Beamforming Structure Research Articles

Generalized Beamforming Design for Cooperative MIMO Multirelay Networks with Infinite Constraints and Imperfect CSI

A generalized base station-relay-user equipment (BS-Relay-UE) beamforming design is investigated for a cooperative multiple-input multiple-output (MIMO) multirelay networks with imperfect channel state information (CSI). In order to minimize the worst-case mean square error (MSE) which is subject to a semi-infinite (SI) relay power constraints, a generalized optimal beamforming structure for the relay amplifying matrix is effectively proposed, and then the SI relay power constraints are converted into linear matrix inequalities (LMIs) version. In such conversion, the objective problem recasts as a decoupled biconvex semidefinite programming (SDP) one which can be efficiently solved by the proposed alternating algorithm. The system performance has been verified in terms of worst-case MSE using a set of qualitative analyses. The results show us that the proposed beamforming method outperforms the conventional schemes and can also effectively reduce the computational complexity when it is compared to the cutting-set schemes and also to the nonrobust ones.

Joint hybrid precoder and combiner design for multi‐stream transmission in mmWave MIMO systems

Millimeter wave (mmWave) communications have been considered as a key technology for future 5G wireless networks since it can provide orders-of-magnitude wider bandwidth than current cellular bands. To overcome the severe propagation loss of the mmWave channel, an economic and energy-efficient analogue/digital hybrid precoding and combining transceiver architecture is widely used in mmWave massive multiple-input multiple-output (MIMO) systems. The digital precoding/combining layer offers more freedom than pure analogue one and enables multi-stream transmission. In this study, the authors consider the problem of codebook-based joint hybrid precoder and combiner design for multi-stream transmission in mmWave MIMO systems. The authors propose to jointly select an analogue precoder and combiner pair for each data stream successively, which can maximise the channel gain as well as suppress the interference between different data streams. Then, the digital precoder and combiner are computed based on the obtained effective baseband channel to further mitigate the interference and maximise the sum-rate. Both fully-connected and partially-connected hybrid beamforming structures are investigated. Simulation results demonstrate that the proposed algorithms exhibit prominent advantages in combating interference between different data streams and offer satisfactory performance improvements compared with the existing codebook-based hybrid beamforming schemes.

Analysis of Photonics-Based RF Beamforming With Large Instantaneous Bandwidth

Since the photonics-based true time delay could significantly broaden the instantaneous bandwidth of a phased antenna array system, solutions utilizing wideband signals could be enabled to considerably enhance the functionality and performance of RF systems. To investigate the features of the wideband beamforming, a comprehensive theoretical model is developed in this paper to analyze the photonics-based broadband beamforming network for uniform linear arrays. In the proposed model, the performance of the beamforming network over the operational frequency band is intuitively depicted through a two-dimensional spatial-temporal frequency response, in which both the spatial frequency (or the corresponding observation angle) and the temporal frequency are adopted as independent variables. In addition, cross correlation of the original signal and the signal that undergoes the beamforming network is calculated to define a wideband pattern and a new figure of merit, so that the waveform-dependent overall response over a large bandwidth can be evaluated. Based on the theoretical model, a time-domain method for pattern measurement is proposed and experimentally demonstrated, which offers the coincident result as the frequency-domain method but is more convenient to be conducted. Numerical results of several typical photonics-based beamforming structures are presented to investigate the impact of nonidealities on the two-dimensional response and the proposed figure of merit.

Channel Reciprocity Calibration in TDD Hybrid Beamforming Massive MIMO Systems

Hybrid analog-digital (AD) beamforming structure is a very attractive solution to build low cost massive multiple-input multiple-output (MIMO) systems. Typically these systems use a set of fixed beams for transmission and reception to avoid the need to obtain channel state information at transmitter (CSIT) for each antenna element individually. However, such a method can not fully exploit the potential of hybrid AD beamforming systems. Alternatively, CSIT can be estimated by assuming a model for the propagation channel, whereas this model is only validated in millimeter-wave (mmWave) band thanks to its poor scattering nature. In this paper, we focus on time division duplex (TDD) systems with hybrid beamforming structure and propose a reciprocity calibration scheme that allows to acquire full CSIT. Different to existing CSIT acquisition methods, our approach does not require any assumption on the channel model and can, in theory, estimate the CSIT up to an arbitrary small error.

Optimizing Channel-Statistics-Based Analog Beamforming for Millimeter-Wave Multi-User Massive MIMO Downlink

In this paper, we consider the design of analog beamformers for the downlink of multi-user massive multiple-input-multiple-output (MIMO) systems. We specifically investigate systems, where both link ends are equipped with hybrid digital/analog beamforming structures, where the analog beamformers are adapted based on second order channel statistics, reducing the training overhead as well as hardware effort. We present a framework for the optimization of such beamformers operating in mm-wave channels, exploiting the directional characteristics and sparse nature of such channels. We develop an approximate upper bound of the ergodic sum capacity, based on which efficient beamforming algorithms are devised. Simulation results show significant performance improvements of the proposed algorithms compared with the state-of-the-art algorithms.

Low-Rank Tensor Decomposition-Aided Channel Estimation for Millimeter Wave MIMO-OFDM Systems

We consider the problem of downlink channel estimation for millimeter wave (mmWave) MIMO-OFDM systems, where both the base station (BS) and the mobile station (MS) employ large antenna arrays for directional precoding/beamforming. Hybrid analog and digital beamforming structures are employed in order to offer a compromise between hardware complexity and system performance. Different from most existing studies that are concerned with narrowband channels, we consider estimation of wideband mmWave channels with frequency selectivity, which is more appropriate for mmWave MIMO-OFDM systems. By exploiting the sparse scattering nature of mmWave channels, we propose a CANDECOMP/PARAFAC (CP) decomposition-based method for channel parameter estimation (including angles of arrival/departure, time delays, and fading coefficients). In our proposed method, the received signal at the BS is expressed as a third-order tensor. We show that the tensor has the form of a low-rank CP decomposition, and the channel parameters can be estimated from the associated factor matrices. Our analysis reveals that the uniqueness of the CP decomposition can be guaranteed even when the size of the tensor is small. Hence the proposed method has the potential to achieve substantial training overhead reduction. We also develop Cramer-Rao bound (CRB) results for channel parameters, and compare our proposed method with a compressed sensing-based method. Simulation results show that the proposed method attains mean square errors that are very close to their associated CRBs, and presents a clear advantage over the compressed sensing-based method in terms of both estimation accuracy and computational complexity.

Hybrid Analog and Digital Beamforming for mmWave OFDM Large-Scale Antenna Arrays

Hybrid analog and digital beamforming is a promising candidate for large-scale millimeter wave (mmWave) multiple-input multiple-output (MIMO) systems because of its ability to significantly reduce the hardware complexity of the conventional fully digital beamforming schemes while being capable of approaching the performance of fully digital schemes. Most of the prior work on hybrid beamforming considers frequency-flat channels. However, broadband mmWave systems are frequency-selective. In broadband systems, it is desirable to design common analog beamformer for the entire band while employing different digital (baseband) beamformers in different frequency sub-bands. This paper considers the hybrid beamforming design for systems with orthogonal frequency division multiplexing modulation. First, for a single-user MIMO (SU-MIMO) system where the hybrid beamforming architecture is employed at both transmitter and receiver, we show that hybrid beamforming with a small number of radio frequency (RF) chains can asymptotically approach the performance of fully digital beamforming for a sufficiently large number of transceiver antennas due to the sparse nature of the mmWave channels. For systems with a practical number of antennas, we then propose a unified heuristic design for two different hybrid beamforming structures, the fully connected and the partially connected structures, to maximize the overall spectral efficiency of an mmWave MIMO system. Numerical results are provided to show that the proposed algorithm outperforms the existing hybrid beamforming methods, and for the fully connected architecture, the proposed algorithm can achieve spectral efficiency very close to that of the optimal fully digital beamforming but with much fewer RF chains. Second, for the multiuser multiple-input single-output case, we propose a heuristic hybrid percoding design to maximize the weighted sum rate in the downlink and show numerically that the proposed algorithm with practical number of RF chains can already approach the performance of fully digital beamforming.

Cell Selection Technique for Millimeter-Wave Cellular Systems with Hybrid Beamforming.

In this paper, a cell selection technique for millimeter-wave (mm-wave) cellular systems with hybrid beamforming is proposed. To select a serving cell, taking into account hybrid beamforming structures in a mm-wave cellular system, the angles of arrival and departure for all candidate cells need to be estimated in the initialization stage, requiring a long processing time. To enable simultaneous multi-beam transmissions in a multi-cell environment, a cell and beam synchronization signal (CBSS) is proposed to carry beam IDs in conjunction with cell IDs. A serving cell maximizing the channel capacity of the hybrid beamformer is selected with the estimated channel information and the optimum precoder. The performance of the proposed technique is evaluated by a computer simulation with a spatial channel model in a simple model of a mm-wave cellular system. It is shown by simulation that the proposed technique with the CBSS can significantly reduce the processing time for channel estimation and cell selection, and can achieve additional gains in channel capacity, or in bit error rate, compared to that obtained by conventional techniques.

Structured beamforming designs for spectral efficiency and energy efficiency in a three‐node amplify‐and‐forward relay network

The amplify-and-forward (AF) relay system with consideration of the weak direct link is studied. As different data streams are transmitted by the source, there is interference between the different data links. In order to decode the data reliably, the source beamforming for the direct link is designed to make the interference of the source–destination link as low as possible. In the first stage, in order to avoid the interference being amplified by the relay, the source beamforming for the relay link is designed to cancel the inter-link interference. In the second stage, beamforming of the relay is designed to maximise the spectral efficiency (SE). Two types of source beamformings are proposed by combining the null space vectors of useful signal and by combining the orthogonal subspace vectors of the interference signal, respectively. The obtained beamforming structures are not only used for the SE optimisation problem, but also the energy efficiency (EE) optimisation problem. Simulation results show that the proposed beamforming design algorithms can obtain higher SE or higher EE compared with existing methods.

Hybrid information and energy transfer in ultra-dense HetNets

Wireless energy transfer is a promising technique to power sensors and mobile devices in order to perform functions beyond the constraints of their batteries. We envision that future ultra-dense heterogeneous networks (UDHetNets) are capable of realizing hybrid information and energy transfer (HIET) with an elaborated architecture design. To enable effective HIET in the designed UDHetNets with massive multiple-input multiple-output (MIMO), three features of wireless energy transfer, i.e., the known transmission signal, the helpful interference signals and the linear beamformer structure, as well as their typical applications are considered and presented in detail. Numerical results study and clearly demonstrate the advantages of the designed HIET systems over existing schemes.

On the design of time-domain implementation structure for steerable spherical modal beamformers with arbitrary beampatterns

It is noted that the existing time-domain implementation structure for steerable spherical modal beamformers is only applicable to the specific beamformers with rotationally symmetric beampatterns about the look direction, which may limit its applications. To overcome the restriction, this paper presents an alternative time-domain implementation structure for spherical modal beamformers using the Wigner-D function, which enables three-dimensional beam steering with arbitrary patterns. In particular, a necessary condition for guaranteeing only real-valued operations to make the time-domain implementation viable is derived. Design examples are presented to demonstrate the effectiveness of the presented time-domain modal beamformer structure.

Low complexity asymptotically unitary algorithm for hybrid beamforming in mmWave communication systems

In millimeter wave (mmWave) massive multiple-input multiple-output (MIMO) systems, because of the high hardware cost and high power consumption, the traditional fully digital beamforming (DBF) cannot be implemented easily. Meanwhile, analog beamforming which is implemented with phase shifters has high availability but suffers poor performance. Considering the advantages of above two, a potential solution is to design an appropriate hybrid analog and digital beamforming structure, where the available iterative optimization algorithm can get performance close to fully digital processing, but solving this sparse optimization problem faces with a high computational complexity. The key challenge of seeking out hybrid beamforming (HBF) matrices lies in leveraging the trade-off between the spectral efficiency performance and the computational complexity. In this paper, we propose an asymptotically unitary hybrid precoding (AUHP) algorithm based on antenna array response (AAR) properties to solve the HBF optimization problem. Firstly, we get the optimal orthogonal analog and digital beamforming matrices relying on the channel's path gain in absolute value by taking into account that the AAR matrices are asymptotically unitary. Then, an improved simultaneously orthogonal matching pursuit (SOMP) algorithm based on recursion is adopted to refine the hybrid combining. Numerical results demonstrate that our proposed AUHP algorithm enables a lower computational complexity with negligible spectral efficiency performance degradation.

High-performance beamformer and low-complexity detector for DF-based full-duplex mimo relaying networks

In this paper, we consider a full-duplex multiple-input multiple-output (MIMO) relaying network with the decode-and-forward (DF) protocol. Due to the full-duplex transmissions, the self-interference from the relay transmitter to the relay receiver degrades the system performance. We thus propose an iterative beamforming structure (IBS) to mitigate the self-interference. In this method, the receive beamforming at the relay is optimized to maximize the signal-to-interference- plus-noise-ratio (Max-SINR), while the transmit beamforming at the relay is optimized to maximize the signal-to-leakage-plusnoise- ratio (Max-SLNR). To further improve the performance, the receive and transmit beamforming matrices are optimized between Max-SINR and Max-SLNR in an iterative manner. Furthermore, in the presence of the residual self-interference, a low-complexity whitening-filter (WF) maximum likelihood (ML) detector is proposed. In this detector, a WF is designed to transform a colored interference- plus-noise to a white noise, while the singular value decomposition is used to convert coupled spatial subchannels to parallel independent ones. From simulations, we find that the proposed IBS performs much better than the existing schemes. Also, the proposed low-complexity detector significantly reduces the complexity of the conventional ML (CML) detector from exponential time (an exponential function of the number of the source transmit antennas) to polynomial one while achieving a slightly better BER performance than the CML due to interference whitening.

Low Complexity and Robust Codebook-Based Analog Beamforming for Millimeter Wave MIMO Systems

Millimeter-wave (mm-Wave) MIMO systems have been proposed to achieve higher spectral efficiency via the hybrid beamforming structure, which consists of analog beamforming and digital beamforming. In analog beamforming, each antenna subarray generates a codebook-based directional beam, which determines the equivalent MIMO channel. Then, digital beamforming can be applied to fully exploit the spatial multiplexing gain of MIMO channels. In this paper, we propose a low-complexity analog beam selection scheme to achieve near-optimal spectral efficiency for the split hybrid beamforming system. The core of our scheme is the beam selection criterion, which is derived from capacity analysis. Furthermore, we propose a beam switching algorithm to ensure the robustness when blockage occurs. Through simulations under different channel conditions, the near-optimal performance of our scheme is demonstrated, and the beam switching algorithm is able to ensure robust network connectivity and achieve higher channel capacity when the blockage is relived.

Channel Estimation for Millimeter-Wave Multiuser MIMO Systems via PARAFAC Decomposition

We consider the problem of uplink channel estimation for millimeter wave (mmWave) systems, where the base station (BS) and mobile stations (MSs) are equipped with large antenna arrays to provide sufficient beamforming gain for outdoor wireless communications. Hybrid analog and digital beamforming structures are employed by both the BS and the MS due to hardware constraints. We propose a layered pilot transmission scheme and a CANDECOMP/PARAFAC (CP) decomposition-based method for joint estimation of the channels from multiple users (i.e., MSs) to the BS. The proposed method exploits the intrinsic low-rank structure of the multiway data collected from multiple modes, where the low-rank structure is a result of the sparse scattering nature of the mmWave channel. The uniqueness of the CP decomposition is studied, and the sufficient conditions for essential uniqueness are obtained. The conditions shed light on the design of the beamforming matrix, the combining matrix, and the pilot sequences, and meanwhile provide general guidelines for choosing system parameters. Our analysis reveals that our proposed method can achieve a substantial training overhead reduction by leveraging the low-rank structure of the received signal. Simulation results show that the proposed method presents a clear advantage over a compressed sensing-based method in terms of both estimation accuracy and computational complexity.

Millimetre Level Accuracy GNSS Positioning with the Blind Adaptive Beamforming Method in Interference Environments.

The use of antenna arrays in Global Navigation Satellite System (GNSS) applications is gaining significant attention due to its superior capability to suppress both narrowband and wideband interference. However, the phase distortions resulting from array processing may limit the applicability of these methods for high precision applications using carrier phase based positioning techniques. This paper studies the phase distortions occurring with the adaptive blind beamforming method in which satellite angle of arrival (AoA) information is not employed in the optimization problem. To cater to non-stationary interference scenarios, the array weights of the adaptive beamformer are continuously updated. The effects of these continuous updates on the tracking parameters of a GNSS receiver are analyzed. The second part of this paper focuses on reducing the phase distortions during the blind beamforming process in order to allow the receiver to perform carrier phase based positioning by applying a constraint on the structure of the array configuration and by compensating the array uncertainties. Limitations of the previous methods are studied and a new method is proposed that keeps the simplicity of the blind beamformer structure and, at the same time, reduces tracking degradations while achieving millimetre level positioning accuracy in interference environments. To verify the applicability of the proposed method and analyze the degradations, array signals corresponding to the GPS L1 band are generated using a combination of hardware and software simulators. Furthermore, the amount of degradation and performance of the proposed method under different conditions are evaluated based on Monte Carlo simulations.

Antenna Selection and Hybrid Beamforming for Simultaneous Wireless Information and Power Transfer in Multi-Group Multicasting Systems

In this paper, low-cost alternatives to full digital beamforming, namely, antenna selection and hybrid beamforming, are proposed for simultaneous wireless information and power transfer in a multi-group multicasting scenario. The joint problem can be outlined as the design of beamformer weight vectors and power splitting ratios in order to satisfy both signal-to-interference-plus-noise -ratio and harvested power constraints at each user with minimum transmission power. We first develop an efficient algorithm for antenna selection by converting the original mixed integer programming problem into a continuous one and adapting feasible point pursuit-successive convex approximation. Second, a new hybrid beamforming structure is presented for multi-group multicasting. Both continuous and discrete-phase hybrid beamformers are considered in this content. Two algorithms for continuous-phase case are developed by employing two competing techniques. In addition, a special two-bit discrete-phase hybrid beamformer design is considered for practical systems. The integer constraints are converted into linear equality and inequalities for this specific structure and an efficient algorithm is designed. The proposed algorithms are compared for different scenarios revealing some interesting characteristics of each technique.

Optimal Semiadaptive Transmission With Artificial-Noise-Aided Beamforming in MISO Wiretap Channels

This paper studies the design of artificial-noise-aided (AN-aided) secure transmission in slow-fading multiple-input–single-output (MISO) channels. We consider the scenario where a multiantenna transmitter sends messages to a single-antenna legitimate receiver in the presence of multiple noncolluding single-antenna eavesdroppers. It is assumed that the transmitter possesses instantaneous channel state information (CSI) of the legitimate channel but only the statistics of the eavesdropper's channels. Instead of adopting the well-known adaptive and nonadaptive transmission schemes, we consider the newly proposed semiadaptive scheme, in which the communication rate is fixed, and the secrecy rate is adaptively adjusted according to the legitimate channel's CSI. Compared with the adaptive scheme, a major advantage of fixing the communication rate is that the codebook can be fixed, and thus, the encoder and decoder designs are both simplified. We consider a generalized AN-aided beamforming structure, which allows arbitrary beamforming direction. Specifically, we focus on the problem of maximizing the secrecy throughput on the premise of reliable and secure transmission. By solving this problem, the optimal beamforming direction, power-allocation parameters, and secrecy rate are derived in closed form, and the optimal communication rate is obtained numerically. Finally, simulation results are presented to show the performance of the semiadaptive scheme.

Degrees of Freedom of Interference Channels With Hybrid Beamforming

We study the sum degrees of freedom (DoF) of interference channels with hybrid beamforming in which each transmitter $i$ uses $M_i^{\prime}$ antennas and $M_i$ RF chains and each receiver $i$ uses $N_i^{\prime}$ antennas and $N_i$ RF chains, where $M_i\leq M_i^{\prime}$ and $N_i\leq N_i^{\prime}$ , $\forall i=1,2,\ldots,K$ , and hybrid beamforming composed of analog and digital precoders is employed at each node. For the two-user case, we completely characterize the sum DoF for an arbitrary number of antennas and RF chains by developing an achievable scheme optimized for the hybrid beamforming structure and deriving its matching upper bound. For a general $K$ -user case, we focus on a symmetric case where $M_i=M$ , $N_i=N$ , $M_i^{\prime}=M^{\prime}$ , and $N^{\prime}_i=N^{\prime}$ , $\forall i=1,2,\ldots,K$ , and obtain lower and upper bounds on the sum DoF, which are tight when $\frac{\textbf{max}\{M^{\prime},N^{\prime}\}}{\textbf{min}\{M^{\prime},N^{\prime}\}}$ is an integer. The results show that with a fixed number of RF chains, employing more antennas can increase the sum DoF of interference channel under certain conditions while this cannot improve the sum DoFs of point-to-point channel, multiple access channel, and broadcast channel.

Coordinate Update Algorithms for Robust Power Loading for the MU-MISO Downlink With Outage Constraints

We consider the problem of power allocation for the single-cell multi-user (MU) multiple-input single-output (MISO) downlink with quality-of-service (QoS) constraints. The base station acquires an estimate of the channels and, for a given beamforming structure, designs the power allocation so as to minimize the total transmission power required to ensure that target signal-to-interference-and-noise ratios at the receivers are met, subject to a specified outage probability. We consider scenarios in which the errors in the base station's channel estimates can be modelled as being zero-mean and Gaussian. Such a model is particularly suitable for time division duplex (TDD) systems with quasi-static channels, in which the base station estimates the channel during the uplink phase. Under that model, we employ a precise deterministic characterization of the outage probability to transform the chance-constrained formulation to a deterministic one. Although that deterministic formulation is not convex, we develop a coordinate descent algorithm that can be shown to converge to a globally optimal solution when the starting point is feasible. Insight into the structure of the deterministic formulation yields approximations that result in coordinate update algorithms with good performance and significantly lower computational cost. The proposed algorithms provide better performance than existing robust power loading algorithms that are based on tractable conservative approximations, and can even provide better performance than robust precoding algorithms based on such approximations.