mmWave Multiple-input Multiple-output Channel Research Articles

Hybrid mmWave MIMO Systems Under Hardware Impairments and Beam Squint: Channel Model and Dictionary Learning-Aided Configuration

Low overhead channel estimation based on compressive sensing (CS) has been widely investigated for hybrid wideband millimeter wave (mmWave) multiple-input multiple-output (MIMO) systems. The channel sparsifying dictionaries used in prior work are built from ideal array response vectors evaluated on discrete angles of arrival/departure. In addition, these dictionaries are assumed to be the same for all subcarriers, without considering the impacts of hardware impairments and beam squint. In this manuscript, we derive a general channel and signal model that explicitly incorporates the impacts of hardware impairments, practical pulse shaping functions, and beam squint, overcoming the limitations of mmWave MIMO channel and signal models commonly used in previous work. Then, we propose a dictionary learning (DL) algorithm to obtain the sparsifying dictionaries embedding hardware impairments, by considering the effect of beam squint without introducing it into the learning process. We also design a novel CS channel estimation algorithm under beam squint and hardware impairments, where the channel structures at different subcarriers are exploited to enable channel parameter estimation with low complexity and high accuracy. Numerical results demonstrate the effectiveness of the proposed DL and channel estimation strategy when applied to realistic mmWave channels.

Utilizing Multi-Dimensional MmWave MIMO Channel Features for Location Verification

In this paper, we address the problem of authenticating transmitters in millimeter-wave (mmWave) multiple-input multiple-output (MIMO) communication systems, and propose a location verification scheme based on multi-dimensional mmWave MIMO channel features. In particular, we first examine the mmWave MIMO channel features in terms of azimuth angle of arrival (AAoA), elevation angle of arrival (EAoA), and path gain, and then extract these fine-grained channel features through the maximum-likelihood (ML) estimation method. Based on the extracted feature parameters, authentication validation is cast in the framework of hypothesis testing theory. We also derive the analytical expressions for the typical false alarm and detection rates by using the likelihood ratio test and thus the statistical performance is analytically established. Finally, extensive numerical results are provided to demonstrate the performance of the proposed authentication scheme.

A 3D Non-Stationary MIMO Channel Model for Reconfigurable Intelligent Surface Auxiliary UAV-to-Ground mmWave Communications

Unmanned aerial vehicle (UAV) communications exploiting millimeter wave (mmWave) can satisfy the increasing data rate demands for future wireless networks owing to the line-of-sight (LoS) dominated transmission and flexibility. In reality, the LoS link can be easily and severely blocked due to poor propagation environments such as tall buildings or trees. To this end, we introduce a reconfigurable intelligent surface (RIS), which passively reflects signals with programmable reflection coefficients, between the transceivers to enhance the communication quality. Specifically, in this paper we generalize a three-dimensional (3D) non-stationary wideband end-to-end channel model for RIS auxiliary UAV-to-ground mmWave multiple-input multiple-output (MIMO) communication systems. By modeling the RIS as a virtual cluster, we study the <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">power delivering capability</i> of RIS as well as the <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">fading characteristic</i> of the proposed channel model. Important channel statistical properties are derived and thoroughly investigated, and the impact of RIS reflection phase configurations on these statistical properties is studied, which provides guidelines for the practical system design. The agreement between theoretical and simulated as well as measurement results validate the effectiveness of the proposed channel model.

Online machine learning-based physical layer authentication for MmWave MIMO systems

Transmitter authentication is significantly critical to secure millimeter wave (mmWave) multiple-input multiple-output (MIMO) systems. By utilizing the mmWave MIMO channel and carrier frequency offset (CFO), this paper proposes a novel online machine learning-based physical layer authentication scheme to validate transmitter identities. In particular, with the help of the Gaussian kernel method and representer theorem, we formulate the physical layer authentication model as a binary classification model. Based on the developed classification model and a constructed convex objective function, we then design an online algorithm to achieve updating authentication parameters, and thus establish a novel online machine learning-based physical layer authentication scheme. Based on the developed authentication model and theories of statistical hypothesis testing, we statistically derive the analytical expressions for false alarm and detection rates for the proposed authentication scheme. Finally, we carry out extensive experiments to verify the authentication performance in terms of the false alarm and detection rates. In addition, we investigate the related authentication efficiency issues (e.g., convergence process) and the capability of resisting against spoofing attacks in mmWave MIMO systems.

Performance analysis of a millimeter wave MIMO channel estimation method in an embedded multi-core processor

The emerging Multi-Processor System-on-Chip (MPSoC) technology, which combines heterogeneous computing with the high performance of field programmable gate arrays (FPGA), is a promising platform for a large number of applications, including wireless communications and vehicular technology. In this specific application context, when multiple-input multiple-output (MIMO) scenarios are considered, the system usually has to manage a large number of communication links among sensors and antennas involving different vehicles and users. Millimeter wave (mmWave) communications are one of the key technology enablers toward achieving high data rates in beyond 5G systems (B5G). Communication at these frequency bands usually involves the use of large antenna arrays, often requiring high computational resources. One of the candidate platforms able to manage a huge number of communications is the Xilinx Zynq UltraScale+ EG Heterogeneous MPSoC, which is composed of a dual-core Cortex-R5, a quad-core ARM Cortex-A53, a graphics processing unit (GPU) and a high-end FPGA. This work analyzes the computational performance that requires a recent mmWave MIMO channel estimation algorithm in a platform of this kind. As a first approach, we will focus our work on the performance that can be achieved via the quad-core ARM Cortex-A53. To this end, we will use the libraries for numerical algebra (BLAS and LAPACK). The results show that our reference implementation is able to manage a large MIMO communication system with 256 antennas without exhausting platform resources.

Deep Transfer Learning for Site-Specific Channel Estimation in Low-Resolution mmWave MIMO

We consider the problem of channel estimation in low-resolution multiple-input multiple-output (MIMO) systems operating at millimeter wave (mmWave) and present a deep transfer learning (DTL) approach that exploits previously trained models to speed up site adaptation. The proposed model is composed of a feature extractor and a regressor, with only the regressor requiring training for the new environment. The DTL approach is evaluated using two 3D scenarios where ray-tracing is performed to generate the mmWave MIMO channels used in the simulations. Under the defined testing setup, the proposed DTL approach can reduce the computational cost of the training stage without decreasing the estimation accuracy.

Particle Filter Based Nonlinear Data Detection in Presence of CFO for Frequency Selective mmWave MIMO-OFDM Systems

The nonlinear distortions attributed by the radio frequency (RF) power amplifier (PA) and other RF circuits from the enormous bandwidth of millimeter wave (mmWave) and high frequency design limitations of the integrated circuits involved, degrade the performance of the hybrid mmWave multiple-input multiple-output (MIMO) orthogonal frequency division multiplexing (OFDM) systems. This nonlinear distortions in the hybrid mmWave systems cause nonlinear coupling of the hybrid precoder with the data signals. Further, it induces intercarrier interference (ICI) in the OFDM systems, which also involves the interference from the precoders of other subcarriers. These difficulties in collusion with frequency selective channel and carrier frequency offset (CFO) may pose great challenges to the estimation accuracy of these parameters (channel gains and CFO) and signal detection. The nonlinearity causes the target posterior distribution for data detection as non-Gaussian and analytically intractable. In this work, we present a novel pilot assisted maximum likelihood (ML) based framework for estimating the CFO with PA impairment in the time domain by formulating a low dimensional equivalent channel matrix. The low dimensional equivalent channel matrix is composed of hybrid precoders-combiners, high dimensional MIMO channel, and the nonlinearly distorted components from PA. We further propose a group-sparse Bayesian learning (G-SBL) based semi-blind channel estimator in the time domain, which incorporates the CFO and nonlinearity of PA in its estimation process. With the estimated channel, a procedure to obtain the hybrid precoder and combiner matrices for data transmission is developed next. An iterative algorithm based on particle filter (PF) that effectively handles the nonlinear coupling of precoder matrix with data, and ICI is also proposed for data detection. The performance of the algorithms are evaluated on two different channel models: (a) synthetic geometric based mmWave channel (b) realistic mmWave channel for an urban microcell (UMi) environment. To validate the efficacy of the CFO and channel estimator, the Cramer-Rao bound (CRB) and Bayesian CRB (BCRB) are derived respectively.

A Trajectory-Driven 3D Non-Stationary mm-Wave MIMO Channel Model for a Single Moving Point Scatterer

This paper proposes a new non-stationary three-dimensional (3D) channel model for a physical millimeter wave (mm-Wave) multiple-input multiple-output (MIMO) channel. This MIMO channel model is driven by the trajectory of a moving point scatterer, which allows us to investigate the impact of a single moving point scatterer on the propagation characteristics in an indoor environment. Starting from the time-variant (TV) channel transfer function, the temporal behavior of the proposed non-stationary channel model has been analyzed by studying the TV micro-Doppler characteristics and the TV mean Doppler shift. The proposed channel model has been validated by measurements performed in an indoor environment using a MIMO radar kit operating at 24 GHz. For the measurement campaign, we used a single swinging pendulum as a model for a moving point scatterer. The trajectory of the pendulum has been captured by an inertial measurement unit attached to the pendulum and by a motion capture camera system. The measured trajectories are fed into the proposed mm-Wave MIMO channel model. The results obtained for the micro-Doppler characteristics show an excellent agreement between the proposed MIMO channel model and real-world measured channels in the presence of a moving point scatterer. We believe that our model can serve as a basis for the development of novel non-stationary MIMO channel models capturing the effects caused by moving objects and people.

Second-Order Statistics-Based Semi-Blind Techniques for Channel Estimation in Millimeter-Wave MIMO Analog and Hybrid Beamforming

Semi-blind (SB) channel estimation is conceived for millimeter wave (mmWave) analog-beamforming (AB) and hybrid-beamforming (HB)-based multiple-input multiple-output (MIMO) systems, which also exploits the data symbols for improving the estimation accuracy. A novel aspect of the proposed framework is that it directly estimates the analog beamformer/ combiner weights without necessitating the estimation of the entire mmWave MIMO channel matrix. By involving powerful matrix perturbation theoretic techniques, a closed-form expression is derived for the mean-squared-error (MSE) of the mmWave-AB-SB algorithm. As a further novelty, our mmWave-HB-SB technique relies on the decomposition of the channel matrix as the product of a decorrelating and a unitary matrix. Subsequently, the former is estimated purely relying on the unknown data symbols, whereas the latter is estimated exclusively from the training vectors. A lower bound on the MSE of the proposed mmWave-HB-SB technique is derived using the constrained Cramer-Rao lower bound (CRLB) framework. Furthermore, the performance gain of our mmWave-HB-SB technique over the conventional purely training-based scheme is also quantified analytically. Our simulation results demonstrate the superiority of the techniques advocated over the existing solutions and also verify the accuracy of our analytical findings.

Multi-Frequency Multi-Scenario Millimeter Wave MIMO Channel Measurements and Modeling for B5G Wireless Communication Systems

Millimeter wave (mmWave) bands have been utilized for the fifth generation (5G) communication systems and will no doubt continue to be deployed for beyond 5G (B5G). However, the underlying channels are not fully investigated at multi-frequency bands and in multi-scenarios by using the same channel sounder, especially for the outdoor, multiple-input multiple-output (MIMO), and vehicle-to-vehicle (V2V) conditions. In this paper, we conduct multi-frequency multi-scenario mmWave MIMO channel measurements with 4 × 4 antennas at 28, 32, and 39 GHz bands for three cases, i.e., the human body and vehicle blockage measurements, outdoor path loss measurements, and V2V measurements. The channel characteristics, including blockage effect, path loss and coverage range, and non-stationarity and spatial consistency, are thoroughly studied. The blockage model, path loss model, and time-varying channel model are proposed for mmWave MIMO channels. The channel measurement and modeling results will be of great importance for further mmWave communication system deployments in indoor hotspot, outdoor, and vehicular network scenarios for B5G.

Channel-Statistics-Based Hybrid Precoding for Millimeter-Wave MIMO Systems With Dynamic Subarrays

This paper investigates the hybrid precoding design for millimeter wave (mmWave) multiple-input multiple-output (MIMO) systems with finite-alphabet inputs. The mmWave MIMO system employs partially-connected hybrid precoding architecture with dynamic subarrays, where each radio frequency (RF) chain is connected to a dynamic subset of antennas. We consider the design of analog and digital precoders utilizing statistical and/or mixed channel state information (CSI), which involve solving an extremely difficult problem in theory: First, designing the optimal partition of antennas over RF chains is a combinatorial optimization problem, whose optimal solution requires an exhaustive search over all antenna partitioning solutions; Second, the average mutual information under mmWave MIMO channels lacks closed-form expression and involves prohibitive computational burden; Third, the hybrid precoding problem with given partition of antennas is nonconvex with respect to the analog and digital precoders. To address these issues, this study first presents a simple criterion and the corresponding low complexity algorithm to design the optimal partition of antennas using statistical CSI. Then it derives the lower bound and its approximation for the average mutual information, in which the computational complexity is greatly reduced compared to calculating the average mutual information directly. In addition, it also shows that the lower bound with a constant shift offers a very accurate approximation to the average mutual information. This paper further proposes utilizing the lower bound approximation as a low-complexity and accurate alternative for developing a manifold-based gradient ascent algorithm to find near optimal analog and digital precoders. Several numerical results are provided to show that our proposed algorithm outperforms existing hybrid precoding algorithms.

Quasi-Static and Time-Selective Channel Estimation for Block-Sparse Millimeter Wave Hybrid MIMO Systems: Sparse Bayesian Learning (SBL) Based Approaches

This paper develops schemes for block-sparse channel estimation in millimeter wave (mmWave) multiple-input multiple-output (MIMO) systems that exploit the spatial sparsity inherent in such channels. Initially, a novel sparse Bayesian learning (SBL) based block-sparse channel estimation technique is developed for a mmWave hybrid MIMO system with multiple measurement vectors, which overcomes the shortcomings of the existing orthogonal matching pursuit-based framework. This is subsequently extended to a temporally correlated block-sparse mmWave MIMO channel. Further, an online recursive hierarchical Bayesian Kalman Filter is developed for the estimation of a time-selective mmWave MIMO channel. Bayesian Cramer–Rao bounds are also derived for the proposed static and time-selective mmWave MIMO channel estimation schemes followed by precoder/combiner design employing the SBL-based imperfect channel estimates. Simulation results are presented to demonstrate the improved performance of the proposed SBL-based channel estimation techniques in comparison to the popular OMP-based scheme proposed recently.

A novel 3D GBSM for mmWave MIMO channels

In this paper, a novel three dimensional (3D) wideband geometry-based stochastic model (GBSM) for millimeter wave (mmWave) multiple-input multiple-output (MIMO) channels is proposed. A homogeneous Poisson point process (PPP) is used to generate the clusters in 3D space. The transmitter (Tx) and receiver (Rx) are surrounded by two spheres. The scatterers distributed in the two spheres are introduced to mimic the clustering effects of multipath components (MPCs) in delay and angular domains. The large-scale path loss model and line-of-sight (LOS) probability model are taken into account to make the channel model realistic. In addition, mmWave channel measurements are conducted in an indoor environment. Simulation results based on the two-sphere channel model are compared with measurement results and good agreements are achieved, which validates the proposed channel model. The results indicate that the proposed channel model has good adaptivity and can model the mmWave channel accurately.

Channel Estimation in Broadband Millimeter Wave MIMO Systems With Few-Bit ADCs

We develop a broadband channel estimation algorithm for millimeter wave (mmWave) multiple input multiple output (MIMO) systems with few-bit analog-to-digital converters (ADCs). Our methodology exploits the joint sparsity of the mmWave MIMO channel in the angle and delay domains. We formulate the estimation problem as a noisy quantized compressed-sensing problem and solve it using efficient approximate message passing (AMP) algorithms. In particular, we model the angle-delay coefficients using a Bernoulli–Gaussian-mixture distribution with unknown parameters and use the expectation-maximization forms of the generalized AMP and vector AMP algorithms to simultaneously learn the distributional parameters and compute approximately minimum mean-squared error (MSE) estimates of the channel coefficients. We design a training sequence that allows fast, fast Fourier transform based implementation of these algorithms while minimizing peak-to-average power ratio at the transmitter, making our methods scale efficiently to large numbers of antenna elements and delays. We present the results of a detailed simulation study that compares our algorithms to several benchmarks. Our study investigates the effect of SNR, training length, training type, ADC resolution, and runtime on channel estimation MSE, mutual information, and achievable rate. It shows that, in a mmWave MIMO system, the methods we propose to exploit joint angle-delay sparsity allow 1-bit ADCs to perform comparably to infinite-bit ADCs at low SNR, and 4-bit ADCs to perform comparably to infinite-bit ADCs at medium SNR.

Adaptive SM-MIMO for mmWave Communications With Reduced RF Chains

In this paper, a novel multiple-input multiple-output (MIMO) transmission scheme, termed as receive antenna selection (RAS)-aided spatial modulation MIMO (SM-MIMO), is proposed for millimeter-wave (mmWave) communications. It employs the spatial modulation (SM) concept and the RAS technique to tackle the costs of the multiple radio frequency (RF) chains at both link ends. Moreover, we develop a pair of RAS algorithms for the proposed mmWave RAS-SM scheme based on the capacity maximization (max-capacity) and the bit-error rate (BER) minimization criteria, which are formulated as two combinatorial optimization problems. The theoretical gradients of the capacity and the BER with respect to RAS variables are derived and the convexities of these problems are discussed. Furthermore, a novel iterative algorithm through jointly designing the log-barrier algorithm (LbA) and the simplified conjugate gradient method is proposed for RAS optimization. Our simulation results show that the proposed RAS-SM schemes are capable of achieving considerable performance gains over conventional norm-based and eigenvalue-based schemes in mmWave MIMO channels, while avoiding an overwhelming complexity imposed by exhaustive search.

Low Complexity Interference Alignment for mmWave MIMO Channels in Three-Cell Mobile Network

Millimeter wave (mmWave) communications are an important candidate technique in 5G networks for features, supporting ultra-dense small cells and mobile data offloading. However, ultra-dense nodes and increasing data traffic bring in vast interference. This paper investigates low complexity non-iterative interference alignment (IA) schemes for multiple-input multiple-output (MIMO) interference broadcast channels in mmWave communications. The authors focus on the three-cell mobile network model in which each base station supports no more than two users within its cell. There is already a closed-form IA solution for the case that one cell has two users, while the other two have one user in each, which can be denoted as {2,1,1}. This paper considers different settings and proposes corresponding IA schemes. First, two IA schemes based on multi-step for the asymmetric setting {2,2,1} are presented, five degree of freedom (DoF) could be achieved. Then, for the symmetric setting {2,2,2}, a novel IA solution with lower complexity and a joint method combining IA with non-iterative multi-user MIMO technique are proposed, and they can achieve six DoF. The simulation results indicate that our non-iterative schemes have similar sum-rate capacity performances with the iterative ones in existing work, and the complexity is effectively reduced.

Training Beam Sequence Design for Millimeter-Wave MIMO Systems: A POMDP Framework

In this paper, adaptive training beam sequence design for efficient channel estimation in large millimeter-wave(mmWave) multiple-input multiple-output (MIMO) channels is considered. By exploiting the sparsity in large mmWave MIMO channels and imposing a Markovian random walk assumption on the movement of the receiver and reflection clusters, the adaptive training beam sequence design and channel estimation problem is formulated as a partially observableMarkov decision process (POMDP) problem that finds non-zero bins in a two-dimensional grid. Under the proposed POMDP framework, optimal and suboptimal adaptive training beam sequence design policies are derived. Furthermore, a very fast suboptimal greedy algorithm is developed based on a newly proposed reduced sufficient statistic to make the computational complexity of the proposed algorithm low to a level for practical implementation. Numerical results are provided to evaluate the performance of the proposed training beam design method. Numerical results show that the proposed training beam sequence design algorithms yield good performance.