Space-alternating Generalized Expectation-maximization Research Articles

Joint Estimation of Time, Frequency Offsets, and Channel Gains With ICIs in EF Multi-relay DMIMO-OFDM System

The cooperative communication or distributed multiple-input multiple-output (DMIMO) system, combined with orthogonal frequency division multiplexing (OFDM), is considered as an emerging paradigm for link reliability, high data rate, and coverage extension in fifth-generation (5G) wireless communication systems. The DMIMO system employs multiple relays with single or multiple antennas that opportunistically form virtual antenna array (VAA) in between the source and destination. Moving to the DMIMO-OFDM system from the conventional network with uncoordinated nodes requires robust synchronization and tracking. The signal received at the destination is characterized by multiple timing offsets (MTOs), multiple carrier frequency offsets (MCFOs), and frequency-selective channel gains. In this paper, we address the issue of joint time frequency and channel gain estimation for the estimate-and-forward (EF) relaying protocol. EF is a cost-effective solution but provides coarse estimation at the relays introducing intercarrier interferences (ICIs). OFDM system is very sensitive to the ICIs. We propose two iterative estimators: expectation conditional maximization (ECM) and space-alternating generalized expectation maximization (SAGE) to jointly estimate MTOs, MCFOs, and channel gains in the presence of ICIs. The robustness of the estimators is analyzed through mathematical formulation and simulations. The performances of the estimators are measured in terms of mean square error (MSE) and bit error rate (BER). The MSE performance is further verified with the theoretical Cramer–Rao lower bound (CRLB) derived. Simulation results show that the proposed estimators provide a significant performance gain in the DMIMO-OFDM system with MIMO configuration at the relays compared to the single-input single-output (SISO) system.

60-GHz Millimeter-Wave Channel Measurements and Modeling for Indoor Office Environments

The millimeter-wave (mmWave) band will be used for the fifth-generation communication systems. In this paper, 60-GHz mmWave channel measurements and modeling are carried out for indoor office environments. The rotated directional antenna-based method and uniform virtual array-based method are adopted and compared to investigate the 60-GHz channel in a 3-D space, simultaneously covering azimuth and coelevation domains. The multipath component parameters including power, delay, azimuth, and elevation angles are estimated with the space-alternating generalized expectation–maximization estimation algorithm, and then processed with the K-means clustering algorithm. An extended Saleh–Valenzuela model with both delay and angular cluster features is used to characterize the measured channel, and the intercluster and intracluster parameters are extracted. We find that the azimuth departure angles are diverse and highly related to the antenna position and measurement environment, while the elevation departure angles are more related to the antenna height difference and confined in a relatively small direction range. The azimuth angle spread is much larger than the elevation angle spread either in global level or in cluster level. The results agree with the studies in the literature and channel models in IEEE standards.

A Semi-Blind Channel Estimation Algorithm for Massive MIMO Systems

In this letter, we propose a semi-blind iterative space-alternating generalized expectation maximization (SAGE)-based channel estimator for massive MIMO systems. The method updates the pilot-based minimum mean square error (MMSE) estimate iteratively with the help of the SAGE algorithm. Pilot-based estimators require additional pilot symbols for enhancing accuracy, whereas the proposed estimator uses data symbols. Several of the existing estimators assume complete information on large scale fading coefficients of the interfering cells which requires heavy overhead. However, the proposed estimator solves this problem by an estimate obtained from the received samples. Further, we show that the proposed estimator converges almost in one iteration, and achieves appreciable improvement over the existing pilot-based and data-aided estimators in a pilot contaminated scenario.

Channel Measurements, Modeling, Simulation and Validation at 32 GHz in Outdoor Microcells for 5G Radio Systems

In this paper, based on outdoor microcellular channel measurements at 32 GHz for 5G radio systems, a comprehensive channel modeling, simulation, and validation are performed. The directional-scan-sounding measurements using a horn antenna rotated with an angular step at the receiver are carried out, which constitutes a virtual array to form a single-input multiple-output radio channel. The directional- and omni-directional path-loss models are developed by using close-in and floating-intercept methods. Non-parametric and parametric methods are applied to extract large-scale channel parameters (LSPs). The non-parametric method is based on the definition of a channel parameter, whereas the parametric method is derived by the space-alternating generalized expectation–maximization (SAGE) algorithm, which can de-embed an antenna pattern. It is found that the LSPs in the angular domain are significantly different by using the two methods; however, the LSPs in the delay domain almost stay the same. By comparing the LSPs with the parameter table at 32 GHz with 3GPP standard, it is found that 3GPP LSPs should be corrected at the International Telecommunications Union-assigned millimeter wave (mmWave) frequencies for 5G. In this paper, the channel simulation is implemented by using the quasi-deterministic radio channel generator (QuaDRiGa) platform recommended by 3GPP. By comparing the LSPs with the simulated and measured results, it is found that QuaDRiGa is a good platform at the mmWave band, even if it is originally developed for channel simulation below 6 GHz. The results of this paper are important and useful in the simulations and design of future 5G radio systems at 32 GHz.

On the Detection of Multiple‐Access Spatial Modulations

The detection problem for the Multiple-access Spatial modulations (M-SM) is investigated in this paper, where multiple transmitters adopting spatial modulation communicate to the receiver at the same time. The optimal Maximum-likelihood (ML) detection suffers from the high computational complexity, while Sphere decoding (SD) can not reduce the complexity effectively because of the multiple active antennas in M-SM. In order to avoid the high complexity, a Space-alternating generalized expectation-maximization (SAGE) algorithm aided List-projection (S-LP) detector is proposed and applied to M-SM systems. The received signal vector is firstly projected onto the subspaces spanned by the columns of channel matrices corresponding to the possible active antennas. Then some combinations of antenna indices with the largest projections are selected as candidate index sets, based on which, a modified SAGE algorithm is applied to update the candidate symbols. Both analysis and simulation results show that the proposed S-LP detector achieves a near-optimum performance with a significantly reduced complexity compared with ML and SD detection.

Antenna De-Embedded Characterization for 13–17-GHz Wave Propagation in Indoor Environments

High-gain directional antennas such as pyramidal horns have been widely used in higher frequency band channel measurements. Channel models established based on directional channel observations are antenna-specific and subject to the direction-scanning method adopted. To de-embed the impact of the antenna's responses from propagation channels, an array signal model is proposed that formulates the received signals as the outputs of a virtual array generated via antenna rotating. We first show by simulations that high-resolution parameter estimation methods, such as the space-alternating generalized expectation-maximization (SAGE) algorithm derived based on this model, are applicable to extract multipath components. The results are system-independent provided the antenna-rotating strategy satisfies certain conditions. Then, measurements conducted by using two types of horn antennas for characterizing 13–17-GHz wave propagation in a laboratory demonstrate the de-embedding effect by using the proposed scheme.

Frequency-Asynchronous Multiuser Joint Channel-Parameter Estimation, CFO Compensation, and Channel Decoding

This paper investigates a channel-coded multiuser system operated with orthogonal frequency-division multiplexing (OFDM) and interleaved division multiple-access (IDMA). To realize the potential advantage of OFDM-IDMA, two challenges must be addressed. The first challenge is the estimation of multiple channel parameters. An issue is how to contain the estimation errors of the channel parameters of the multiple users, considering that the overall estimation errors may increase with the number of users because the estimations of their channel parameters are intertwined with each other. The second challenge is that the transmitters of the multiple users may be driven by different RF oscillators. The associated frequency asynchrony may cause multiple CFOs at the receiver. Compared with a single-user receiver where the single CFO can be compensated away, a particular difficulty for a multiuser receiver is that it is not possible to compensate for all the multiple CFOs simultaneously. To tackle the two challenges, we put forth a framework to solve the problems of multiuser channel-parameter estimation, CFO compensation, and channel decoding jointly and iteratively. The framework employs the space alternating generalized expectation-maximization (SAGE) algortihm to decompose the multisuser problem into multiple single-user problems, and the expectation-conditional maximization (ECM) algorithm to tackle each of the single-user subproblems. Iterative executions of SAGE and ECM in the framework allow the two aforementioned challenges to be tackled in an optimal manner. Simulations and real experiments based on software-defined radio indicate that, compared with other approaches, our approach can achieve significant performance gains.

Modeling City-Canyon Pedestrian Radio Channels Based on Passive Sounding in In-Service Networks

Recently, a measurement campaign for characterizing time-variant radio channels in city-canyon environments was conducted along a 2-km-long pedestrian shopping street in Shanghai. A passive sounding approach was adopted where a software-defined-radio platform is used as a receiver (Rx) to record downlink signals transmitted by base stations (BSs) in an in-service Universal Mobile Telecommunications System (UMTS). Channel impulse responses are calculated from the data received in common pilot channels, and a space-alternating generalized expectation–maximization (SAGE) algorithm is applied to estimate delays, Doppler frequencies, and complex attenuations of multipath, which are further grouped into clusters characterized by time-evolving parameters. Based on the observations from a total of 70 BSs, stochastic models are established for composite channel parameters, cluster-level characteristics, and the time variabilities of these parameters. The novelties of the models lie in the passive data acquisition, which leads naturally to superior model ergodicity and higher fidelity than the standard models constructed based on active sounding. Furthermore, the models proposed here also exploit a new channel categorization method that takes into account the realistic impact of system configurations, such as the usage of multiple remote radio units in a single BS.

A Spatial Model of the UWB Off-Body Channel in Indoor Environments

In this paper, we present novel ultrawideband (UWB) off-body channel measurement campaigns in indoor environments aiming the characterization of the delay and the angular properties of the channel. Measurements were performed by using isolated UWB antenna and body-mounted antennas on different positions. Multipath and cluster parameters are estimated by means of space alternating generalized expectation-maximization (SAGE) and a clustering algorithm. These estimates allow an analysis of the variations of the channel properties due to the presence of the body. Notably, we observe strong modifications of the spatial characteristics of the channel. The delay spread is characterized as a function of the body orientation and the antenna position on the body. In addition, a modeling of the angles-of-arrival based on a Laplacian distribution is given. A cluster modeling is provided along with parameters. Finally, the part of diffuse multipath components not detected by SAGE algorithm is analyzed in function of the communication scenario.

A Spherical-Wavefront-Based Scatterer Localization Algorithm Using Large-Scale Antenna Arrays

In this letter, a spherical-wavefront-based parametric signal model is proposed by considering the architecture using a large-scale antenna array. A space-alternating generalized expectation-maximization (SAGE)-based localization algorithm is derived and adopted to localize the first-and last-hop scatterers along the propagation paths between the transmitter and the receiver. Simulations are conducted to evaluate the performance of the localization algorithm. An outdoor measurement campaign with a 1600-element virtual planar array is carried out to verify the localization performance in reality. Those results show the advantages of using a spherical-wavefront-based signal model and the SAGE-based algorithm in the scatterer localization.

Joint Frequency Offset and Channel Estimation in Distributed MIMO-OFDM Systems

In recent times, cooperative communications or distributed multi-input multi-output (DMIMO) systems are being considered as key enabler for increasing spectral efficiency and coverage area in 4G and beyond wireless communication system. DMIMO system employs multiple relays each with single or multiple antennas in between the source and destination to form a virtual antenna array. However, a few of the fundamental difficulties in deployment of DMIMO networks with coherent communications are synchronization, tracking of independent oscillators, and channel estimation. The signal received at the destination is characterized by multiple carrier frequency offsets (MCFOs) and MIMO channel effects due to sparsely distributed relay nodes. In this paper, we address the issue of joint estimation of frequency offset and channel gains in a DMIMO orthogonal frequency division multiplexing (OFDM) systems deploying multiple antennas at the relays. We consider estimate-and-forward (EF) protocol for relaying where the coarse estimation process at the low cost relays generates inter carrier interference (ICI) in a multi-carrier system resulting in severe performance degradation and decrease in reliability of the network. The two iterative estimators, expectation conditional maximization (ECM) and space-alternating generalized expectation maximization (SAGE), are proposed to jointly estimate MCFOs and channel in the presence of ICI. The robustness of the estimators are evaluated through mathematical analysis and validated using simulations. The performance of the estimators is measured in terms of mean square error (MSE) and bit error rate (BER). Simulation results show that the proposed estimators provide a significant performance gain in DMIMO-OFDM systems with MIMO configuration at the relays compared to single-input single-output (SISO) system.

A Centralized Preamble Detection-Based Random Access Scheme for LTE CoMP Transmission

For the coordinated multipoint (CoMP) transmission in Long-Term Evolution (LTE) systems, its performance is greatly impacted by the estimation of timing offsets (TOs) between cell-edge user equipment (UE) and transmit points, which is supposed to be dealt with by using the random access (RA) procedure. Available RA schemes for the CoMP transmission offer poor RA performance in terms of multiuser detection, TO estimation, power estimation, and access delays. To improve the RA performance and fully exploit the CoMP structure, in this paper, we propose a novel centralized parallel RA (CP-RA) scheme, which performs in threefold. First, a novel RA subchannel allocation scheme is proposed to suppress mutual interference between coordinated users and noncoordinated users. Second, an iterative parallel interference cancelation (IPIC)-based multiuser detection and estimation algorithm is proposed on the basis of the space-alternating generalized expectation–maximization (SAGE) algorithm. Finally, the coordinated diversity of the system structure could be exploited to implement centralized multiuser detection. Analyses and simulation results show that the proposed RA scheme is able to provide satisfied RA performance compared with existing schemes.

Performance Comparison of SAGE and MUSIC for Channel Estimation in Direction-Scan Measurements

In this paper, the performances of a space-alternating generalized expectation-maximization (SAGE) algorithm and a MUltiple Signal Identification Classification (MUSIC) technique are compared when they are used to estimate the parameters of multipath components in a propagation channel from measurement data acquired by stepping a horn antenna in directions. The impacts of the horn antenna’s half-power beamwidth (HPBW) and the stepping strategy on root mean squared estimation error and the intrinsic resolution of the estimators are investigated through simulations. The results demonstrate that the performances of both methods rely on the settings of the direction-scan strategy and the antenna HPBW. In general, the MUSIC algorithm, which owns a superior resolution, is less sensitive to the scan configuration and more suitable for scenarios of high signal-to-noise power ratio compared with the SAGE algorithm. Measurement data collected at 13–17 GHz is processed by using both algorithms. The results show that the MUSIC technique can be used to provide similar results with those of the SAGE algorithm at a time consumption significantly reduced.

SAGE Based Data Detection for Multiuser Spatial Modulation With Large Number of Receive Antennas

In this letter, we propose to exploit the concept of space-alternating generalized expectation maximization (SAGE) to resolve the data detection for multiuser spatial modulation (SM) systems with a large number of receive antennas. The proposed SAGE based detector recursively perform data detection for each user with multiuser interference (MUI) cancellation from the other users. The standard SAGE detector may converge to a local extremum point which results in observable performance degradation under the high signal-to-noise (SNR) region. To further improve the performance, we propose a new list recursive SAGE based detector, where at each cycle during the iteration procedure, the redundant MUI terms are removed and a very small list of detection candidates are reserved for each user. The simulation results are provided which show that the proposed list recursive detector can closely approach the single-user performance benchmark, and can substantially outperform the existing competitor especially with QAM constellations.

Parameter estimation using the sliding-correlator’s output for wideband propagation channels

In this contribution, a high-resolution parameter estimation algorithm is derived based on the Space-Alternating Generalized Expectation-maximization (SAGE) principle for extracting multipath parameters from the output of sliding correlator (SC). The SC allows calculating channel impulse responses with a sampling rate less than that required by Nyquist criterion, and hence is widely used in real-time wideband (e.g., >500 MHz) channel sounding for the fifth generation wireless communication scenarios. However, since the sounding signal needs to be sent repetitively, the SC-based solution is unacceptable for time-variant channel measurements. The algorithm proposed here estimates multipath parameters by using a parametric model of both low- and high-frequency components of the SC’s output. The latter was considered as distortions and discarded in the conventional SC-based channel sounding. The new algorithm allows estimating path parameters with less repetitions of transmitting the sounding signal and still exhibits higher estimation accuracy than the conventional method. Simulations are conducted and illustrate the root mean square estimation errors and the resolution capability of the proposed algorithm with respect to the bandwidth and the length of the SC’s output. These studies pave the way for measuring time-variant wideband propagation channels using SC-based solutions.

Analysis and Design of Channel Estimation in Multicell Multiuser MIMO OFDM Systems

This paper investigates the uplink transmission in multicell multiuser multiple-input multiple-output (MIMO) orthogonal frequency-division multiplexing (OFDM) systems. The system model considers imperfect channel estimation, pilot contamination (PC), and multicarrier and multipath channels. Analytical expressions are first presented on the mean square error (MSE) of two classical channel estimation algorithms [i.e., least squares (LS) and minimum mean square error (MMSE)] in the presence of PC. Then, a simple H-infinity (H-inf) channel estimation approach is proposed to have good suppression to PC. This approach exploits the space-alternating generalized expectation-maximization (SAGE) iterative process to decompose the multicell multiuser MIMO (MU-MIMO) problem into a series of single-cell single-user single-input single-output (SISO) problems, which reduces the complexity significantly. According to the analytic results given herein, increasing the number of pilot subcarriers cannot mitigate PC, and a clue for suppressing PC is obtained. It is shown from the results that the H-inf has better suppression capability to PC than classical estimation algorithms. Its performance is close to that of the optimal MMSE as the length of channel impulse response (CIR) is increased. By using the SAGE process, the performance of the H-inf does not degrade when the number of antennas is large at the base station (BS).

Joint Channel Estimation and Symbol Detection for OFDM Systems in Rapidly Time-Varying Sparse Multipath Channels

In this paper, we propose a space-alternating generalized expectation maximization (SAGE) based joint channel estimation and data detection algorithm in compressive sensing (CS) framework for orthogonal frequency-division multiplexing (OFDM) systems in rapidly time-varying sparse multipath channels. Using dynamic parametric channel model, the sparse multipath channel is parameterized by a small number of distinct paths, each represented by the path delays and path gains. In our model, we assume that the path gains rapidly vary within the OFDM symbol duration while the number of paths and path delays vary symbol by symbol. Since the convergency of the SAGE algorithm needs statistically independent parameter set of interest to be estimated, we specifically choose the discrete orthonormal Karhunen---Loeve basis expansion model (DKL-BEM) to provide statistically independent BEM coefficients within one OFDM symbol duration and use just a few significant BEM coefficients to represent the rapidly time-varying path gains. The resulting SAGE algorithm that also incorporates inter-channel interference cancellation updates the data sequences and the channel parameters serially. The computer simulations show that our proposed algorithm has better channel estimation and symbol error rate performance than that of the orthogonal matching pursuit algorithm that is commonly proposed in the CS literature.

Experimental Multipath-Cluster Characteristics of 28-GHz Propagation Channel

In this paper, a channel measurement campaign is introduced, which utilizes direction-scan-sounding to capture the spatial characteristics of 28-GHz wave propagation channels with 500-MHz sounding bandwidth in office environments. Both line-of-sight and non-line-of-sight scenarios were considered. Measurements were performed by fixing a transmit pyramidal horn antenna, and rotating another one in the receiver site at 10° steps in azimuth. The antenna outputs are viewed as array signals, and a space-alternating generalized expectation-maximization (SAGE) algorithm is applied to estimate delay and angular parameters of multipath components. Benefiting from high resolution achieved by using the SAGE and deembedding of antenna radiation pattern and system responses, more multipath clusters with less spreads in delay and azimuth are found per channel compared with existing works on 28-GHz propagation. The statistics of channel parameters extracted here constitute a preliminary stochastic multipath-cluster spatial channel model.

Pilot-Aided Joint Estimation of Doubly Selective Channel and Carrier Frequency Offsets in OFDMA Uplink With High-Mobility Users

In this paper, we propose a novel pilot-aided joint channel and carrier frequency offset (CFO) estimation method for orthogonal frequency-division multiple access (OFDMA) uplink systems with users operating in time- and frequency-selective (doubly selective) fading environments. We use Bernstein basis polynomials (BBPs) to capture rapid time variations of the channel, which avoids the identifiability issue in estimating large number of actual channel coefficients. We make use of space-alternating generalized expectation–maximization maximum a posteriori probability (SAGE-MAP) algorithm for the joint estimation of CFOs and channel coefficients. The convergence properties of the proposed method is assessed and proved analytically. The exact Bayesian Cramer–Rao bound (BCRB) for the MAP estimation problem is also derived and is shown to be comparable to the mean squared error (MSE) of the proposed technique.

Joint Frequency Offset and Channel Estimation for Distributed MIMO in Time-Varying Channels

In this paper, the joint estimation of frequency offsets and channel for distributed MIMO system in time-varying channel is discussed. We assume that each pair of transmit and receive antennas has a different frequency offset. We promote the multi-parameter estimation based on expectation conditional maximization (ECM) and space-alternating generalized expectation-maximization (SAGE) for a MIMO system operating under a flat-fading environment to the multi-p arameter estimation using EM algorithm for distributed MIMO systems in time-varying channel. Theoretical analysis and simulation results indicate that the improvement can well compensate for the performance loss caused by time-variability and achieve good performance for time-varying distributed MIMO systems