Space-alternating Generalized Expectation-maximization Algorithm Research Articles

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.

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.

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 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.

A study of uplink and downlink channel spatial characteristics in an urban micro scenario at 28 GHz

This paper presents an empirical study of the uplink and downlink azimuth angle of arrival (AoA) in an urban micro (UMi) scenario at 28 GHz. At present, most UMi measurements are conducted in the downlink and then the uplink situation is inferred assuming channel reciprocity. Although the channel correlation coefficient of the uplink and downlink can be as high as 0.8, this does not mean that they are the same. Only a real uplink measurement can accurately describe its channel conditions, and this is what this study does. A receiver equipped with a rotatable horn antenna is mounted at the base station and the user terminal, respectively, in simulating the uplink and downlink. To improve the angular resolution, we extract the multipath components (MPCs) using the space-alternating generalized expectation-maximization algorithm. Also, a spatial lobe approach is used to cluster the MPCs in the power angular spectrum. By matching MPCs with objects in the environment, we find that direct propagation and first-order reflections are dominant in line-of-sight and non-line-of-sight cases. By comparing our measurement with those in standard channel models, we verify that the AoA of clusters follows a Gaussian distribution in the uplink and downlink. In addition, a two-dimensional Gaussian distribution for ray AoA and power is established to reflect their correlation.

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.

Cluster-Based Millimeter-Wave Outdoor-to-Indoor Propagation Characteristics Based on 32 GHz Measurement Analysis

Although the fifth-generation (5G) networks are deployed at millimeter-wave (mmWave) frequencies, little information about the multipath clustering statistics for mmWave outdoor-to-indoor (O2I) propagation has been reported. This letter attempts to overcome this deficiency somewhat by investigating cluster-based propagation statistics for mmWave O2I that are based upon measurements. The measurements were conducted at 32 GHz at two office buildings. The multipath components (MPCs) were resolved by the space-alternating generalized expectation-maximization algorithm and the MPC clustering was performed by the K -power-means algorithm. We observed that numerous reflections bouncing back-and-forth between the windows cause large numbers of clusters. Other statistics such as the number of rays per clusters, cluster power and shadowing, cluster delay, and angular spread were also calculated.

Performance Analysis of a SAGE-Based Semi-Blind Channel Estimator for Pilot Contaminated MU Massive MIMO Systems

Massive multiple-input multiple-output (M-MIMO) is one of the key ingredients in the upcoming 5G technology. The benefits associated with M-MIMO rely largely on the accuracy of channel state information (CSI) available at the base station (BS). The existing literature mostly employs pilot-aided schemes which require additional pilots for improving their CSI accuracy; additionally, pilot contamination degrades their performance to a large extent. In this paper, we design a Space-Alternating Generalized Expectation-Maximization (SAGE) based semi-blind estimator for pilot contaminated multi-user (MU) M-MIMO systems. It utilizes both pilot and a few data symbols for CSI estimation through two stages, namely initialization and iterative SAGE (ISAGE). We obtain an initial channel estimate with the help of a pilot-aided linear minimum mean squared error (LMMSE) estimator in the initialization stage. The acquired initial estimate from the former stage is then iteratively updated by SAGE algorithm with the joint usage of pilot and a few data symbols in ISAGE stage. The inclusion of data information in ISAGE stages' estimation process aids in simultaneous improvement of CSI accuracy and spectral efficiency (SE) of a M-MIMO system; which is unlikely for a pilot based estimation scheme. Through simulations, we show that our estimator obtains a considerable improvement over the existing pilot-aided schemes in terms of mean squared error (MSE), bit error rate (BER), SE, and energy efficiency (EE) at a nominal increase in complexity. Besides, on average, it achieves convergence in almost two iterations. We also derive modified Cramer-Rao lower bound (MCRLB) to validate the estimation efficacy of our estimator. We evaluate a closed-form expression for lower bound on UL achievable rate of MU M-MIMO systems under both perfect and imperfect CSI scenario. We also discuss the trade-off between SE and EE.

Electromagnetic Parameter Calibration for a Broadband Ray-Launching Simulator With SAGE Algorithm for Millimeter-Wave Communications

The millimeter-wave (mmWave) communication is a promising solution to future high-speed data transmission. To study the impact of its wireless channel, a ray-launching simulator is developed to generate deterministic channel models according to realistic scenario descriptions. For such channel modeling, the material parameters play an important role in the electromagnetic numerical computing of multi-path components (MPCs) and should be calibrated according to channel measurement results. Our contribution in this paper is three-fold: we conduct the channel measurement in an indoor scenario for extracting mmWave channel characteristics, apply the Hungarian algorithm to pair measured and simulated propagation MPCs and apply the SAGE algorithm for the parameter calibration of materials impacting on the MPCs. Note that the proposed material parameter calibration method is general for the various radio propagation environment, not limited by the indoor or outdoor scenarios. Moreover, it avoids independent measurement of specific materials in a given scenario, thus greatly reducing the difficulty of obtaining material parameters. The result shows that the space alternating generalized expectation-maximization (SAGE) algorithm achieves a good match between measurement and simulation with a reasonable computational effort.

A Cluster-Based Three-Dimensional Channel Model for Vehicle-to-Vehicle Communications

Vehicle-to-vehicle (V2V) communications have received a lot of attention as it can significantly improve efficiency and safety of road traffic. In general, V2V scenarios have some special features such as high mobility of transceivers, low antenna height, and small communication ranges, which significantly affect the propagation characteristics. Therefore, an accurate channel model is required to characterize V2V propagation channel. However, some important features of V2V channels have not been well characterized, for example, most existing V2V channel models tend to only consider the distribution of multipath components (MPCs) in a horizontal dimension, whereas ignoring vertical dimension, which is inconsistent with the distribution of MPCs in the actual channel. Moreover, the dynamic clusters of MPCs have not been well modeled in the existing V2V models. Therefore, in order to better model the V2V channel, a cluster-based three-dimensional (3D) channel model is proposed in this paper, which is based on the measurements conducted at 5.9 GHz in urban and suburban scenarios. In the proposed model, the distribution of MPCs clusters in both horizontal and vertical dimensions is considered. The space-alternating generalized expectation-maximization algorithm is used to extract MPCs, and the clustering and tracking algorithms are used to identify and track the clusters of dynamic MPCs. In the proposed model, all MPC clusters are divided into two categories: global-clusters and scatterer-clusters, and the distribution of the two clusters are characterized by a series of inter- and intra-cluster parameters. It is found that both the azimuth spread and the elevation spread follow the lognormal distribution. In addition, the power of MPCs within a cluster has the truncated-Gaussian distribution, whereas the angle of MPCs within a cluster has the Laplacian distribution. Finally, the accuracy of the model is verified by comparing the measurements and simulations.

Timing and Frequency Synchronization and Doubly Selective Channel Estimation for OFDMA Uplink

In this brief, a novel algorithm is proposed for timing and frequency synchronization and doubly selective channel (DSC) estimation in the uplink of orthogonal frequency division multiple access systems. By using a basis expansion model (BEM) to represent a DSC, a maximum likelihood approach is proposed to jointly estimate the timing and carrier frequency offsets of different users as well as the BEM coefficients of the time-varying channels. A space-alternating generalized expectation-maximization algorithm is then employed to transform the maximization problem for all users into several simpler maximization problems for a single user. Implementation issues are investigated and, the computational complexity and mean square error of the proposed scheme are evaluated. Performance assessment of the new scheme shows a significant improvement as compared with previous methods.

Joint TOA/DOA Estimation Using the SAGE Algorithm in OFDM Systems with Virtual Carriers

In this paper, we investigate the space-alternating generalized expectation-maximization (SAGE) algorithm with virtual carriers (VCs) in orthogonal frequency division multiplexing (OFDM) systems. The channel frequency response (CFR) at VCs cannot be estimated accurately due to edge effect after inverse discrete Fourier transform (IDFT). To solve the problem, an improved channel estimation method is introduced to minimize the errors of CFR via iterative technique. Then we apply the SAGE algorithm to estimate the direction of arrival (DOA) and time of arrival (TOA). The SAGE algorithm shows more excellent performance with higher resolution ability than subspace-based algorithms. Based on Monte Carlo trials, we test the performance of the improved method in terms of mean absolute error (MAE) at different signal-to-noise ratios (SNR). Simulation results indicate that the improved method behaves better at any SNR than the conventional DFT-based method.

Frequency Characteristics of Geometry-Based Clusters in Indoor Hall Environment at SHF Bands

This paper presents an analysis of geometry-based cluster frequency dependency at super-high-frequency bands, including 3, 10, and 28 GHz. First, multipath components were extracted from the measured data by using the space-alternating generalized expectation-maximization algorithm. Then, geometry-based clusters were estimated by using the enhanced scattering point-based KPowerMeans (SPKPM) algorithm. Finally, the frequency dependencies of their scattering intensities were discussed with the assistance of physical optics. The analysis results showed that the SPKPM could also be applied to obtain reasonable scattering locations at multiple frequencies in most cases. In addition, reflection on smooth surfaces was the dominant mechanism of clustering where there was no frequency dependence, whereas diffraction, scattering, and shadowing were significant causes of frequency dependence. Assuming that the line-of-sight is obstructed, diffraction, scattering, and shadowing accounted for 30–40% of the entire channel in terms of power, which was not negligible and thus the channel was largely frequency-dependent. The analysis results are expected to provide crucial insights for multiple-frequency channel modeling for fifth-generation wireless systems.

Wireless channel parameter estimation algorithms: Recent advances and future challenges

Temporal and three-dimensional (3D) spatial information is important for the characterization of wireless channels. In this paper, the commonly used array signal processing (ASP) methods to estimate channel parameters are summarized. Firstly, algorithms that can be used to estimate azimuth angle of arrival (AAoA) and elevation AoA (EAoA) are introduced. They include multiple signal classification (MUSIC), estimation of signal parameter via rotational invariance techniques (ESPRIT), and Unitary ESPRIT algorithms. Secondly, algorithms that can be used to jointly estimate delay, AAoA, and EAoA are given. They include joint angle and delay estimation (JADE) MUSIC, JADE ESPRIT, shift-invariance (SI) JADE, and space-alternating generalized expectation-maximization (SAGE) algorithms. We also propose an improved SI-JADE algorithm to further reduce computation complexity by incorporating with the Unitary ESPRIT algorithm. Performance of the above algorithms to extract only spatial information and to jointly extract temporal and spatial information is compared in both synthetic and 60 GHz real channel environments. Simulation results show that with the inclusion of delay estimation, the joint temporal and spatial estimation algorithms can provide better resolution than algorithms estimating only angles. Measurement data processing results show that MUSIC algorithm can provide comparable results with SAGE algorithm in estimating AAoA and EAoA. SI-JADE and the improved SI-JADE algorithms are also applicable to process 60 GHz channel measurement data. However, MUSIC, SI-JADE, and the improved SI-JADE algorithms can greatly reduce computational burden compared with SAGE algorithm. At last, some future directions are pointed out.

Position and Orientation Estimation Through Millimeter-Wave MIMO in 5G Systems

Millimeter wave signals and large antenna arrays are considered enabling technologies for future 5G networks. While their benefits for achieving high-data rate communications are well-known, their potential advantages for accurate positioning are largely undiscovered. We derive the Cram\'{e}r-Rao bound (CRB) on position and rotation angle estimation uncertainty from millimeter wave signals from a single transmitter, in the presence of scatterers. We also present a novel two-stage algorithm for position and rotation angle estimation that attains the CRB for average to high signal-to-noise ratio. The algorithm is based on multiple measurement vectors matching pursuit for coarse estimation, followed by a refinement stage based on the space-alternating generalized expectation maximization algorithm. We find that accurate position and rotation angle estimation is possible using signals from a single transmitter, in either line-of- sight, non-line-of-sight, or obstructed-line-of-sight conditions.

Cluster-Based 3-D Channel Modeling for Massive MIMO in Subway Station Environment

In this paper, a massive multiple-input multiple-output (MIMO) channel measurement campaign with 256-element virtual rectangular array at the base station was conducted. The typical hotspot scenario, subway station, is considered, and the measurements were conducted at 6 GHz with a bandwidth of 100 MHz. A hybrid clustering approach is proposed to characterize the cluster evolution over the large-scale array. In the hybrid approach, we apply the space-alternating generalized expectation maximization algorithm to estimate the multipath components (MPCs), and use the multipath component distance-based tracking algorithm and the KPowerMeans algorithm for MPCs tracking and clustering. A cluster partition algorithm is further proposed to adjudge the clusters association over the array, and output the final clustering results. Under such a scheme, cluster-based model parameters are provided with detailed analysis. The extracted parameters include overall angle distribution, global angular spread, inter-cluster parameters, and intra-cluster parameters. The obtained model parameters can be fed into the new channel simulator for massive MIMO. This is useful for the design and application of the practical massive MIMO system in the future.

A novel 3D frequency domain SAGE algorithm with applications to parameter estimation in mmWave massive MIMO indoor channels

Millimeter wave (mmWave) and massive multiple-input multiple-output (MIMO) wireless communication channels show some new characteristics different from conventional channels. In order to have an in-depth understanding of mmWave massive MIMO channels, we conduct channel measurements at 16, 28, and 38 GHz frequency bands using virtual large horizontal planar arrays in an indoor office environment. First, a three dimensional (3D) frequency domain (FD) parameter estimation algorithm extended from the space alternating generalized expectation-maximization (SAGE) algorithm is proposed and used to process the measurement data. Second, by dividing the large array into several sub-arrays and calculating power delay profiles (PDPs), power azimuth angle profiles (PAAPs), and power elevation angle profiles (PEAPs), we analyze the changes of delay, azimuth angle of arrival (AAoA), and elevation AoA (EAoA) over the large array. We find that the spatial cross-correlation functions (SCCFs) calculated along different directions of the planar array exhibit significant variations. Third, the comparison of the averaged PDPs (APDPs) at three different frequency bands shows that the attenuation increases when mmWave channels move to high frequency bands. Furthermore, SCCFs of channels at three frequency bands are also compared for two uniform linear arrays (ULAs). We draw conclusion that the correlation coefficients can be affected by not only measurement environments, but also the relative angle between transmitter (Tx) pointing direction and receiver (Rx) large array, and the operating frequency bands.

Multi-Frequency mmWave Massive MIMO Channel Measurements and Characterization for 5G Wireless Communication Systems

Most millimeter wave (mmWave) channel measurements are conducted with different configurations, which may have large impacts on propagation channel characteristics. In addition, the comparison of different mmWave bands is scarce. Moreover, mmWave massive multiple-input multiple-output (MIMO) channel measurements are absent, and new propagation properties caused by large antenna arrays have rarely been studied yet. In this paper, we carry out mmWave massive MIMO channel measurements at 11-, 16-, 28-, and 38-GHz bands in indoor environments. The space-alternating generalized expectation-maximization algorithm is applied to process the measurement data. Important statistical properties, such as average power delay profile, power azimuth profile, power elevation profile, root mean square delay spread, azimuth angular spread, elevation angular spread, and their cumulative distribution functions and correlation properties, are obtained and compared for different bands. New massive MIMO propagation properties, such as spherical wavefront, cluster birth-death, and non-stationarity over the antenna array, are validated for the four mmWave bands by investigating the variations of channel parameters. Two channel models are used to verify the measurements. The results indicate that massive MIMO effects should be fully characterized for mmWave massive MIMO systems.

Dynamic propagation characteristics estimation and tracking based on an EM-EKF algorithm in time-variant MIMO channel

In cognitive radio (CR), it is important to understand the multi-dimension and multi-scale characteristics of the dynamic multiple-input multiple-output (MIMO) channels obtained from observations. In this paper, to estimate and track propagation path parameters in time-variant MIMO channels, we propose an expectation maximization-extended Kalman filter (EM-EKF) in the frequency domain. The proposed algorithm can capture the dynamic channel with a high accuracy and a low time consumption. We use the EKF in the frequency domain to detect existed paths and to continue to track how the paths evolve over time. Then, we formulate a frequency-domain EM method to estimate the new paths in the dynamic propagation channel. Simulation results demonstrate that the proposed approach has an improved performance in terms of parametric estimation and a lower time consumption compared with the comparative space-alternating generalized expectation-maximization algorithm (SAGE).