Analog-digital Precoding Research Articles

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.

Performance analysis of insertion loss incorporated hybrid precoding for massive MIMO

<abstract> <p>Due to an increase in the number of users and a high demand for high data rates, researchers have resorted to boosting the capacity and spectral efficiency of the next-generation wireless communication. With a limited RF chain, hybrid analog digital precoding is an appealing alternative. The hybrid precoding approach divides the beamforming process into an analog beamforming network and a digital beamforming network of a reduced size. As a result, numerous hybrid beamforming networks have been proposed. The practical effects of signal processing in the RF domain, such as the additional power loss incurred by an analog beamforming network, were not taken into account. The effectiveness of hybrid precoding structures for massive MIMO systems was examined in this study. In particular, a viable hardware network realization with insertion loss was developed. Investigating the spectral and energy efficiency of two popular hybrid precoding structures, the fully connected structure, and the subconnected structure, it was found that in a massive MIMO, the subconnected structure always performed better than the fully connected structure. Characterizing the effect of quantized analog precoding, it was shown that the subconnected structure was able to achieve better performance with fewer feedback bits than the fully connected structure.</p> </abstract>

Hybrid Analog and Digital Beamforming for RIS-Assisted mmWave Communications

Reconfigurable intelligent surface (RIS) assisted millimeter wave (mmWave) communications has been envisioned as a prominent technology for future wireless networks, since it is capable of simultaneously providing abundant spectrum resources and favorable propagation environments. The small wavelength at mmWave bands also enables the widespread use of large antenna arrays, of which the hybrid beamforming structure has emerged as a cost-effective solution. In this paper, we aim to minimize the sum-mean-square-error (sum-MSE) in the RIS-assisted mmWave multiuser multiple input multiple output (MU-MIMO) system by jointly optimizing the hybrid analog-digital precoders and the RIS reflection matrix. We demonstrate that the role of RIS in assisting mmWave communications can be completely replaced by a large-scale Kronecker-structured hybrid array. Moreover, an accelerated Riemannian gradient algorithm using majorization minimization technique is proposed to tackle the unit-modulus constrained analog precoder/RIS design. Under the assumption of perfect channel state information (CSI), we firstly consider the single-user MIMO (SU-MIMO) setup and propose an effective alternating minimization (AM) procedure to characterize the system performance limit. Moreover, a two-stage scheme is developed for low-complexity implementation. This AM procedure is then extended to the general MU-MIMO scenario. In addition, we develop a novel enhanced regularized zero-forcing (ERZF) scheme for simultaneously combating strong noise in the low-SNR regime and mitigating multi-user interference (MUI) in the high-SNR regime. The optimality of our proposed algorithms is validated for some simplified practical scenarios. Numerical results illustrate that the proposed algorithms outperform existing benchmark schemes in terms of the actual complexity and performance.

Hybrid Precoder Using Stiefel Manifold Optimization for Mm-Wave Massive MIMO System

Due to the increasing demand for fast data rates and large spectra, millimeter-wave technology plays a vital role in the advancement of 5G communication. The idea behind Mm-Wave communications is to take advantage of the huge and unexploited bandwidth to cope with future multigigabit-per-second mobile data rates, imaging, and multimedia applications. In Mm-Wave systems, digital precoding provides optimal performance at the cost of complexity and power consumption. Therefore, hybrid precoding, i.e., analog–digital precoding, has received significant consideration as a favorable alternative to digital precoding. The conventional methods related to hybrid precoding suffer from low spectral efficiency and large processing time due to nested loops and the number of iterations. A manifold optimization-based algorithm using the gradient method is proposed to increase the spectral efficiency to be near optimal and to speed up the processing speed. A comparison of performances is shown using the simulation outcomes of the proposed work and those of the existing techniques.

Design of Hybrid Precoding for Millimeter-Wave MIMO-NOMA Systems Based on User Fairness

This letter studies the design of hybrid precoding in millimeter-Wave (mmWave) multiple input multiple output-non orthogonal multiple access (MIMO-NOMA) systems. To guarantee the rate performance for all served users, we formulate the optimization problem of joint analog precoding (AP) and digital precoding (DP) vectors based on maximum and minimum (Max-Min) fairness to maximize the minimal achievable rate of users, i.e., we design different HP vectors for each user from the perspective of fairness. This can be solved by the proposed two-stage optimization scheme. First, the AP matrix and the DP vectors of each user are alternately designed, where the AP and DP vectors can be obtained by using the Semi-Definite Relaxation algorithm and the proposed boundary-compressed particle swarm optimization (BC-PSO) algorithm, respectively. Then, the optimal scaling factors obtained based on the Karush-Kuhn-Tucker (KKT) condition are introduced to further to improve the Max-Min rate. Simulation results show that the proposed scheme performs better than existing schemes.

MDL-AltMin: A Hybrid Precoding Scheme for mmWave Systems With Deep Learning and Alternate Optimization

The hybrid precoding structure composed of analog and digital precoders has received increasing attention in mmWave massive <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">multiple-input multiple-output</i> (MIMO) systems because it can balance the energy consumption and <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">spectral efficiency</i> (SE). However, it is challenging to obtain the optimal hybrid precoding scheme by joint optimization with lower computational complexity. This letter proposes a hybrid precoding scheme based on <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">model-driven deep learning and alternate minimization</i> (MDL-AltMin), which is implemented by alternately solving analog precoder and digital precoder. During the alternation, we design an <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">analog precoding network</i> (AP-Net) to solve the phase shift network in analog precoder with the goal of maximizing SE. The digital precoder is solved by the Lagrange multiplier method. In each alternate optimization process, the criteria for convergence is to minimize the error between the hybrid precoder and the optimal fully digital precoder. The simulation results show that the SE of our proposed scheme is very close to the fully digital precoding scheme based on singular value decomposition with lower computational complexity.

Hybrid Precoding Based on Partial Connection for Millimeter-Wave Massive MIMO System

Aiming at poor system performance in existing partially connected hybrid precoding schemes, in this paper, we propose a partially connected hybrid precoding scheme based on alternating optimization with the auxiliary precoder. In particular, the spectral efficiency optimization problem is transformed into a sub-optimization problem under certain constraints. For each sub-optimization problem, we use the singular value decomposition method to optimize the analog precoder and digital precoder alternately, and optimal solutions are provided for both digital and analog precoders in each alternate iteration. Moreover, we design a heuristic algorithm to calculate the initial analog precoder as the starting point for alternating optimization, which speeds up the convergence speed. The simulation results show that the proposed algorithm is at least 16.2% higher than the existing two traditional partially connected algorithms at 20 dB received SNR with almost no increase in complexity.

Sparse Hybrid Precoding for Power Minimization With an Adaptive Antenna Structure in Massive MIMO Systems

In massive multiple-input multiple-output (MIMO) systems employing hybrid analog-digital precoder, there are two commonly used antenna structures that have their own pros and cons, namely, the fully-connected antenna structure (FCAS) and the partially-connected antenna structure (PCAS). The FCAS achieves better spectrum efficiency (SE) even with reduced radio frequency (RF) chains, but the hardware cost and power consumption are still grievous. Contrarily, the PCAS has less hardware cost and power consumption, but suffers from severe performance loss. In this paper, by combining the advantages of both structures, we first propose a sparse adaptive antenna structure (SAAS) for the implementation of the hybrid precoder, which can jointly control the on/off state of all phase shifters (PS) and RF chains through a switch network. Then, a sparse hybrid precoding (SHP) optimization problem based on the proposed SAAS is established aiming at minimizing the total power consumption under individual average data rate requirements. To tackle the challenging non-smooth non-convex stochastic optimization (NSO) emerged with the SHP design and reduce the power consumption of PSs and RF chains, we propose a sparse smooth approximation based an online algorithm to find a stationary point of the NSO problem and establish its convergence. Simulations verify that the proposed antenna structure and algorithm achieve a better balance between power consumption and system throughput than the existing schemes.

Hybrid Precoding for Mixture Use of Phase Shifters and Switches in mmWave Massive MIMO

A variable-phase-shifter (VPS) architecture with hybrid precoding for mixture use of phase shifters and switches, is proposed for millimeter wave massive multiple-input multiple-output communications. For the VPS architecture, a hybrid precoding design (HPD) scheme, called VPS-HPD, is proposed to optimize the phases according to the channel state information by alternately optimizing the analog precoder and digital precoder. To reduce the computational complexity of the VPS-HPD scheme, a low-complexity HPD scheme for the VPS architecture (VPS-LC-HPD) including alternating optimization in three stages is then proposed, where each stage has a closed-form solution and can be efficiently implemented. To reduce the hardware complexity introduced by the large number of switches, we consider a group-connected VPS architecture and propose a HPD scheme, where the HPD problem is divided into multiple independent subproblems with each subproblem flexibly solved by the VPS-HPD or VPS-LC-HPD scheme. Simulation results verify the effectiveness of the propose schemes and show that the proposed schemes can achieve satisfactory spectral efficiency performance with reduced computational complexity or hardware complexity.

Covert Rate Optimization of Millimeter Wave Full-Duplex Communications

In this paper, we consider the problem of full-duplex covert millimeter wave (mmWave) communications, where a mmWave transmitter (Alice) sends information signals to its intended receiver (Bob) covertly in the presence of a watchful warden (Willie). For covering the presence of Alice, Bob operates in the full-duplex mode and generates jamming signals with a time-varying power. We investigate the covert rate optimization for both the single data stream case and the multiple data streams case under the constraints of the detection error probability at Willie. Specifically, for the single data stream case, we analytically characterize the minimum detection error probability at Willie and establish a framework for optimizing the analog beamforming, transmit power, and analog jamming jointly. As for the case of multiple data streams, we derive a tractable lower bound of the minimum detection error probability at Willie and formulate a joint optimization of the hybrid precoder and analog jamming design problem for the maximization of the achievable covert rate. Although the joint design problem is nonconvex, we adopt the penalty decomposition technique to handle the effect of the coupling between the analog precoder and digital precoder paving the way for the development of an iterative algorithm to locate its Karush-Kuhn-Tucker (KKT) solution. Finally, we show that our proposed joint design algorithm can be adapted to handle the multi-antenna Willie scenario and simulation results show that our proposed joint design algorithms can achieve significantly better performance as compared with some benchmark schemes.

Uplink millimeter-wave multi-cell multi-user massive multi-input multi-output systems

In this paper, we delve into the maximized spectral efficiency (SE) of millimeter-wave (mmWave) multicell multiuser massive MIMO Systems for uplink transmission with low-resolution phase shifters (LRPSs). Millimeter-wave massive multiple-input multiple-output (mMIMO) is an important technology for upcoming cellular networks which will provide higher bandwidth and throughput than current wireless systems and networks. LRPSs are commonly used to minimize power consumption, maximize spectral efficiency and diminish the complexity of hybrid precoder and combiner. In this paper, we consider a hybrid analog-digital precoder and combiner design with LRPSs for mmWave multi-cell multiuser mMIMO systems for uplink transmission to spectral efficiency in terms of iterations. The proposed technique outperforms when compared to traditional optimization approaches concerning spectral efficiency and bit error rate (BER). We show through simulation results that our designs with LRPSs outperform standard iteration procedures.

Hybrid Precoding for Millimeter Wave MIMO: Trace Optimization Approach

The hybrid precoding problem in point-to-point millimeter wave (mmWave) multiple input multiple output (MIMO) for narrowband channel is established as a Frobenius norm minimization problem. It is translated into trace minimization problem, and two algorithms are proposed to solve it. In the first method based on alternating minimization, we alternately determine the analog precoder and digital precoder, keeping the other constant to minimize the trace. The analog precoding subproblem with the fixed digital precoder is converted into a semi-definite programming (SDP) problem and solved by block coordinate descent (BCD) algorithm with suitable modifications. In the second method, we segregate the analog precoding and digital precoding subproblems by considering orthogonality of analog precoder. The analog precoding is further rephrased as a trace maximization problem and solved by an iterative power method by enforcing orthogonality constraint on the analog precoder. The adapted form of modified Gramm-Schmidt orthogonalization procedure is employed to impose orthogonality on the analog precoder. The proposed methods are extended for wideband channel by considering orthogonal frequency division multiplexing (OFDM). The proposed methods not only exhibit a good performance but also come with lower computational complexity when compared to existing methods with comparable performances.

Two-Timescale End-to-End Learning for Channel Acquisition and Hybrid Precoding

In this paper, we propose an end-to-end deep learning-based joint transceiver design algorithm for millimeter wave (mmWave) massive multiple-input multiple-output (MIMO) systems, which consists of deep neural network (DNN)-aided pilot training, channel feedback, and hybrid analog-digital (HAD) precoding. Specifically, we develop a DNN architecture that maps the received pilots into feedback bits at the receiver, and then further maps the feedback bits into the hybrid precoder at the transmitter. To reduce the signaling overhead and channel state information (CSI) mismatch caused by the transmission delay, a two-timescale DNN composed of a long-term DNN and a short-term DNN is developed. The analog precoders are designed by the long-term DNN based on the CSI statistics and updated once in a frame consisting of a number of time slots. In contrast, the digital precoders are optimized by the short-term DNN at each time slot based on the estimated low-dimensional equivalent CSI matrices. A two-timescale training method is also developed for the proposed DNN with a binary layer. We then analyze the generalization ability and signaling overhead for the proposed DNN based algorithm. Simulation results show that our proposed technique significantly outperforms conventional schemes in terms of bit-error rate performance with reduced signaling overhead and shorter pilot sequences.

Securing Massive MIMO Systems: Secrecy for Free With Low-Complexity Architectures

Passively overheard massive multiple-input multiple-output (MIMO) settings are capable of suppressing eavesdroppers via narrow beamforming towards legitimate receivers. This implies that secrecy is obtained almost for free in these settings. This study shows that this is a valid property for a large class of low-complexity massive MIMO transmitters. The investigations consider two dominant approaches for complexity reduction, namely antenna selection and hybrid analog-digital precoding . It is shown that using either approach, the information leakage per achievable sum-rate vanishes as the number of transmit antennas grows large. The results demonstrate that, as the transmit array size grows large, the normalized information leakage obtained by antenna selection and hybrid analog-digital precoding converges to zero double-logarithmically and logarithmically , respectively. The analytical results are confirmed for various benchmark architectures via numerical simulations.

A novel committee machine hybrid precoding and combining algorithm for mmWave massive MU-MIMO systems

Millimeter-wave (mmWave) massive multi-user multiple input multiple output (MU-MIMO) systems employ hybrid analog-digital precoding/combining design, to reduce the number of radio-frequency (RF) chains without large sum-rate performance loss. Committee machines combine several expert algorithms to yield better reliable estimates to those of its constituent experts. However, several committee machines approach mainly rely on the ‘quality’ of the joint support-set of expert algorithms combine by committee machine. In this paper, we present hybrid analog-digital precoder and combiner designs for mmWave massive MU-MIMO systems by exploiting the intersection of the estimated support-sets, namely, common support-set of ‘expert’ algorithms in a committee machine methodology. With S denoting the sparsity level, the proposed algorithms perform two essential tasks to identify in which subspace, generated by not more than S columns of the matrix of array response vectors, the optimal hybrid analog-digital precoders or combiners lie: Firstly, the selection of the committee machine common support set, which accepts the section where both the ‘experts’ agree. Secondly, if some column indices of the optimal hybrid analog-digital precoders or combiners do not lie in the current common support-set for the correct spanning space, −the algorithm searches over the matrix of array response vectors and selects column indices that exhibit the highest correlation with the signal residual, to acquire the remaining support. We derive the theoretical analysis for performance enhancement of the proposed algorithm. Simulation results demonstrate that the proposed design allows mmWave massive MU-MIMO systems to approach their unconstrained performance limits, and exhibits substantial sum-rate performance improvement over existing regularized channel diagonalization based schemes and the beam steering solution.

Deep double-pilot-based hybrid precoding in UAV-enabled mmWave massive MIMO

Unmanned aerial vehicle (UAV)-enabled communication system provides flexibility and reliability compared to conventional ones. Millimeter wave (mmWave) and massive multiple-input–multiple-output (MIMO) have widely been researched since recent years, which are promising techniques for the next and even the later generation communication system. Hybrid precoding, as a method to reduce the high cost in hardware and power brought by massive antenna array, develops fiercely and is often combined to deep learning, a kind of popular optimization tool, which brings an overwhelming performance. On the other hand, there are not so many attentions about the hybrid precoding in time-varying mmWave massive MIMO, which is necessary to be considered in a UAV-enabled communication scenario because the performance will degrade seriously if the channel changed while the transmitter and receiver use the precoding matrix corresponding to the expired channel, yet. In this paper, we propose a double-pilot-based hybrid precoding system, which completes analog precoding and digital precoding separately—predicting the previous one using deep learning structure and updating equivalent channel frequently for the post one by enhancing the frequency of equivalent channel estimation.

Hybrid Beamforming for mmWave Massive MIMO Systems Employing DFT-Assisted User Clustering

Hybrid analog-digital precoding has been recognized as a promising potential solution to facilitate implementation of massive multiple-input multiple-output systems in the millimeter wave spectrum. Hybrid transceivers reduce the radio frequency chain count and cost by dividing the task of precoding between the digital and analog processing domains, but near-optimal design of the hybrid precoders is non-trivial and their optimal design is analytically intractable. This is due to the joint optimization of digital and analog precoding matrices as well as extra constraints for analog precoders due to their realization by analog phase shifters. Additionally, hybrid transceivers can be implemented via two architectures, either fully-connected or partially-connected. In this paper, we make use of projection algorithms to greatly simplify the design problem of the digital baseband and analog precoders into two optimization subproblems whose optimal solutions can be found. We also incorporate in the design a simplified user clustering algorithm based on the discrete Fourier transform, where users within the same and overlapping angular bins in the beam-space domain are grouped together. Simulation results demonstrate the proposed hybrid precoding and user clustering algorithm outperforms existing algorithms.

Principal Component Analysis-Based Broadband Hybrid Precoding for Millimeter-Wave Massive MIMO Systems

Hybrid analog-digital precoding is challenging for broadband millimeter-wave (mmWave) massive MIMO systems, since the analog precoder is frequency-flat but the mmWave channels are frequency-selective. In this paper, we propose a principal component analysis (PCA)-based broadband hybrid precoder/combiner design, where both the fully-connected array and partially-connected subarray (including the fixed and adaptive subarrays) are investigated. Specifically, we first design the hybrid precoder/combiner for fully-connected array and fixed subarray based on PCA, whereby a low-dimensional frequency-flat precoder/combiner is acquired based on the optimal high-dimensional frequency-selective precoder/combiner. Meanwhile, the near-optimality of our proposed PCA approach is theoretically proven. Moreover, for the adaptive subarray, a low-complexity shared agglomerative hierarchical clustering algorithm is proposed to group the antennas for the further improvement of spectral efficiency (SE) performance. Besides, we theoretically prove that the proposed antenna grouping algorithm is only determined by the slow time-varying channel parameters in the large antenna limit. Simulation results demonstrate the superiority of the proposed solution over state-of-the-art schemes in SE, energy efficiency (EE), bit-error-rate performance, and the robustness to time-varying channels. Our work reveals that the EE advantage of adaptive subarray over fully-connected array is obvious for both active and passive antennas, but the EE advantage of fixed subarray only holds for passive antennas.

Two-Step Codeword Design for Millimeter Wave Massive MIMO Systems With Quantized Phase Shifters

In this paper, a two-step codeword design approach for millimeter wave (mmWave) massive MIMO systems is presented. Ideal codewords are first designed, which ignores the hardware constraints in terms of phase shifter resolution and the number of RF chains. Based on the ideal codewords, practical codewords are then obtained taking the hardware constraints into consideration. For the ideal codeword design in the first step, additional phase is introduced to the beam gain to provide extra degree of freedom. We develop a phase-shifted ideal codeword design (PS-ICD) method, which is based on alternative minimization with each iteration having a closed-form solution and can be extended to design more general beamforming vectors with different beam patterns. Once the ideal codewords are obtained in the first step, the practical codeword design problem in the second step is to approach the ideal codewords by considering the hardware constraints of the hybrid precoding structure in terms of phase shifter resolution and the number of RF chains. We propose a fast search based alternative minimization (FS-AltMin) algorithm that alternatively designs the analog precoder and digital precoder. Simulation results verify the effectiveness of the proposed methods and show that the codewords designed based on the two-step approach outperform those designed by the existing approaches.

A Comprehensive Survey on Millimeter Wave Communications for Fifth-Generation Wireless Networks: Feasibility and Challenges

Fifth-generation (5G) cellular networks will almost certainly operate in the high-bandwidth, underutilized millimeter-wave (mmWave) frequency spectrum, which offers the potentiality of high-capacity wireless transmission of multi-gigabit-per-second (Gbps) data rates. Despite the enormous available bandwidth potential, mmWave signal transmissions suffer from fundamental technical challenges like severe path loss, sensitivity to blockage, directivity, and narrow beamwidth, due to its short wavelengths. To effectively support system design and deployment, accurate channel modeling comprising several 5G technologies and scenarios is essential. This survey provides a comprehensive overview of several emerging technologies for 5G systems, such as massive multiple-input multiple-output (MIMO) technologies, multiple access technologies, hybrid analog-digital precoding and combining, non-orthogonal multiple access (NOMA), cell-free massive MIMO, and simultaneous wireless information and power transfer (SWIPT) technologies. These technologies induce distinct propagation characteristics and establish specific requirements on 5G channel modeling. To tackle these challenges, we first provide a survey of existing solutions and standards and discuss the radio-frequency (RF) spectrum and regulatory issues for mmWave communications. Second, we compared existing wireless communication techniques like sub-6-GHz WiFi and sub-6 GHz 4G LTE over mmWave communications which come with benefits comprising narrow beam, high signal quality, large capacity data transmission, and strong detection potential. Third, we describe the fundamental propagation characteristics of the mmWave band and survey the existing channel models for mmWave communications. Fourth, we track evolution and advancements in hybrid beamforming for massive MIMO systems in terms of system models of hybrid precoding architectures, hybrid analog and digital precoding/combining matrices, with the potential antenna configuration scenarios and mmWave channel estimation (CE) techniques. Fifth, we extend the scope of the discussion by including multiple access technologies for mmWave systems such as non-orthogonal multiple access (NOMA) and space-division multiple access (SDMA), with limited RF chains at the base station. Lastly, we explore the integration of SWIPT in mmWave massive MIMO systems, with limited RF chains, to realize spectrally and energy-efficient communications.