Space-alternating Generalized Expectation-maximization Research Articles

Channel parameter estimation for millimeter-wave cellular systems with hybrid beamforming

To achieve high data rates defined in 5G, the use of millimeter-waves and massive-MIMO are indispensable. To benefit from these technologies, an accurate estimation of the channel parameters is crucial. We propose a novel two-stage algorithm for channel parameters estimation. In the first stage, coarse estimation is accomplished by applying parameter estimation via interpolation based on a DFT grid (PREIDG) with a fixed look-up table (LUT), while the second stage refines the estimates by means of the space-alternating generalized expectation maximization (SAGE) algorithm. The two-stage algorithm uses discrete Fourier transform beamforming vectors which are efficiently implemented by a Butler matrix in the analog domain. We found that this methodology improves the estimates compared to the auxiliary beam pair (ABP) method. The two-stage algorithm shows efficient performance in the low signal to noise ratio regime for the channel parameters i.e. angles of departure, complex path gains and delays of the multipaths. Finally, we derived the Cramér-Rao lower bound (CRLB) to assess the performance of our two-stage estimation algorithm.

Multi-Band Time of Arrival Estimation for Long Term Evolution (LTE) Signals

This paper presents a method for estimating the time of arrival (ToA) of long term evolution (LTE) signals received on multiple separate transmission bands by the same base station (BS) mast. By exploiting the overall bandwidth occupied by the different signals and the correlation between the corresponding channel impulse responses, a higher precision is achieved with respect to the usually adopted single-band approach whenever the time-correlation among the bands is sufficiently high. The ToA estimation is carried out by generalizing the space-alternating generalized expectation-maximization (SAGE) algorithm to the multi-band context, proving that the availability of multiple bands provides a reduced standard deviation for the estimated ToA, with a limited increase of the computational cost. The main analyzed issue consists in the management of the asynchrony between transmitters belonging to distinct cellular operators, which is addressed by developing a suitable method to combine the contributions provided by the different bands. The method is validated by simulations in dual- and tri-band scenarios, and is further applied to real dual-band signals measured through a portable setup and experimentally acquired from an LTE BS mast covering multiple cells.

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.

FDD Channel Inference Methods With Experimental Performance Evaluation

Massive multiple-input multiple-output (MIMO) attracts considerable interest by increasing the spectral efficiency, and which may be adopted in future communication system. Both base station (BS) and user equipment (UE) can be equipped with large-scale antennas using frequency division duplex (FDD) schemes. The major obstacle that reduces the performance is the overhead due to the reference signal. Moreover, the channel state information (CSI) of the uplink (UL) channel cannot be simply used for downlink (DL) pre-coding. In this paper, we focus on reconstructing wireless channels on a frequency band by observing the channel response on neighboring frequency band. The inference of DL channel is conducted by utilizing parameters of multipath components extracted from UL observations, using high resolution estimation algorithms, e.g. the Space-Alternating Generalized Expectation-maximization (SAGE). Four calibration methods are proposed to improve the quality of the inferred DL channel response. Those four methods take into account the channel composition based on the availability of the initial channel observations. Their performance is demonstrated by using real massive MIMO measurements. The results show these calibration methods have their individual application scenarios and all outperform in Line-of-Sight (LoS) scenarios. These calibration methods prove a methodological way to improve the correlation of neighboring channel.

Multi-frequency channel characterization for massive MIMO communications in lobby environment

In this paper, a massive multiple input multiple output (MIMO) channel measurement campaign with two setups is conducted in an indoor lobby environment. In the first setup, two types of 256-element virtual uniform rectangular arrays (URAs), i.e., the 4×64 virtual URA and the 64×4 virtual URA are used. The carrier frequency is 11 GHz; in the second setup, measurements are performed at 4, 6, 11, 13, 15, 18 GHz at two different user locations. The channel characterization is presented by investigating the typical channel parameters, including average power delay profile (APDP), K factor, root mean square (RMS) delay spread, and coherence bandwidth. Moreover, the channel characteristics in angular domain are investigated by applying the space-alternating generalized expectation-maximization (SAGE) algorithm. The extracted multipath components (MPCs) are preliminarily clustered by visual inspection, and related to the interacting objects (IOs) in physical environment. Multipath structures at multiple frequency bands are examined. Direction spread of departure is estimated to evaluate the directional dispersion at the base station (BS) side. The results in this paper can help to reveal the propagation mechanisms in massive MIMO channels, and provide a foundation for the design and application of the practical massive MIMO system.

Distributed Target Localization with Inaccurate Collaborative Sensors in Multipath Environments

Location-aware networks are of great importance for both civil lives and military applications. Methods based on line-of-sight (LOS) measurements suffer sever performance loss in harsh environments such as indoor scenarios, where sensors can receive both LOS and non-line-of-sight (NLOS) measurements. In this paper, we propose a data association (DA) process based on the expectation maximization (EM) algorithm, which enables us to exploit multipath components (MPCs). By setting the mapping relationship between the measurements and scatters as a latent variable, coefficients of the Gaussian mixture model are estimated. Moreover, considering the misalignment of sensor position, we propose a space-alternating generalized expectation maximization (SAGE)-based algorithms to jointly update the target localization and sensor position information. A two dimensional (2-D) circularly symmetric Gaussian distribution is employed to approximate the probability density function of the sensor's position uncertainty via the minimization of the Kullback-Leibler divergence (KLD), which enables us to calculate the expectation step with low computational complexity. Moreover, a distributed implementation is derived based on the average consensus method to improve the scalability of the proposed algorithm. Simulation results demonstrate that the proposed centralized and distributed algorithms can perform close to the Monte Carlo-based method with much lower communication overhead and computational complexity.

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.

An Empirical Air-to-Ground Channel Model Based on Passive Measurements in LTE

In this paper, a recently conducted measurement campaign for unmanned-aerial-vehicle channels is introduced. The downlink signals of an in-service long-time-evolution network, which is deployed in a suburban scenario were acquired. Five horizontal and five vertical flight routes were considered. The channel impulse responses (CIRs) are extracted from the received data by exploiting the cell-specific signals, and the underlying physical propagation mechanisms are interpreted by exploiting the propagation graph modeling approach. Based on the CIRs, the parameters of multipath components are estimated by using a high-resolution algorithm derived according to the space-alternating generalized expectation-maximization (SAGE) principle. Based on the SAGE results, channel characteristics including the path loss, shadow fading, fast fading, delay spread, and Doppler frequency spread are thoroughly investigated for different heights and horizontal distances, which constitute a stochastic model.

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.

Measurement-Based Characterization of Train-to-Infrastructure 2.6 GHz Propagation Channel in a Modern Subway Station

Channel characterization is essential when planning wireless communication deployments. We consider the wireless channel characterization in a modern subway station and its corresponding entrance tunnel, a topic greatly overlooked in the literature. We setup a Long-Term Evolution (LTE) Evolved NodeB (eNodeB) transmitter in the middle of the platform of a modern station in the Madrid Metro, Spain, to cyclically transmit frequency-division duplex (FDD) LTE signals at a carrier frequency of 2.6 GHz with a bandwidth of 10 MHz. Two receivers were used to investigate both the eNodeB-train and the eNodeB-mobile links. The train was moving at a constant speed of 18 km/h from the entrance tunnel until it is completely stopped at the end of the station. Using the multipath components extracted with the space-alternating generalized expectation-maximization (SAGE) algorithm, we characterized the wireless channel response for both links based on the following parameters: power delay profile, root mean square delay spread, Doppler power spectral density, small-scale fading distribution, and K-factor.

Iterative Receiver with Low Complexity for Downlink Multicarrier Communications over Rapidly Time‐Varying Channels

This study proposes an iterative, joint channel estimation, equalization, and data detection method in the presence of high mobility for a multicarrier downlink system that communicates over rapidly time‐varying channels. The proposed method uses a basis expansion method (BEM) which has low computational complexity and helps to reduce the number of coefficients needed to represent a time‐varying channel and therefore is extremely easy to implement practically. Unlike the current literature, which is almost entirely focused on the uplink communication systems due to their computational costs, this method prioritizes the goal of being feasible in a downlink system with a reasonable performance. The proposed suboptimal algorithm is based on the space‐alternating generalized expectation‐maximization (SAGE) algorithm and the time‐varying channel is represented by orthogonal basis functions obtained by means of discrete Walsh‐Hadamard transform (DWHT). The resulting receiver iterates between maximum a posteriori (MAP) based channel estimation in the subspace spanned by the orthogonal basis functions and successive interference cancellation. Numerical examples show that the proposed algorithm has a satisfactory symbol error rate with low computational complexity and also has a reasonable peak‐to‐average power ratio (PAPR) reduction effect.

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.

Target Localization for a Distributed SIMO Sonar With an Isogradient Sound Speed Profile

A distributed single-input multiple-output (SIMO) sonar system makes use of a sound source and a distributed star receiver network to localize targets. Compared with the terrestrial target localization, there are more challenges for underwater target localization. The underwater sound speed varies with depth, temperature, and salinity. As a result, the propagation path of the acoustic signal is not a straight line. It makes existing straight-line based distance measurements less accurate. Furthermore, time synchronization, which is closely related to time-based localization, has to be carried out because of the absence of GPS and clock differences of underwater devices. In this paper, we take the sound speed variation and time synchronization into account and propose two underwater target localization algorithms, namely, the space-alternating generalized expectation maximization-based underwater target localization (SAGE-UTL) and the nonlinear weighted least squares based underwater target localization (NWLS-UTL), for the distributed SIMO sonar system. The SAGE-UTL algorithm is designed for the situation, where the central receiver of the star receiver network needs to remain silent for its own safety. On the other hand, the NWLS-UTL algorithm is designed for the other situation, where the silence of the central receiver is not required. We assume that all the receivers are not synchronized, and the speed variation can be approximately modeled by a depth-dependent sound speed profile. Our proposed algorithms can jointly achieve target localization and time synchronization. We evaluate the SAGE-UTL and the NWLS-UTL algorithms with several numerical simulations. The results show good performance of our proposed algorithms compared with the Cramer–Rao bound and the tailored benchmark algorithms, such as the approximate nonlinear least squares algorithm and the approximate space-alternating generalized expectation maximization based underwater target localization algorithm.

Experimental Characterization and Multipath Cluster Modeling for 13–17 GHz Indoor Propagation Channels

The traffic explosion of mobile communications increasingly requires effective and realistic fifth-generation (5G) channel models. Recently, we have conducted measurement campaigns in lecture hall and laboratory scenarios using steerable beam antennas for characterizing 13–17 GHz channels. The Space-Alternating Generalized Expectation–maximization (SAGE) algorithm was applied to estimate the multipath components (MPCs) in delay and angle of arrival domains. These estimated MPCs were further grouped into clusters via the threshold-based approach. It is noticeable that the observed channel characteristics obtained using the SAGE algorithm are less antenna-specific than those using the raw received signals. The scatterer locations identified from the MPCs show excellent agreement with the physical objects in the environment. Moreover, we found that the configurations of antenna-half-power-beamwidth and rotation step size exert great influence on the channel characteristics. These results provide important references for the existing 5G channel sounding and data processing, which naturally leads to fidelity of future channel models.

Joint Estimation of MCFOs and Channel Gains for Two-Way Multi-Relay Systems With High Mobility

This letter proposes space-alternating generalized expectation maximization and expectation conditional maximization-based joint estimation of multiple carrier frequency offsets and channel gains for two-way relay network with multiple relays. The method iteratively updates least square estimates with less time and stable convergence. We adopt discrete prolate spheroidal and Karhunen-Loeve basis expansion models to capture rapid time variations of channel. Proposed estimators result in acceptable performance for very high user mobility (corresponds to long term evolution for railway). The derived Cramer-Rao lower bound is shown to be comparable with MSE performances.

Scatterer Localization Using Large-Scale Antenna Arrays Based on a Spherical Wave-Front Parametric Model

In this contribution, an algorithm based on the space-alternating generalized expectation–maximization principle is proposed for estimating the locations of scatterers involved in the last-hops of propagation paths when a large-scale antenna array is used in a receiver for channel measurement. The underlying generic parametric model is constructed under the spherical wave-front assumption, which allows characterizing a path with a new parameter, i.e., the distance between the scatterer at the last-hop of the path and a specific receiving antenna, additional to the conventional parameters characterizing a specular path under the plane wave-front assumption. Cramer–Rao lower bounds of mean squared errors are derived for the parameter estimators in a single-path scenario, and their accuracy is evaluated through Monte Carlo simulations. The performance of the algorithm when being applied in reality is also evaluated through experiments conducted in an office with a carrier frequency of 9.5 GHz, a bandwidth of 500 MHz, and the receiver equipped with a 121-element virtual array. The proposed signal model and algorithm can be extended to the case of localizing the scatterers in the first- and last-hops of paths when large-scale antenna arrays are used in both the transmitter and the receiver.

TOA source localization and DOA estimation algorithms using prior distribution for calibrated source

This paper presents an a priori probability density function (pdf)-based time-of-arrival (TOA) source localization algorithms. Range measurements are used to estimate the location parameter for TOA source localization. Previous information on the position of the calibrated source is employed to improve the existing likelihood-based localization method. The cost function where the prior distribution was combined with the likelihood function is minimized by the adaptive expectation maximization (EM) and space-alternating generalized expectation–maximization (SAGE) algorithms. The variance of the prior distribution does not need to be known a priori because it can be estimated using Bayes inference in the proposed adaptive EM algorithm. Note that the variance of the prior distribution should be known in the existing three-step WLS method [1]. The resulting positioning accuracy of the proposed methods was much better than the existing algorithms in regimes of large noise variances. Furthermore, the proposed algorithms can also effectively perform the localization in line-of-sight (LOS)/non-line-of-sight (NLOS) mixture situations.

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.