Hybrid Precoding for Millimeter Wave MIMO Systems: A Matrix Factorization Approach

When wireless transmission is performed over the bandwidth in the order of a gigahertz, high-resolution analog-to-digital converters (ADCs), and the large number of radio frequency chains significantly increase the power consumption. To address this issue, one promising technique is to use low-resolution, even one-bit ADCs. Another promising technique is to apply a hybrid precoding architecture to reduce the number of RF chains. In this paper, we propose to combine those techniques to reduce the hardware costs in multi-input multi-output system. Our objective is to optimize the hybrid precoder with the aim of increasing the achievable rate. To this end, we first derive an expression for the achievable rate in flat fading channels based on the Bussgang theorem, which is able to reformulate the nonlinear quantitative process as a linear function with identical first- and second-order statistics. To solve the non-convex hybrid precoding design problem, we treat the hybrid precoding design as a matrix factorization problem, which can be solved with an efficient alternating minimization algorithm. That is, we solve the digital precoder and the analog precoder in an alternative way in two separate subproblems. To find the optimal precoder in the first subproblem, we first prove the optimal structure of the digital precoding matrix. With it, we transfer the digital precoding design to a power allocation problem, the closed-form solution of which is then optimally found by using Karush–Kuhn–Tucker conditions. In the second subproblem, due to the non-convex modulus-norm constraint, it is challenging to directly solve the analog precoder. To resolve this problem, we propose to optimize the phases in the analog precoding matrix and adopt the subgradient algorithm to find the local optimal solution. Our simulation results show that the proposed hybrid precoding design effectively improves the achievable rates.

In Millimetre Wave (mmWave) Multiple-Inputs Multiple-Output (MIMO) systems, hybrid precoders are introduced the reduced number of Radio Frequency (RF) chains. In the existing hybrid precoder using Phase Shifter (PS) network consume high energy, the cost of hardware and the performance loss in the system is high. In this paper, Adaptive Cross-Entropy (ACE) based Kalman Hybrid Precoder for the frequency selective mmWave MIMO channel in time domain approach is proposed. ACE based kalman hybrid precoder is designed and develops for Switch and Inverter (SI) based architecture. In addition, Kalman based digital precoder is develop and compare with MMSE digital precoder. Simulation results show the ACE based kalman hybrid precoding for SI architecture is provide the low energy consumption, and higher Spectral Efficiency (SE) compares to the existing Two-Stage (TS) hybrid precoder, Antenna Selection (AS) and Cross-Entropy (CE) based hybrid precoders.

Multiple Input Multiple Output (MIMO) systems with limited Radio Frequency (RF) chains play a pivotal role in the Fifth Generation (5G) of wireless networks. However, the transmitter of Generalized Spatial Modulation MIMO (GSM-MIMO) systems that characterized by a single RF chain and multiple active antennas is capable of reducing both the energy consumption and the transmitter cost. In this paper, combining GSM-MIMO systems with the fully digital Geometric Mean Decomposition (GMD)-based precoding scheme and Analog Beamforming (ABF) into Hybrid Beamforming (HBF) regime is presented for Millimeter-wave (mmWave) massive MIMO systems which is a key enabler for 5G networks. In addition, applying the norm-based user selection algorithm in GSM-MIMO scheme with GMD-based hybrid precoding is proposed, and referred to as Multiuser Steered GSM-MIMO (MUS-GSM-MIMO) scheme. Simulation results demonstrate that the proposed schemes are capable of achieving considerable performance gains over the conventional GSM-MIMO schemes, while avoiding the overwhelming costs of multiple RF chains. Therefore, the proposed schemes are very efficient and highly suitable for large-scale and 5G wireless networks.

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.

This paper investigates hybrid precoding for millimeter-wave (mmWave) multi-group multicasting systems with the consideration of max-min fairness. We formulate it as the optimization problem of maximizing the minimum signal-to-interference-plus-noise ratio among all users subject to a total transmit power constraint and constant modulus constraints. The problem is nonconvex and hard to solve due mainly to the nonlinear coupling of the digital precoder and the analog precoders. By resorting to the recently proposed penalty dual decomposition (PDD) method, the max-min hybrid precoding problem reduces to repeatedly solving four subproblems, each of which admits simple solution. Numerical results validate the effectiveness of the proposed max-min fairness hybrid precoding algorithm.

The concept of generalized spatial modulation (GenSM) aided millimeter wave (mm-wave) multiple-input multiple-output (MIMO) has recently attracted substantial research interest, as it benefits from the large bandwidth of mm-wave MIMO, while maintaining a reduced number of radio frequency (RF) chains. However, due to the lack of precoding design, the preceding GenSM-aided mm-wave MIMO schemes suffered from severe performance loss. Inspired by the reduced-RF-chain structure making implementation cost low while maintaining the benefit of GenSM, in this paper, we incorporate the technique of hybrid precoding into GenSM-aided mm-wave MIMO, where a hybrid digital and analog precoding regime is proposed to enhance the system's achievable rate. Moreover, a closed-form expression is proposed to provide an accurate approximation to the spectral efficiency (SE) achieved by the proposed scheme. The proposed expression is further simplified in the region of high signal-to-noise ratio (SNR). By exploiting the proposed SE expressions as low-complexity cost functions, two algorithms, i.e. the gradient ascent algorithm and the high-SNR approximation algorithm, are exploited to optimize the hybrid precoders in terms of SE maximization. Finally, numerical simulations are provided to substantiate the superior SE performance achieved by the proposed scheme over other GenSM-aided mm-wave MIMO schemes as well as the state-of-the-art mm-wave MIMO systems.

Hybrid precoding for millimeter wave (mmWave) multiple-input multiple-output (MIMO) systems has attracted much attention in recent years for subarray architecture compared to array architecture because of its low cost and low power consumption. This is due to the small number of required phase shifters in the subarray architecture. In this paper, we investigate the issue of hybrid precoding for the subarray architecture in narrowband mmWave MIMO systems. First, we derive the spectral efficiency of the subarray architecture with hybrid precoding and discuss the problem formulation. Then, we propose two low-complexity hybrid precoding algorithms for the subarray architecture for narrowband mmWave MIMO systems. In the first algorithm, the hybrid precoding matrix is divided into subarrays submatrices and each subarray submatrix is then divided into vectors. The analog precoding of each subarray is determined from the first vector of the subarray submatrix, which is then used to determine the elements of the digital precoder from all vectors in the subarray submatrix (vector by vector) using a simple maximum ratio combining (MRC) method. The proposed algorithm is called vector-by-vector (VBV) hybrid precoding. Finally, to further enhance the system performance, the proposed VBV precoding in the first algorithm is also combined with an iterative solution, and the resulting algorithm is called iterative VBV precoder. Simulation results verify that the proposed precoding algorithms outperform that of the successive interference cancellation-based subarray precoding and has a performance that is close to that obtained by the fully-connected spatially sparse precoding in various system settings, with lower complexity.

Beam Division Multiple Access (BDMA) with hybrid precoding has recently been proposed for multi-user multiple-input multiple-output (MU-MIMO) systems by simultaneously transmitting multiple digitally precoded users’ data-streams via different beams. In contrast to most existing works that assume the number of radio frequency (RF) chains must be greater than or equal to that of data-streams, this work proposes a novel BDMA downlink system by first grouping transmitting data-streams before digitally precoding data group by group. To fully harvest the benefits of this new architecture, a greedy user grouping algorithm is devised to minimize the inter-group interference while two digital precoding approaches are developed to suppress the intra-group interference by maximizing the signal-to-interference-and-noise ratio (SINR) and the signal-to-leakage-and-noise ratio (SLNR), respectively. As a result, the proposed BDMA system requires less RF chains than the total number of transmit data-streams. Furthermore, we optimize the power allocation to satisfy each user’s quality of service (QoS) requirement using the D.C. (difference of convex functions) programming technique. Simulation results confirm the effectiveness of the proposed scheme.

Economical and energy-efficient analog/digital hybrid beamforming has been widely considered as a promising approach for millimeter wave (mmWave) multiple-input multiple-output (MIMO) systems. While most hybrid beamforming techniques consider a fully-connected structure with a large number of phase shifters (PSs), the partially-connected structure has drawn more attention recently since it requires much less PSs and can further improve energy-efficiency. However, the impractical assumption of infinite or high resolution of PSs in existing solutions frustrates the real-world deployment of hybrid beamforming designs, and low- resolution PSs are typically adopted to reduce the hardware complexity and power consumption. In an effort to achieve maximum hardware efficiency, this paper focuses on the partially-connected architecture with one-bit (binary) PSs and considers the problem of joint hybrid precoder and combiner design for such mmWave MIMO systems. We propose to successively design the analog beamformers associated with each pair of sub- array, aiming at conditionally maximizing the spectral efficiency. A novel binary analog precoder and combiner optimization algorithm is proposed under a rank-1 approximation of the interference-included equivalent channel with polynomial complexity in the number of antennas. Then, the digital precoder and combiner are computed based on the obtained effective baseband channel to further enhance the spectral efficiency. Simulation results demonstrate the advantages of proposed hardware-efficiency hybrid precoder and combiner design.

The cell-free MIMO concept relying on hybrid precoding constitutes an innovative technique capable of dramatically increasing the network capacity of millimeter-wave (mmWave) communication systems. It dispenses with the cell boundary of conventional multi-cell MIMO systems, while drastically reducing the power consumption by limiting the number of radio frequency (RF) chains at the access points (APs). In this paper, we aim for maximizing the weighted sum rate (WSR) of mmWave cell-free MIMO systems by conceiving a low-complexity hybrid precoding algorithm. We formulate the WSR optimization problem subject to the transmit power constraint for each AP and the constant-modulus constraint for the phase shifters of the analog precoders. A block coordinate descent (BCD) algorithm is proposed for iteratively solving the problem. In each iteration, the classic Lagrangian multiplier method and the penalty dual decomposition (PDD) method are combined for obtaining near-optimal hybrid analog/digital precoding matrices. Furthermore, we extend our proposed algorithm for deriving closed-form expressions for the precoders of fully digital cell-free MIMO systems. Moreover, we present the convergency analysis and complexity analysis of our proposed method. Finally, our simulation results demonstrate the superiority of the algorithms proposed for both fully digital and hybrid precoding matrices.

In this paper, we study the hybrid beamforming for the wideband mmWave multiuser MIMO-OFDM system. We characterize the frequency-dependent beam angle problem, i.e., beam squint effect. Firstly, we extend the mmWave channel model from the Saleh-Valenzuela representation with the consideration of beam squint. Secondly, a two-tier hybrid beamforming is proposed to achieve the maximum spectral efficiency in wideband mmWave multiuser MIMO-OFDM system. In the first tier, the Rotman lens array is adopted as the analog precoder to provide true-time-delay (TTD) and reduce the beam squint impairment. Moreover, the first-tier baseband precoder is designed based on block diagonalization (BD) to cancel inter-user interference. We further consider the finite spatial resolution and power leakage problem of the lens array. The second-tier hybrid precoder is proposed to collect the leak power with the phase shifter array. The optimal second-tier hybrid precoder design is formulated as the matrix factorization problem, and the two-tier hybrid precoding algorithm is based on the alternative minimization. It is found that both the beam squint and frequency-selective effect should be considered in the wideband mmWave system. Simulation results show that the proposed two-tier hybrid precoder could reduce beam squint impairment and inter-user interference, and could approximate to the optimal full-digital precoder with much fewer RF chains.

This chapter is attempted to provide a survey of the advanced concepts and related issues involved in Multiple Input Multiple Output (MIMO) systems. MIMO system technology has been considered as a really significant foundation on which to build the next and future generations of wireless networks. The chapter addresses advanced MIMO techniques such as polarization diversity and antenna selection. We gradually provide an overview of the MIMO features from basic to more advanced topics. The first sections of this chapter start by introducing the key aspects of theMIMO theory. TheMIMO systemmodel is first presented in a genericway. Then, we proceed to describe diversity schemes used in MIMO systems. MIMO technology could exploit several diversity techniques beyond the spatial diversity. These techniques essentially cover frequency diversity, time diversity and polarization diversity. We further provide the reader with a geometrically based models for MIMO systems. The virtue of this channel modeling is to adopt realisticmethods for modeling the spatio-temporal channel statistics from a physical wave-propagation viewpoint. Two classes for MIMO channel modeling will be described. These models involve the Geometry-based Stochastic ChannelModels (GSCM) and the Stochastic channel models. Besides the listedMIMO channel models already described, we derive and discuss capacity formulas for transmission over MIMO systems. The achieved MIMO capacities highlight the potential of spatial diversity for improving the spectral efficiency of MIMO channels. When Channel State Information (CSI) is available at both ends of the transmission link, the MIMO system capacity is optimally derived by using adaptive power allocation based on water-filling technique. The chapter continues by examining the combining techniques for multiple antenna systems. Combining techniques are motivated for MIMO systems since they enable the signal to noise ratio (SNR) maximization at the combiner output. The fundamental combing techniques are the Maximal Ratio Combining (MRC), the Selection Combining (SC) and the Equal Gain Combining(EGC). Once the combining techniques are analyzed, the reader is introduced to the beamforming processing as an optimal strategy for combining. The use of multiple antennas significantly improves the channel spectral efficiency. Nevertheless, this induces higher system complexity of the communication system and the communication system performance is effected due to correlation between antennas that need to be deployed at the same terminal. As such, the antenna selection algorithm for MIMO systems is presented. To elaborate on this point, we introduce Space time coding techniques for MIMO systems and we evaluate by simulation the performance of the communication system. Next, we emphasis on multi polarization techniques for MIMO systems. As a background, we presume that the reader has a thorough understanding of antenna theory. We recall the basic antenna theory and concepts that are used throughout the rest of the chapter. We rigorously introduce the 3D channel model over the Non-Line of Sight (NLOS) propagation channel for MIMO system with polarized antennas. We treat the depolarization phenomena and we study its effect on MIMO system capacity. The last section of the chapter provides a scenario for collaborative sensor nodes performing distributed MIMO system model which is devoted to sensor node localization in Wireless Sensor Networks. The localization algorithm is based on beamforming processing and was tested by simulation. Our chapter provides the reader by simulation examples for almost all the topics that have been treated for MIMO system development and key issues affecting achieved performance.

In this letter, we study the performance of a downlink multiuser massive multiple-input multiple-output (MIMO) system with sub-connected structure over limited feedback channels. Tight rate approximations are theoretically analyzed for the system with pure analog precoding and hybrid precoding. The effect of quantized analog and digital precoding is characterized in the derived expressions. Furthermore, it is revealed that the pure analog precoding outperforms the hybrid precoding using maximal-ratio transmission (MRT) or zero forcing (ZF) under certain conditions, and we theoretically characterize the conditions in closed form with respect to signal-to-noise ratio (SNR), the number of users and the number of feedback bits. Numerical results verify the derived conclusions on both Rayleigh channels and mmWave channels.

The main limitation of using a multiple antenna architecture is the complexity and high cost of the hardware in the radio frequency (RF) section, which rise with an increase in the number of antennas. In addition, RF circuit mismatches [1-3] and coupling [4] grow with an increase in the number of antennas; consequently, these factors also limit the use of high numbers of antennas at the transceiver.One solution to compensate for the extra hardware cost and RF circuit imperfection is the utilization of a single RF front-end in a multiple input multiple output (MIMO) system, where a single RF path is used instead of multiple parallel RF paths. This results in an RF section that has lower complexity and cost, a simpler RF design, a compact size, and lower power consumption.A conventional MIMO receiver with N antennas at the receiver is shown in Figure 10.1. The receiver uses multiple parallel RF front-ends, where the number of RF front-ends is equal to the number of antennas. In this architecture, the baseband processing section decodes N received baseband paths to recover the signal and obtain the diversity or spatial multiplexing gain. To realize a single RF frontend path, orthogonal transmission of multiple RF streams over a single front-end must be recognized. In the following subsections, the different techniques to realize a single RF front-end in a MIMO system are discussed.KeywordsRadio FrequencyAntenna SelectionRadio Frequency CircuitRadio Frequency TransceiverSingle Radio FrequencyThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Millimeter wave (mmWave) communication systems are considered to be a promising technology enabling gigabit-per-second data rates, as the mmWave band offers large transmission bandwidth. However, precoding in mmWave systems cannot be performed in digital domain, due to the large number of radio frequency chains required. Deploying a hybrid precoding transceiver architecture, where mmWave precoding is divided among digital and analog processing domains, is an attractive and cost-efficient alternative. Yet, the design of near-optimal hybrid precoders is a non-trivial optimization problem. In this paper, we consider transmit precoding and receive combining in mmWave systems with large antenna arrays in a partially-connected structure, then we make use of projection algorithms to greatly simplify the design problem of digital baseband and analog radio frequency precoders into two sub-optimization problems whose optimal solutions can be found. We also develop a channel estimation algorithm to estimate mmWave channel parameters via a codebook of beamforming vectors obtained through the discrete Fourier transform design. The results illustrate that the system using the proposed projection hybrid precoding and channel estimation algorithms approaches the spectral efficiency achievable when perfect channel knowledge is available.