Space-alternating Generalized Expectation-maximization Research Articles

Low complexity joint angle and delay estimation for underwater multipath acoustic channel based on sparse Bayesian learning

In the field of underwater acoustic communication, multipath signals arrive at the receiving end with different angles and path delays, which can cause degradation in communication quality. When performing angle-delay joint estimation, sparse Bayesian learning (SBL) has many advantages over traditional methods, such as high accuracy, resolution and global minimum results, but at the cost of high computational complexity. Regarding this, in this study, we propose a low-complexity SBL based framework to jointly estimate the angle and delay of the received signal. We first propose a low-complexity approximation SBL algorithm applied to joint estimation, which can keep the super-resolution and estimation accuracy but significantly reduce the computation time. To further tackle the problem of performance degradation of the approximate algorithm in underwater low signal-to-noise ratio environments, we utilize above result as a starting point for the space-alternating generalized Expectation Maximization (SAGE) algorithm to achieve a more precise estimation. Simulation and experimental results demonstrate that the proposed algorithm has an excellent performance in various underwater multipath scenarios.

Model-based clustering of multipath propagation in powerline communication channels

Powerline communication (PLC) channels are known to exhibit multipath propagation behaviour. The authors present a model-based framework to address the challenge of clustering multipath propagation components (MPCs) in PLC channels for indoor low-voltage (LV) environments. The framework employs a range of finite-mixture models (FMMs), including the gamma mixture model, the inverse gamma mixture model, the Gaussian mixture model, the inverse Gaussian mixture model, the Nakagami mixture model, the inverse Nakagami mixture model (INMM) and the Rayleigh mixture model, to identify clusters of MPCs. A measurement campaign of an unknown indoor LV PLC channel is conducted to obtain a channel response. From the channel response, the delay and magnitude parameters of the MPCs are extracted using the space-alternating generalised expectation maximisation algorithm adopted only for these parameters. A maximum likelihood approach and the expectation–maximisation algorithm are employed to fit the FMMs to the MPC delay-magnitude dataset to cluster MPCs in the delay domain. The results of the model-fitting process are then evaluated using the corrected Akaike information criterion (AICc), which enables a fair comparison of the candidate models over the feasible and finite range of clusters. A novel algorithm is introduced for estimating the feasible and finite range of clusters using the extracted delay and magnitude MPC parameters. The AICc’s ranking results show that the INMM model provides the best fit. Davies–Bouldin (DB) and Calinski–Harabasz (CH) indexes are used to compare the model-based clustering approach to the conventional distance-based clustering methods. Validation results show that CH and DB indexes closely agree in the optimal number of MPC clusters for model-based clustering, which corresponds to the most within-cluster compactness of MPCs and to the most between-cluster separation in the delay domain.

Expectation-maximization type algorithms for direction of arrival estimation in unknown nonuniform noise

The expectation–maximization (EM) algorithm updates all of the parameter estimates simultaneously, which is not applicable to direction of arrival (DOA) estimation in unknown nonuniform noise. In this work, we present several computationally efficient EM-type algorithms, which update the parameter estimates sequentially, for solving both the deterministic and stochastic maximum–likelihood (ML) direction finding problems in unknown nonuniform noise. Specifically, we design a generalized EM (GEM) algorithm and a space-alternating generalized EM (SAGE) algorithm for computing the deterministic ML estimator. Simulation results show that the SAGE algorithm outperforms the GEM algorithm. Moreover, we design two SAGE algorithms for computing the stochastic ML estimator, in which the first updates the DOA estimates simultaneously while the second updates the DOA estimates sequentially. Simulation results show that the second SAGE algorithm outperforms the first one.

Joint Channel Parameter Estimation and Scatterers Localization

In this paper, the novel extended space-alternating generalized expectation-maximization (SAGE) algorithm, providing joint propagation channel multi-path component (MPC) estimation and scatterer localization underlying spherical-wavefront multipath model, is proposed. Two geometry-based models are aided for estimating the first and last hop scatterers under different bouncing orders. The performance of the proposed algorithm, as called geometry-aided SAGE (GA-SAGE), is illustrated by means of the Cramér-Rao lower bound derived for parameter estimates and the root-mean-square-estimation-errors (RMSEEs) obtained through and Monte-Carlo simulations, which shows the applicability both near- and far-field estimation. Finally, the GA-SAGE is applied to processing the experimental data obtained from measurements in an indoor office environment by using a single-input multiple-output (SIMO) configuration. The obtained results show that the method proposed outperforms the traditional SAGE algorithm in terms of MPCs estimation accuracy, convergence rate, and the extra capability of localizing scatterers involved in different bouncing order propagation paths. It is considered useful in environment sensing alike applications and makes the GA-SAGE an efficient and effective tool for the development of geometry-based stochastic channel models capable of reproducing channel realizations of the so-called spatial consistency or spatial non-stationarity, which are the basis for the design of transmission technologies using extremely-large antenna array (ELAA) for 5G and beyond.

An Improved High-Resolution Parameter Estimation Algorithm Incorporating Beamforming Techniques

When the conventional Space-Alternating Generalized Expectation-maximization (SAGE) algorithm is used to estimate the incident angle of the signal received by an antenna array with fixed aperture, the accuracy and resolvability of angle estimation are affected and limited by the aperture of the antenna array. Therefore, in order to improve the angle estimation accuracy and resolvability beyond the limitation, we propose a beamforming (BF)-incorporated SAGE (BFI-SAGE) algorithm, which is a SAGE-based improved high-resolution parameter estimation (HRPE) algorithm, and it steers the orientation of beam utilizing a predefined BF weighting matrix. A non-uniform scanning mode is determined to achieve higher angle estimation accuracy in the angle range of interest, and the analysis of the angle estimation performance is performed for the cases of uniform and non-uniform scanning modes, respectively. The resolvability performance of the algorithm is also discussed.

A Powerful Joint Modulation and STBC Identification Algorithm for Multiuser Uplink SC-FDMA Transmissions

Owing to the rapid development and broad adoption of multiple antenna communication systems over the past few years, space-time block coding (STBC) identification has emerged as a crucial responsibility for smart radios. The majority of previous analysis of STBC identification assumed that the utilized modulation schemes for single-user and uncoded broadcasts were known. This paper investigates the challenge of joint STBC and modulation identification for uplink transmissions with numerous users in single-carrier frequency division multiple access (SC-FDMA) systems using coded transmissions. Multi-user channel estimation brings us one step closer to implementing the proposed design in real-world systems. We additionally employ the channel decoder’s deliverables, which are common in many real-world systems, to enhance the identifying and estimating procedures. Mathematical findings prove that a recursive approach can be utilized to tackle the maximum likelihood (ML) problem of simultaneous STBC and modulation identification with channel estimation. Distinguishing the superimposed signals that originate at the base-station (BS) is accomplished with the use of the space-alternating generalized expectation-maximization (SAGE) algorithm. After that, an expectation-maximization (EM) engine is deployed to make the necessary adjustments to the parameters being considered for each user. The success of the above-mentioned architecture for usage in practical applications is demonstrated by the simulation results obtained under various conditions.

Measurement-Based Wideband Space-Time Channel Models for 77GHz Automotive Radar in Underground Parking Lots

In recent years, with the rapid development of Advanced Driver Assistance Systems (ADAS), vehicular millimeter-wave (mmWave) radar plays an important role in urban intelligent transportation system. Self-interference caused by multipath in radar channel is a widely concerned problem. However, the research on radar channel propagation characteristics is very limited and there are few models for radar channel available. In this paper, we propose a pioneering research for radar channel model. Based on measurement data, channel characteristics are analysed using the space-alternating generalized expectation-maximization (SAGE) algorithm. An empirical statistical model is established for the 77GHz mmWave radar channel in the underground parking lot scenario, which is one of the most challenging environments because of time-variation and abundant multipaths, filling the gap in the field. A path-association algorithm is used to obtain multipath component (MPC) trajectories in delay, Doppler frequency and power domains. Additionally, some trajectory (in range domain) features are analysed. Moreover, based on geometric analysis of trajectories in range domain, the deterministic component of trajectories is modeled, and then a novel method for discrimination between actual targets and ghost images is proposed and verified by simulation and measurement data.

Cluster-Based Characterization and Modeling for UAV Air-to-Ground Time-Varying Channels

With the deep integration between the unmanned aerial vehicle (UAV) and wireless communication, UAV-based air-to-ground (AG) propagation channels need more detailed descriptions and accurate models. In this paper, we aim to conduct cluster-based characterization and modeling for AG channels. To our best knowledge, this is the first study that concentrates on the clustering and tracking of multipath components (MPCs) for time-varying AG channels. Based on measurement data at 6.5 GHz with a bandwidth of 500 MHz, we first estimate potential MPCs utilizing the space-alternating generalized expectation-maximization (SAGE) algorithm. Then, we cluster the extracted MPCs by employing K-Power-Means (KPM) algorithm under multipath component distance (MCD) measure. For characterizing time-variant clusters, we exploit a clustering-based tracking (CBT) method, which efficiently quantifies the survival lengths of clusters. Ultimately, we establish a cluster-based channel model, and validations illustrate the accuracy of the proposed model. This work not only promotes a better understanding of AG propagation channels but also provides a general cluster-based AG channel model with certain extensibility.

Multifrequency array calibration in presence of radio frequency interferences

Radio interferometers are phased arrays producing high-resolution images from the covariance matrix of measurements. Calibration of such instruments is necessary and is a critical task. This is how the estimation of instrumental errors is usually done thanks to the knowledge of referenced celestial sources. However, the use of high sensitive antennas in modern radio interferometers (LOFAR, SKA) brings a new challenge in radio astronomy because they are more sensitive to Radio Frequency Interferences (RFI). The presence of RFI during the calibration process generally induces biases in state-of-the-art solutions. The purpose of this paper is to propose an alternative to alleviate the effects of RFI. For that, we first propose a model to take into account the presence of RFI in the data across multiple frequency channels thanks to a low-rank structured noise. We then achieve maximum likelihood estimation of the calibration parameters with a Space Alternating Generalized Expectation-Maximization (SAGE) algorithm for which we derive originally two sets of complete data allowing closed-form expressions for the updates. Numerical simulations show a significant gain in performance for RFI corrupted data in comparison with some more classical methods.

Toward Fine-Grained Indoor Localization Based on Massive MIMO-OFDM System: Experiment and Analysis

Fine-grained indoor localization has attracted attention recently because of the rapidly growing demand for indoor location-based services (ILBS). Specifically, massive (large-scale) multiple-input and multiple-output (MIMO) systems have received increasing attention due to high angular resolution. This paper presents an indoor localization testbed based on a massive MIMO orthogonal frequency-division multiplexing (OFDM) system, which supports physical-layer channel measurements. Instead of exploiting channel state information (CSI) directly for localization, we focus on positioning from the perspective of multipath components (MPCs), which are extracted from the CSI through the space-alternating generalized expectation-maximization (SAGE) algorithm. On top of the available MPCs, we propose a generalized fingerprinting system based on different single-metric and hybrid-metric schemes. We evaluate the impact of the varying antenna topologies, the size of the training set, the number of antennas, and the effective signal-to-noise ratio (SNR). The experimental results show that the proposed fingerprinting method can achieve centimeter-level positioning accuracy with a relatively small training set. Specifically, the distributed uniform linear array obtains the highest accuracy with about 1.63-2.5-cm mean absolute errors resulting from the high spatial resolution.

An ARMA-Filter Based SAGE Algorithm for Ranging in Diffuse Scattering Environment

Range-based positioning using wireless signal has gained remarkable attention in past decades. Accurately extracting the distance information, i.e., estimating parameters of individual multipath, is of interest. It has been shown that diffuse multipath component (DMC) in wireless propagation channel has significant influence on channel estimation and, thus, the ranging performance. In addition to specular component (SC), DMC should be considered in order to improve the estimated accuracy of channel paths’ parameters and, thus, the ranging performance. In this paper, we extend the quasi-maximum likelihood space-alternating generalized expectation-maximization (SAGE) algorithm by incorporating an autoregressive moving average (ARMA) filter to estimate the channel parameters under the presence of DMC. The parameters of both DMC and SC are estimated in an iterative approach, where the DMC is assumed as colored noise and the ARMA-filter is used to estimate the contributions from DMC. The validation of the algorithm based on measured data shows that both SC and DMC can be accurately estimated by the proposed approach. A comparison with standard SAGE and AR-SAGE is conducted, where the results reveal that the proposed method outperforms other two approaches in terms of ranging accuracy.

STBC Identification for Multi-User Uplink SC-FDMA Asynchronous Transmissions Exploiting Iterative Soft Information Feedback of Error Correcting Codes

With the advancement and widespread implementation of multiple-input multiple-output (MIMO) wireless communication systems over the last decade, space-time block coding (STBC) identification has become a critical task for intelligent radios. Previous examinations of STBC identification were focused on single-user transmissions over single-carrier and multi-carrier systems in combination with uncoded broadcasts. Practical systems, on the other hand, contain many users and employ error-correcting codes. For the first time in literature, this work explores the problem of STBC identification for multi-user uplink transmissions in single-carrier frequency division multiple access (SC-FDMA) systems. We take another step closer to real systems by addressing asynchronous transmissions and by conducting multi-user channel estimation. We also exploit the outputs of the channel decoder, which is usually used in many practical systems, to improve the identification and estimation processes. The mathematical analysis demonstrates that the maximum-likelihood (ML) solution of STBC identification, channel estimation, and synchronization can be executed by an iterative approach. The space-alternating generalized expectation-maximization (SAGE) algorithm is used to separate the overlaid signals arriving at the base-station (BS). The parameters under consideration for each user are then updated using an expectation-maximization (EM) processor. Simulation results show that the proposed architecture outperforms other identification methods published in the literature while maintaining a reasonable level of processing time.

Measurements and Characterization for Millimeter-Wave Massive MIMO Channel in High-Speed Railway Station Environment at 28 GHz

The millimeter-wave (mmWave) and massive multiple-input multiple-output (MIMO) wireless communication technologies provide vital means to resolve many technical challenges of the fifth-generation (5G) or beyond 5G (B5G) network. Analyzing the measured datasets extracted from the channel measurements can provide insight into the characteristics of radio channels in different scenarios. Therefore, mmWave massive MIMO channel measurements, simulation, and modeling are carried out in the high-speed railway waiting hall environments at 28 GHz. The multipath components (MPCs) parameters are estimated for line-of-sight (LOS) and non-line-of-sight (NLOS) scenarios based on the space-alternating generalized expectation-maximization (SAGE) algorithm. Delay spread (DS), azimuth angle of arrival (AAoA), and elevation angle of arrival (EAoA) are analyzed. And they are processed by using the K-mean algorithm. In addition, propagation characteristics are simulated based on the improved ray tracing method of shooting and bouncing ray tracing/image (SBR/IM). The correctness of the improved ray tracing method is verified by comparing the measured results with the simulated results. The large-scale path loss (PL) is characterized based on close-in (CI) free-space reference distance model and the floating-intercept (FI) path loss model. Furthermore, statistical distributions for root-mean-square delay spread (RMS DS) are investigated. The Gaussian distribution best fits the measured data of RMS delay spread. Finally, multipath clustering is identified using the multipath component distance (MCD). The analysis of these results from mmWave massive MIMO channel measurements and simulation may be instructive for the deployment of the 5G or B5G wireless communications systems at 28 GHz.

Measurement and comparative analysis of channel parameters of different antenna forms in 5G millimeter wave frequency band

Based on the 5G millimeter wave application frequency band, we carry out channel measurement and channel parameter comparative analysis of omnidirectional antenna, horn antenna and array antenna. The space-alternating generalized expectation-maximization (SAGE) algorithm is used to extract multipath channel parameters, including multipath delay, angle of arrival, multipath strength, etc., and the cluster parameters for multipath components are extracted based on the multipath component distance (MCD) algorithm. The comparison and analysis of the channel parameter differences obtained by different antenna types at the same measurement point show that the channel measurement results of different antennas in the same scenario are quite different. The path loss of the omnidirectional antenna is the smallest, and the root mean square(RMS) delay extension and RMS angle extension of the array antenna are the smallest, and the horn antenna can get more clusters. This article provides comparative analysis data of channel parameter results of different antenna forms for 5G millimeter wave band channel modeling.

Measurement-Based Channel Characterization for 5G Downlink Based on Passive Sounding in Sub-6 GHz 5G Commercial Networks

Under the impetus of global communications organizations, 5G mobile communications becomes a hot technology and moves towards commercial use. In this paper, we propose an efficient downlink channel characterization scheme based on passive sounding in sub-6 GHz 5G commercial network. We first introduce the framework of passive sounding system containing a space-time-division multiplexing (STDM) sounder. Then we elaborate the extraction procedure for 5G downlink signals including synchronization signal block (SSB) and channel state information reference signal (CSI-RS) according to New Radio (NR) technical specifications proposed by 3GPP. Through a pilot test in the anechoic chamber, we also demonstrate the practice of signal extraction. Besides, we derive a dual-polarimetric space-alternating generalized expectation-maximization (SAGE) algorithm which matches with the passive sounding system for multi-dimensional channel parameter estimation. The estimator performance is analyzed by synthetic channel simulation, and results reveal its high accuracy and robustness. Finally, we verify the feasibility of the proposed scheme through analyzing channel characteristics derived from passive sounding in stationary field measurements respectively conducted in industrial park and parking lot with the 5G commercial network built by China Unicom Communications Corporation (CUCC).

Two-Dimensional Channel Parameter Estimation for Millimeter-Wave Systems Using Butler Matrices

In this paper, a novel two-dimensional parameter estimation method is proposed for frequency-selective millimeter-wave (mmWave) channels by probing a limited number of Kronecker products of discrete Fourier transform (DFT) beams, which are efficiently implemented in the analog domain by a novel combination of Butler matrices. The proposed strategy firstly estimates the channel parameters by using a modified parameter estimation via interpolation based on a DFT grid (PREIDG) algorithm. In a second step, high-resolution channel parameter estimation is achieved even in the low signal-to-noise-ratio (SNR) using the space-alternating generalized expectation-maximization (SAGE) algorithm. The proposed modified PREIDG algorithm outperforms state-of-the-art methods, e.g., the auxiliary beam pair (ABP) method while the SAGE algorithm achieves the derived Cramér-Rao lower bound (CRLB). Numerical results demonstrate that excellent estimation performance can be achieved for angle of departure (AoD) azimuth and elevation with addition to delay and complex path gain of each path even in the low SNR regime.

LoRay: AoA Estimation System for Long Range Communication Networks

In this paper, we introduce a comprehensive angle of arrival (AoA) estimation solution for the long range (LoRa) communication network. Termed the LoRa array (LoRay), the proposed system constitutes hardware and software solutions to estimate the AoA of the received signals in real life urban environments. The hardware solution is based on converting multiple individual software defined radios (SDR) into a single SDR that consists of multiple RF-channels. The proposed hardware is cost effective, flexible and generic. The software solution, on the other hand, utilizes the space alternating generalized expectation-maximization (SAGE) algorithm to estimate the AoA of highly correlated received signals. The proposed software exploits few samples of the received signal to estimate the AoA of the direct and reflected paths in an intensive multipath environment. The LoRay system has been validated in outdoor urban environments. The experimental results show that the proposed system provides stable and accurate AoA estimates for both the line-of-sight (LoS) and the non-line-of-sight (NLoS) conditions. The AoA of 80% of the received signals have been estimated within an estimation error below 2° and 10° for the LoS and the NLoS locations, respectively.

Experimental Investigation of Frequency Domain Channel Extrapolation in Massive MIMO Systems for Zero-Feedback FDD

Estimating downlink (DL) channel state information (CSI) in frequency division duplex (FDD) massive multi-input multi-output (MIMO) systems generally requires downlink pilots and feedback overheads. Accordingly, this paper investigates the feasibility of zero-feedback FDD massive MIMO systems based on channel extrapolation. We use the high-resolution parameter estimation (HRPE), specifically the space-alternating generalized expectation-maximization (SAGE) algorithm, to extrapolate the DL CSI based on the extracted parameters of multipath components in the uplink channel. We apply the HRPE to two different channel models: the vector spatial signature (VSS) model and the direction of arrival (DOA) model. We verify these methods through real-world channel data acquired from channel measurement campaigns with two different types of channel sounders: a) a switched array-based, real-time, time-domain, outdoors setup at 3.5 GHz, and b) a virtual array-based, high-accuracy, frequency-domain, indoors setup at 2.4 and 5-7 GHz. The performance metrics of the extrapolated channels that we evaluate include the mean squared error, beamforming efficiency, and spectral efficiency in multiuser MIMO scenarios. The results show that the HRPE-based channel extrapolation performs best under the simple VSS model, which does not require array calibration, and if the BS is in an open outdoor environment having line-of-sight (LOS) paths to well-separated users.

Measurement‐Based Experimental Statistical Modeling of Propagation Channel in Industrial IoT Scenario

AbstractThis paper presents 3–4 and 38–40 GHz wideband channel characteristics for industrial internet‐of‐things (IIoT) scenario based on measurements. The channel measurement equipment applied in the measurements consists of a programmable vector network analyzer and necessary auxiliaries. An extensive amount of data in line‐of‐sight (LoS) and non‐line‐of‐sight (NLoS) scenarios is collected with omnidirectional antennas in both transmitter and receiver ends. With the Space‐Alternating Generalized Expectation‐maximization (SAGE) algorithm, the multipath components (MPCs) of the received signals are extracted to calculate the channel model parameters, for example, channel gain coefficient, delay spread, and Ricean K factor. By studying the statistical characteristics of these parameters, a stochastic channel model in IIoT scenario is initially established and compared with the existing indoor channel models. Moreover, the distinctive characteristics of channel parameters in the millimeter wave band and sub‐6 GHz band in the IIoT scenario are demonstrated.

Robust Clock Skew and Offset Estimation for IEEE 1588 in the Presence of Unexpected Deterministic Path Delay Asymmetries

IEEE 1588, built on the classical two-way message exchange scheme, is a popular clock synchronization protocol for packet-switched networks. Due to the presence of random queuing delays in a packet-switched network, the joint recovery of the clock skew and offset from the timestamps of the exchanged synchronization packets can be treated as a statistical estimation problem. In this paper, we address the problem of clock skew and offset estimation for IEEE 1588 in the presence of possible unknown asymmetries between the deterministic path delays of the forward master-to-slave path and reverse slave-to-master path, which can result from incorrect modeling or cyber-attacks. First, we develop lower bounds on the mean square estimation error for a clock skew and offset estimation scheme for IEEE 1588 assuming the availability of multiple master-slave communication paths and complete knowledge of the probability density functions (pdf) describing the random queuing delays. Approximating the pdf of the random queuing delays by a mixture of Gaussian random variables, we then present a robust iterative clock skew and offset estimation scheme that employs the space alternating generalized expectation-maximization (SAGE) algorithm for learning all the unknown parameters. Numerical results indicate that the developed robust scheme exhibits a mean square estimation error close to the lower bounds.