennas. We model each user set as a novel Convolutional Restricted Boltzmann Machine manifold, and the problem is transformed into cluster-oriented multi-manifold learning. The novel Convolutional Restricted Boltzmann Machine manifold learning seeks to learn embedded low-dimensional manifolds through manifold learning in the face of user mobility in clusters. Through proper user clustering, the hybrid precoding is investigated for the sum-rate maximization problem by manifold quasi-conjugate gradient methods. This algorithm avoids the traditional method of processing high-dimensional channel parameters, achieves a high signal-to-noise ratio, and reduces computational complexity. The simulation result table shows that this method can get almost the best summation rate and higher spectral efficiency compared with the traditional method.

Extreme learning machine detector for millimeter-wave massive MIMO systems

In this paper, we present an extreme learning machine (ELM) neural network designed to perform multiple-input multiple-output (MIMO) detection for millimeter-wave (mm-wave) communications operating in the 28 GHz frequency band. The ELM strategy can perform online MIMO combining processing. This method does not require offline training like with deep neural networks. The proposed technique was compared in terms of the achievable bit error rate (BER) and spectral efficiency (SE) to the maximum ratio (MR) and minimum mean squared error (MMSE) MIMO detectors, considering an orthogonal frequency-division multiplexing (OFDM) uplink scheme based on the fifth generation (5G) New Radio standard. Numerical results show that the ELM strategy outperforms the MR and MMSE detectors since this method reduces the inter-user interference effects, specifically for low equivalent isotropic radiated power at the receiver during the uplink communication. Furthermore, the ELM method requires only 16 % of the floating-point operations required by the MMSE detector.

A Deep Learning Framework for Hybrid Beamforming Without Instantaneous CSI Feedback

Hybrid beamformer design plays very crucial role in the next generation millimeter-wave (mm-Wave) massive MIMO (multiple-input multiple-output) systems. Previous works assume the perfect channel state information (CSI) which results heavy feedback overhead. To lower complexity, channel statistics can be utilized such that only infrequent update of the channel information is needed. To reduce the complexity and provide robustness, in this work, we propose a deep learning (DL) framework to deal with both hybrid beamforming and channel estimation. For this purpose, we introduce three deep convolutional neural network (CNN) architectures. We assume that the base station (BS) has the channel statistics only and feeds the channel covariance matrix into a CNN to obtain the hybrid precoders. At the receiver, two CNNs are employed. The first one is used for channel estimation purposes and the another is employed to design the hybrid combiners. The proposed DL framework does not require the instantaneous feedback of the CSI at the BS. We have also investigated the online deployment of DL for channel estimation. We have shown that the proposed approach has higher spectral efficiency with comparison to the conventional techniques. The trained CNN structures do not need to be re-trained due to the changes in the propagation environment such as the deviations in the number of received paths and the fluctuations in the received path angles up to 4 degrees. Also, the proposed DL framework exhibits at least 10 times lower computational complexity as compared to the conventional optimization-based approaches.

Iterative Analog-Digital Multi-User Equalizer for Wideband Millimeter Wave Massive MIMO Systems.

Most of the previous work on hybrid transmit and receive beamforming focused on narrowband channels. Because the millimeter wave channels are expected to be wideband, it is crucial to propose efficient solutions for frequency-selective channels. In this regard, this paper proposes an iterative analog–digital multi-user equalizer scheme for the uplink of wideband millimeter-wave massive multiple-input-multiple-output (MIMO) systems. By iterative equalizer we mean that both analog and digital parts are updated using as input the estimates obtained at the previous iteration. The proposed iterative analog–digital multi-user equalizer is designed by minimizing the sum of the mean square error of the data estimates over the subcarriers. We assume that the analog part is fixed for all subcarriers while the digital part is computed on a per subcarrier basis. Due to the complexity of the resulting optimization problem, a sequential approach is proposed to compute the analog phase shifters values for each radio frequency (RF) chain. We also derive an accurate, semi-analytical approach for obtaining the bit error rate (BER) of the proposed hybrid system. The proposed solution is compared with other hybrid equalizer schemes, recently designed for wideband millimeter-wave (mmWave) massive MIMO systems. The simulation results show that the performance of the developed analog–digital multi-user equalizer is close to full-digital counterpart and outperforms the previous hybrid approach.

Joint measure matrix and channel estimation for millimeter-wave massive MIMO with hybrid precoding

Millimeter-wave (mmWave) massive multiple-input multiple-output (MIMO) with hybrid precoding is a promising technology for future 5G wireless communications. Channel estimation for the millimeter-wave (mmWave) MIMO systems with hybrid precoding can be performed by estimating the path directions of the channel and corresponding path gains. This paper considers joint measure matrix and channel estimation for a massive MIMO system. By exploiting the sparsity of a massive MIMO system, a channel estimation scheme based on a Toeplitz-structured measure matrix and complete complementary sequence (CC-S) is proposed. Moreover, analytic studies show that the measurement matrix based on CC-S yields either optimal performance or feasibility in practice than an independent identically distributed Gaussian matrix. The performance of the scheme is shown with numerical examples.

Hybrid Precoding Design for Adaptive Subconnected Structures in Millimeter-Wave MIMO Systems

Hybrid precoding design for an adaptive subconnected structure offers a compromise between hardware complexity and spectral efficiency in massive multiple-input multiple-output (MIMO) systems at millimeter-wave (mmWave) frequencies. This paper focuses on the impacts of the partial antenna connections on the achievable sum-rate (ASR) performance for the uniform linear array and uniform square planar array configurations in mmWave networks. The subarray architectures consist of the overlapped, interlaced, and dynamically selective subset schemes in mmWave MIMO systems. Notably, on the basis of the ASR maximization, the Gram–Schmidt (GS)-based antenna selection (AS) algorithm is used to acquire an appropriate antenna subset and magnificently simplifies the radio frequency chain–antenna mapping operation in the sequel. Finally, simulation results demonstrate that an adaptive subarray architecture in conjunction with the GS-based AS search strategy is able to accomplish the ASR performance approaching the fully connected architecture with an alleviated demand on both computation and hardware complexities.

Gradient Projection-Based Alternating Minimization Algorithm for Designing Hybrid Beamforming in Millimeter-Wave MIMO Systems

This letter considers the use of alternating minimization (AltMin) framework as the main design principle in determining the optimal weights of hybrid digital and analog beamforming in millimeter-wave massive multiple-input multiple-output systems. However, such framework experiences analog beamformer design problem because analog beamformers are normally constructed using phase shifters (PSs), which result in non-convex constraints, and known solutions suffer from high computational complexity. We address this issue by proposing a simple yet efficient gradient projection (GP)-based AltMin (GP-AltMin) algorithm for hybrid beamforming design problems. In addition, when quantized PSs are adopted, we propose non-uniform PSs on the basis of the Lloyd–Max algorithm for minimizing the performance loss caused by quantization. Simulation results demonstrate that the proposed GP-AltMin algorithm not only has lower complexity but can also achieve spectral efficiency, which is comparable with or higher than those of the state-of-the-art algorithms that use unquantized and low-resolution PSs.

Coverage and Cell-Edge Sum-Rate Analysis of mmWave Massive MIMO Systems With ORP Schemes and MMSE Receivers

In this study, we consider the downlink of millimeter-wave massive multiple-input multiple-output systems that employ orthogonal random precoding (ORP) and minimum-mean-square-error (MMSE) receivers. In the ORP scheme, a precoding matrix consisting of orthogonal vectors is utilized at the transmitter, which provides beamforming gains to enhance the maximum signal-to-interference-plus-noise ratio (SINR) at the receivers. In this study, the ability of the ORP scheme with MMSE receivers to extend the cell coverage and its sum-rate performance for cell-edge users are investigated. In particular, we first derive the approximate distribution of the maximum SINR at the output of the MMSE receiver. Then, to analyze and optimize the ORP scheme with MMSE receivers in terms of coverage and sum-rate performance, the analytical expressions for the downlink coverage probability and sum rate are derived. It is shown that there is a tradeoff between coverage and sum-rate performance in the ORP scheme. In particular, a smaller number of precoding vectors provides larger coverage; however, it leads to a lower sum rate. To achieve optimal tradeoff between coverage and sum rate for the ORP scheme, we propose using multiple random precoder groups over multiple time slots. It is shown that the proposed scheme is capable of significantly enhancing coverage performance while preserving an acceptable sum rate for cell-edge users. The simulation results validate the analytical findings.

Relay Hybrid Precoding Design in Millimeter-Wave Massive MIMO Systems

This paper investigates the relay hybrid precoding design in millimeter-wave massive multiple-input multiple-output systems. The optimal design of the relay hybrid precoding is highly nonconvex, due to the six-order polynomial objective function, six-order polynomial constraint, and constant-modulus constraints. To efficiently solve this challenging nonconvex problem, we first reformulate it into three quadratic subproblems, where one of the subproblems is convex and the other two are nonconvex. Then, we propose an iterative successive approximation (ISA) algorithm to attain the high-approximate optimal solution to the original problem. Specifically, in the proposed ISA algorithm, we first convert the two nonconvex subproblems to convex ones by the relaxation of the constant-modulus constraints, and then we solve the three corresponding convex subproblems iteratively. We theoretically prove that the ISA algorithm converges to a Karush–Kuhn–Tucker point of the original problem. Simulation results demonstrate that the proposed ISA algorithm achieves good performance in terms of achievable rate in both full-connected and subconnected relay hybrid precoding systems.

Energy-Efficient Hybrid Precoding Design for Millimeter-Wave Massive MIMO Systems Via Coordinate Update Algorithms

This paper considers an energy-efficient, hybrid digital, and analog precoding design problem in millimeter-wave massive multiple-input multiple-output systems, in which the analog precoder is realized with a small number of energy-efficient switches and inverters rather than with a large number of high-resolution phase shifters. However, finding the optimal weights of such energy-efficient hybrid precoding requires solving a challenging combinatorial problem. A known solver, namely “adaptive cross-entropy (ACE),” can provide a reasonable solution but its computational complexity is still high. Thus, a simple yet effective coordinate update algorithm (CUA) is proposed in this paper to reduce the computational complexity while maintaining and even improving the achievable rate performance. In addition, we propose a new hybrid precoding architecture that introduces the antenna selection mechanism into the conventional energy-efficient-based hybrid precoding architecture to further reduce energy consumption. Although, the resulting design problem of this new architecture becomes more complex in that the traditional ACE-based solver cannot be applied directly, the proposed CUA-based solver can still handle this problem. The simulation results demonstrate that the proposed CUA-based solver provides the same or even an improved achievable rate performance than the ACE-based solver at a lower complexity. Furthermore, the energy consumption of the proposed hybrid precoding architecture is lower than that of the conventional energy-efficient hybrid precoding architecture.

Spectrum and Energy-Efficient Beamspace MIMO-NOMA for Millimeter-Wave Communications Using Lens Antenna Array

The recent concept of beamspace multiple input multiple output (MIMO) can significantly reduce the number of required radio frequency (RF) chains in millimeter-wave (mmWave) massive MIMO systems without obvious performance loss. However, the fundamental limit of existing beamspace MIMO is that the number of supported users cannot be larger than the number of RF chains at the same time-frequency resources. To break this fundamental limit, in this paper, we propose a new spectrum and energy-efficient mmWave transmission scheme that integrates the concept of non-orthogonal multiple access (NOMA) with beamspace MIMO, i.e., beamspace MIMO-NOMA. By using NOMA in beamspace MIMO systems, the number of supported users can be larger than the number of RF chains at the same time-frequency resources. In particular, the achievable sum rate of the proposed beamspace MIMO-NOMA in a typical mmWave channel model is analyzed, which shows an obvious performance gain compared with the existing beamspace MIMO. Then, a precoding scheme based on the principle of zero forcing is designed to reduce the inter-beam interferences in the beamspace MIMO-NOMA system. Furthermore, to maximize the achievable sum rate, a dynamic power allocation is proposed by solving the joint power optimization problem, which not only includes the intra-beam power optimization, but also considers the inter-beam power optimization. Finally, an iterative optimization algorithm with low complexity is developed to realize the dynamic power allocation. Simulation results show that the proposed beamspace MIMO-NOMA can achieve higher spectrum and energy efficiency compared with the existing beamspace MIMO.

Efficient Codebook-Based Beamforming Algorithm for Millimeter-Wave Massive MIMO Systems

Hybrid beamforming architecture, consisting of a low-dimensional baseband digital beamforming component and a high-dimensional analog beamforming component, has received considerable attention in the context of millimeter-wave massive multiple-input multiple-output systems. This is because it can achieve an effective compromise between hardware complexity and system performance. To avoid accurate estimation of the channel, a codebook-based technique is widely used in analog beamforming components, wherein a transmitter and receiver jointly examine an analog precoder and analog combiner pair according to predesigned codebooks, without using a priori channel information. However, identifying an optimal analog precoder and analog combiner pair using the exhaustive search algorithm (ESA) incurs exponential complexity, causing the number of radio frequency chains to proliferate and hindering the resolution of the phase shifters, which cannot be solved even for highly reasonable system parameters. To reduce the search complexity while maximizing the achievable rate, we propose a low-complexity, near-optimal algorithm developed from a cross-entropy optimization framework. Our simulation results reveal that our algorithm achieves near-optimal performance at a much lower complexity than does the optimal ESA.

Hybrid Beamforming With Discrete Phase Shifters for Millimeter-Wave Massive MIMO Systems

Hybrid digital and analog beamforming design has been the focus of considerable interest in the context of millimeter-wave massive multiple-input multiple-output systems because such a design can provide a flexible compromise between hardware complexity and system performance. However, most existing hybrid beamforming designs usually assume that infinite resolution phase shifters (PSs) are available to produce analog beamformers. In a practical sense, the employment of such shifters with arbitrary phase is infeasible or, at least, is expensive because of hardware limitations. We propose an iterative hybrid transceiver design algorithm, where PSs can only supply discrete phase adjustments, to facilitate low-cost implementation of the analog beamformers via finite resolution PSs while maximizing spectral efficiency. Simulation results reveal that the performance of the proposed algorithm with low-resolution PSs is close to that of the state-of-the-art algorithm with infinite resolution PSs.