Downlink Channel Estimation Research Articles

MISO Channel Estimation and Tracking from Received Signal Strength Feedback

Downlink channel estimation is an important task in any wireless communication system, and 5G massive multiple-input multiple-output in particular—because the receiver must estimate and feed back to the transmitter a high-dimensional multiple-input single-output (MISO) vector channel for each receiving element. This is a serious burden in terms of mobile computation and power, as well as uplink communication overhead. The starting point of this paper is that all existing and emerging wireless communication systems provide basic Received Signal Strength (RSS) / Channel Quality Indicator (CQI) feedback to compensate for temporal channel variations. Is it possible to estimate and track the vector MISO channel from RSS/CQI feedback alone? This paper shows that the answer is affirmative, if one employs time-varying beamforming and phase modulation together with phase retrieval ideas from optics and crystallography. Three efficient algorithms that cover different model assumptions are proposed to track the vector MISO channel on the transmitter's side using only RSS/CQI feedback. Numerical simulation results under various settings validate the efficacy of the proposed algorithms in tracking a slowly time-varying vector MISO channel. Interestingly, this is the first application of phase retrieval where assuming independent and identically distributed Gaussian measurement vectors can be practically justified.

Secure Massive MIMO With the Artificial Noise-Aided Downlink Training

This paper considers a massive MIMO network that includes one multiple-antenna base station, one multiple-antenna eavesdropper, and $K$ single-antenna users. The eavesdropper operates in passive mode and tries to overhear the confidential information from one of the users in the down-link transmission. In order to secure the confidential information, two artificial noise (AN)-aiding schemes are proposed. In the first scheme, AN is injected into the downlink training signals to prevent the eavesdropper from obtaining the correct channel state information of the eavesdropping link. In the second scheme, AN is deployed in both downlink training phase and payload data transmission phase to further degrade the eavesdropping channel. Analytical expressions and tight approximations of the achievable secrecy rate of the considered systems are derived with taking imperfect channel estimation and two types of precoding, i.e., maximum-ratio-transmission and zero-forcing, into consideration. Optimization algorithms for power allocation are proposed to enhance the secrecy performance of the proposed AN-aiding schemes. The results reveal that deploying AN in the downlink training phase of massive MIMO networks does not affect the downlink channel estimation process at users while enabling the system to suppress the downlink channel estimation process at eavesdropper. As a consequence, the proposed AN-aided schemes improve the system performance significantly. Furthermore, implementing AN in both phases allows the considered system having a flexible solution to maximize its secrecy performance at the price of higher complexity.

Omnidirectional Space-Time Block Coding for Common Information Broadcasting in Massive MIMO Systems

In this paper, we design space-time block codes (STBCs) to broadcast the common information omnidirectionally in a massive multiple-input multiple-output downlink. To reduce the burden of the downlink channel estimation and achieve partial spatial diversity from base station (BS) transmit antennas, we propose channel-independently precoded low-dimensional STBC. The precoding matrix and the signal constellation in the low-dimensional STBC are jointly designed to guarantee omnidirectional coverage at any instant time and sufficiently utilize the power amplifier capacities of BS transmit antennas, and at the same time, achieve the full diversity of the low-dimensional STBC. Under this framework, several designs are presented. To provide transmit diversity order of two, a precoded Alamouti code is proposed, which has a fast symbolwise maximum-likelihood (ML) decoding. To provide transmit diversity order of four, a precoded quasi-orthogonal STBC is proposed, which has a pairwise ML decoding. Moreover, a precoded no-zero-entry Toeplitz code and a precoded no-zero-entry overlapped Alamouti code are also proposed. These two codes can achieve a higher diversity order with linear receivers.

Beam-domain hybrid time-switching and power-splitting SWIPT in full-duplex massive MIMO system

In this paper, we consider the beam-domain hybrid time-switching (TS) and power-splitting (PS) simultaneous wireless information and power transfer (SWIPT) protocol design in full-duplex (FD) massive multiple-input multiple-output (MIMO) system, where the FD base station (BS) simultaneously serves a set of downlink half-duplex (HD) users (cellular users) and a set of fixed uplink HD users (fixed sensor nodes) which are uniformly distributed in its coverage area. In order to reduce the computational complexity, we investigate the beam-domain representation of massive MIMO channels based on the basis expansion model, and then the beam-domain SWIPT protocol which lies in intelligently scheduling the users and sensors based on the beam-domain distributions of their associated channels to mitigate SI and enhance transmission efficiency is designed for full-duplex massive MIMO system. The whole beam-domain hybrid TS and PS SWIPT protocol is divided into two phases based on the ideal of TS. The first phase is used for cellular users uplink training and sensor nodes energy harvesting as well as downlink training, wherein the cellular users transmit uplink pilots for uplink channel estimation at the BS, while the BS simultaneously transmits energy signals to the sensor nodes. Based on the idea of PS, the sensor nodes utilize the received energy signals for energy harvesting and downlink channel estimation. In the second phase, the BS forms the transmit beamformers for information transmission to the users as well as the receive beamformers for the sensors transmit their data to the BS simultaneously. By optimizing the TS ratio and transmit powers at the BS in two phases, the system achievable sum rate performance is maximized. Simulation results show the superiority of the proposed protocol on spectral efficiency compared with the existing massive MIMO SWIPT protocol.

Spectral and Energy Efficient Low-Overhead Uplink and Downlink Channel Estimation for 5G Massive MIMO Systems.

Uplink and Downlink channel estimation in massive Multiple Input Multiple Output (MIMO) systems is an intricate issue because of the increasing channel matrix dimensions. The channel feedback overhead using traditional codebook schemes is very large, which consumes more bandwidth and decreases the overall system efficiency. The purpose of this paper is to decrease the channel estimation overhead by taking the advantage of sparse attributes and also to optimize the Energy Efficiency (EE) of the system. To cope with this issue, we propose a novel approach by using Compressed-Sensing (CS), Block Iterative-Support-Detection (Block-ISD), Angle-of-Departure (AoD) and Structured Compressive Sampling Matching Pursuit (S-CoSaMP) algorithms to reduce the channel estimation overhead and compare them with the traditional algorithms. The CS uses temporal-correlation of time-varying channels to produce Differential-Channel Impulse Response (DCIR) among two CIRs that are adjacent in time-slots. DCIR has greater sparsity than the conventional CIRs as it can be easily compressed. The Block-ISD uses spatial-correlation of the channels to obtain the block-sparsity which results in lower pilot-overhead. AoD quantizes the channels whose path-AoDs variation is slower than path-gains and such information is utilized for reducing the overhead. S-CoSaMP deploys structured-sparsity to obtain reliable Channel-State-Information (CSI). MATLAB simulation results show that the proposed CS based algorithms reduce the feedback and pilot-overhead by a significant percentage and also improve the system capacity as compared with the traditional algorithms. Moreover, the EE level increases with increasing Base Station (BS) density, UE density and lowering hardware impairments level.

Mobility-Aware Reconstruction Algorithm for Correlated Nonzero Neighborhood Structured Downlink Channel in Massive MIMO

This paper investigates downlink (DL) channel estimation of frequency division duplex (FDD) massive multiple-input-multiple-output (MIMO) with a finite number of base station (BS) antennas. Based on the performance analysis of DL channel in FDD, it is demonstrated that the interference effect cannot be ignored in the finite region. Also, excessive training overhead is required in conventional channel estimation methods when the number of BS antennas goes large. Therefore, it is necessary to design an algorithm for alleviating the interference in addition to the reduction of pilot overhead. In this paper, a general model is presented to exploit certain sparsity structure of massive MIMO channel in beam domain, which is called nonzero-neighborhood (NZN) structure. Considering the smooth variation of channel paths during two consecutive estimation intervals, a compressed sensing-based algorithm is proposed to efficiently estimate and track NZN-structured DL channel. The convergence behavior and computational complexity of the proposed mobility-aware subspace pursuit (MA-SP) algorithm are analyzed based on restricted isometric property. It is demonstrated that the application of proposed MA-SP algorithm efficiently reduces the required pilot length in channel estimation. Interference analysis shows that inter-cell interference is considerably alleviated in the proposed channel estimation phase without any prior information about interference. Simulation results demonstrate the effectiveness of the proposed MA-SP technique compared with the previous methods.

Distributed Compressed Sensing Aided Sparse Channel Estimation in FDD Massive MIMO System

Massive multi-input multi-output (MIMO), which employs large number of antennas at the base station, can significantly boost the spectral efficiency and multiplexing gain. To fully exploit the huge array gain, the accurate channel state information is required at the transmitter side. However, the associated training overhead for downlink channel estimation consumes large amount of communication resource, especially for frequency division duplexing massive MIMO system. To address this issue, a distributed compressed sensing (DCS)-aided channel estimation approach is proposed, which fully exploits slow variation of the channel statistics in consecutive frames and spatially common sparsity within multiple subchannels in the frequency domain. Specifically, by exploiting the slow variation of the channel statistics, a hybrid training structure is proposed to probe the channel in the current frame based on the support information in previous frame. Then, a DCS-aided channel estimation algorithm, which combines least square method and DCS method, is proposed to estimate the two parts of channel vector in angular domain among different subcarriers. In addition, to effectively acquire the support information at the beginning of communication, a prior information estimation method is proposed by exploiting the uplink-downlink angular reciprocity. Simulation results demonstrate that the proposed approach outperforms the counterparts and is capable to significantly reduce the training overhead for channel estimation.

FDD massive MIMO downlink channel estimation with complex hybrid generalized approximate message passing algorithm

Precise channel state information (CSI) is essential for the massive multiple-input multiple-output (MIMO) system to achieve high spectrum and energy efficiency performance in the forthcoming 5G communication. Combined with angular domain channel sparsity, compressive sensing (CS) technique is introduced to estimate downlink CSI because it can help the frequency division duplex massive MIMO system to overcome the restriction of the limited pilot overhead. Conventional CS techniques consider different entries of the sparse signal as equivalent random variables. However, some scatters around the base station are fixed during practical propagation. Consequently, some propagation beams are more likely to locate within certain angular spread and the corresponding entries of the angular domain channel response vector are more likely to be non-zero valued. While this non-zero probability of a certain entry can be acquired offline by learning and analyzing the historical CSI, it is unnecessary to be estimated again during the sparse reconstruction process. When we describe the non-zero probability of a certain entry with the probabilistic density manner, hybrid prior probabilistic settings are used because of the practical propagation property. Combined with the complex generalized approximated message passing (GAMP) algorithm, a new channel estimation method is introduced in this paper. We define the GAMP algorithm with its intrinsic architecture and amended hybrid probability node settings as hybrid GAMP algorithm. A definite improvement of the pilot consumption as well as the estimation accuracy are simultaneously achieved through our proposed channel estimation method with complex hybrid GAMP algorithm and accurate hybrid settings. By further simulation, the influence of the inaccurate hybrid settings of the sparse channel response vector is drawn that the negative effect is proved to be quite small for the proposed channel estimation method.

FDD Massive MIMO Channel Estimation With Arbitrary 2D-Array Geometry

This paper addresses the problem of downlink channel estimation in frequency-division duplexing (FDD) massive multiple-input multiple-output (MIMO) systems. The existing methods usually exploit hidden sparsity under a discrete Fourier transform (DFT) basis to estimate the cdownlink channel. However, there are at least two shortcomings of these DFT-based methods: 1) they are applicable to uniform linear arrays (ULAs) only, since the DFT basis requires a special structure of ULAs, and 2) they always suffer from a performance loss due to the leakage of energy over some DFT bins. To deal with the above shortcomings, we introduce an off-grid model for downlink channel sparse representation with arbitrary 2D-array antenna geometry, and propose an efficient sparse Bayesian learning (SBL) approach for the sparse channel recovery and off-grid refinement. The main idea of the proposed off-grid method is to consider the sampled grid points as adjustable parameters. Utilizing an in-exact block majorization-minimization (MM) algorithm, the grid points are refined iteratively to minimize the off-grid gap. Finally, we further extend the solution to uplink-aided channel estimation by exploiting the angular reciprocity between downlink and uplink channels, which brings enhanced recovery performance.

Channel Estimation for FDD Multi-User Massive MIMO: A Variational Bayesian Inference-Based Approach

This paper addresses downlink channel estimation for frequency division duplex multi-user massive multiple-input multiple-output systems. Suppose that a base station communicates with $K$ mobile users, then the task is to estimate $K$ channel matrices, each corresponding to one user. Due to the limited scattering in physical propagation, each channel matrix is sparse in the virtual angular domain. Besides, different user links tend to share some common scatterers. As such, different channel matrices may have a partially common sparsity pattern. These observations motivate us to take a variational Bayesian inference based approach for channel estimation. Specifically, we design a Gaussian mixture prior model, which can efficiently capture the individual sparsity in each channel matrix and the partially joint sparsity shared by different channel matrices. Furthermore, we develop a variational expectation maximization strategy to estimate the hyperparameters associated with the prior model and the channel matrices. Compared with the existing counterparts, the proposed approach achieves much better performance in terms of the channel estimation accuracy, while maintaining a low computational complexity.

Simultaneous Wireless Information and Power Transfer for Downlink Multi-User Massive Antenna-Array Systems

We propose a simultaneous wireless information and power transfer scheme based on the power-splitting technique for the downlink of multi-user massive antenna-array systems. The base station (BS) can transmit both the wireless energy and information simultaneously to the user equipments (UEs). Using the harvested energy, each UE can transmit its pilot signal to the BS for the downlink channel estimation by exploiting the channel reciprocity of the time division duplexing system. When the antenna scale is large enough, the ergodic achievable rates of UEs are derived in closed-form. To maximize the minimum achievable rate among all the UEs, an iterative algorithm with low-complexity is proposed to jointly optimize the power allocation coefficients of the BS and the power-splitting ratios of the UEs. In each iteration of the proposed algorithm, the optimal power-splitting ratios can be determined according to the closed-form expressions for a given power allocation coefficient. The convergency, optimality, and complexity of our proposed algorithm are analyzed theoretically. The equal power allocation is shown to be optimal when the transmit power of BS is large enough. Furthermore, the optimal number of antennas is determined to maximize the energy efficiency. Simulation results are provided to validate our closed-form approximations and verify the efficiency of our proposed algorithm.

Beam combination scheme for multi‐user massive MIMO systems

Channel state information (CSI) at the base station (BS) is crucial to fully exploit the advantages of massive multiple-input multiple-output (MIMO) systems. In frequency division duplexing systems, CSI is obtained through downlink channel estimation and uplink CSI feedback. The conventional CSI acquisition scheme, which has been designed based on the beam selection principle, suffers from severe multi-user interference when same beamforming vector is selected for different user equipments (UEs), and the spatial richness of the channel cannot be captured by the selected beamforming vector for the rich scattering environment. To address such issues, a beam combination scheme is proposed by combining multiple selected beamforming vectors for each UE, where the beam combination process is divided into wideband beam group construction and subband combination coefficients acquisition. Simulation results demonstrate that the proposed scheme could achieve considerable increase in the system throughput while maintaining acceptable feedback overhead.

Low-Rank Tensor Decomposition-Aided Channel Estimation for Millimeter Wave MIMO-OFDM Systems

We consider the problem of downlink channel estimation for millimeter wave (mmWave) MIMO-OFDM systems, where both the base station (BS) and the mobile station (MS) employ large antenna arrays for directional precoding/beamforming. Hybrid analog and digital beamforming structures are employed in order to offer a compromise between hardware complexity and system performance. Different from most existing studies that are concerned with narrowband channels, we consider estimation of wideband mmWave channels with frequency selectivity, which is more appropriate for mmWave MIMO-OFDM systems. By exploiting the sparse scattering nature of mmWave channels, we propose a CANDECOMP/PARAFAC (CP) decomposition-based method for channel parameter estimation (including angles of arrival/departure, time delays, and fading coefficients). In our proposed method, the received signal at the BS is expressed as a third-order tensor. We show that the tensor has the form of a low-rank CP decomposition, and the channel parameters can be estimated from the associated factor matrices. Our analysis reveals that the uniqueness of the CP decomposition can be guaranteed even when the size of the tensor is small. Hence the proposed method has the potential to achieve substantial training overhead reduction. We also develop Cramer-Rao bound (CRB) results for channel parameters, and compare our proposed method with a compressed sensing-based method. Simulation results show that the proposed method attains mean square errors that are very close to their associated CRBs, and presents a clear advantage over the compressed sensing-based method in terms of both estimation accuracy and computational complexity.

A Unified Transmission Strategy for TDD/FDD Massive MIMO Systems With Spatial Basis Expansion Model

This paper proposes a unified transmission strategy for multiuser time division duplex (TDD)/frequency division duplex (FDD) massive multiple-input–multiple-output (MIMO) systems, including uplink (UL)/downlink (DL) channel estimation and user scheduling for data transmission. With the aid of antenna array theory and array signal processing, we build a spatial basis expansion model (SBEM) to represent the UL/DL channels with far fewer parameter dimensions. Hence, both the UL and DL channel estimations of multiusers can be carried out with a small amount of training resource, which significantly reduces the training overhead and feedback cost. Meanwhile, the pilot contamination problem in the UL training is immediately relieved by exploiting the spatial information of users. To enhance the spectral efficiency, we also design a greedy user scheduling scheme during the data transmission period. Compared with existing low-rank models, the newly proposed SBEM offers an alternative for channel acquisition without the need for channel statistics and can be applied to both TDD and FDD systems. Various numerical results are provided to corroborate the proposed studies.

Quantization and Feedback of Spatial Covariance Matrix for Massive MIMO Systems With Cascaded Precoding

In this paper, we investigate the quantization and the feedback of downlink spatial covariance matrix for massive multiple-input multiple-output (MIMO) systems with cascaded precoding. Massive MIMO has gained a lot of attention recently because of its ability to significantly improve the network performance. To reduce the overhead of downlink channel estimation and uplink feedback in frequency-division duplex massive MIMO systems, cascaded precoding has been used to convert high-dimensional physical channels into low-dimensional effective channels. For the cascaded precoding, the inner precoder is determined by the downlink spatial covariance matrix, which is unknown in the base station (BS). To address this issue, we propose a spatial spectrum-based approach for the quantization and the feedback of the spatial covariance matrix. In this manner, the BS can obtain partial information on the downlink spatial covariance matrix. Our result shows that the inner precoder based on the proposed approach can be viewed as modulated discrete prolate spheroidal sequences and thus achieves much smaller spatial leakage than the traditional discrete Fourier transform submatrix-based precoding. Practical issues for the application of the proposed approach are also addressed in this paper.

Low-Rank Covariance-Assisted Downlink Training and Channel Estimation for FDD Massive MIMO Systems

We consider the problem of downlink training and channel estimation in frequency division duplex (FDD) massive MIMO systems, where the base station (BS) equipped with a large number of antennas serves a number of single-antenna users simultaneously. To obtain the channel state information (CSI) at the BS in FDD systems, the downlink channel has to be estimated by users via downlink training and then fed back to the BS. For FDD large-scale MIMO systems, the overhead for downlink training and CSI uplink feedback could be prohibitively high, which presents a significant challenge. In this paper, we study the behavior of the minimum mean-squared error (MMSE) estimator when the channel covariance matrix has a low rank or an approximate low-rank structure. Our theoretical analysis reveals that the amount of training overhead can be substantially reduced by exploiting the low-rank property of the channel covariance matrix. In particular, we show that the MMSE estimator is able to achieve exact channel recovery in the asymptotic low-noise regime, provided that the number of pilot symbols in time is no less than the rank of the channel covariance matrix. We also present an optimal pilot design for the single-user case, and an asymptotic optimal pilot design for the multi-user scenario. Last, we develop a simple model-based scheme to estimate the channel covariance matrix, based on which the MMSE estimator can be employed to estimate the channel. The proposed scheme does not need any additional training overhead. Simulation results are provided to verify our theoretical results and illustrate the effectiveness of the proposed estimated covariance-assisted MMSE estimator.

Block Expectation Propagation for Downlink Channel Estimation in Massive MIMO Systems

To address the challenging problem of downlink channel estimation with low pilot overhead in massive multiple-input multiple-output (MIMO) systems, an empirical Bayesian block expectation propagation (EP) algorithm is proposed. Specifically, a block Bernoulli-Gaussian prior channel model is proposed to fit the underlying block sparsity, and a block EP algorithm is derived to estimate the channels more accurately by clustering all the channel taps that pertain to the same delay, while the model parameters are learned by minimizing the Bethe free energy. Simulation results show that the proposed algorithm achieves considerable reduction of pilot overhead in a massive MIMO system with tens of antennas, while maintaining superior channel estimation performance.

Joint interpolation for LTE downlink channel estimation in very high‐mobility environments with support vector machine regression

In this study, the estimation of fast-fading long term evolution (LTE) downlink channels in high-speed applications of LTE advanced is investigated by the authors. A robust channel estimation and interpolation algorithm is essential in order to adequately track the fast time-varying channel response. In this contribution, the multipath fast-fading channel is modelled as a discrete, tapped-delay and finite impulse response filter. Using support vector machine regression (SVR), they develop an extended algorithm to jointly estimate the complex-valued channel frequency response in time and frequency domains, in the presence of fading and non-linear noise from the transmission of known pilot symbols. Furthermore, the channel estimates at the known pilot symbols are interpolated to the unknown data symbols by using the non-linear SVR approach exploiting kernel features. This study integrates both channel estimation at pilot symbols and interpolation at data symbol into the complex SVR interpolation method. The bit error rate and mean square error performances of the authors’ fast-fading channel estimation scheme is demonstrated via simulation for LTE downlink with 64-QAM modulation and 500 km/h velocity under non-linearities.

Joint Channel Training and Feedback for FDD Massive MIMO Systems

Massive multiple-input multiple-output (MIMO) is widely recognized as a promising technology for future 5G wireless communication systems. To achieve the theoretical performance gains in massive MIMO systems, accurate channel state information at the transmitter (CSIT) is crucial. Due to the overwhelming pilot signaling and channel feedback overhead, however, conventional downlink channel estimation and uplink channel feedback schemes might not be suitable for frequency-division duplexing (FDD) massive MIMO systems. In addition, these two topics are usually separately considered in the literature. In this paper, we propose a joint channel training and feedback scheme for FDD massive MIMO systems. Specifically, we firstly exploit the temporal correlation of time-varying channels to propose a differential channel training and feedback scheme, which simultaneously reduces the overhead for downlink training and uplink feedback. We next propose a structured compressive sampling matching pursuit (S-CoSaMP) algorithm to acquire a reliable CSIT by exploiting the structured sparsity of wireless MIMO channels. Simulation results demonstrate that the proposed scheme can achieve substantial reduction in the training and feedback overhead.

FDD Massive MIMO 시스템에서의 적응 채널 추정 기법

In frequency-division duplex (FDD) massive multiple-input multiple-output (MIMO) system, the computational complexity of downlink channel estimation is proportional to the number of antennas at a base station. Therefore, effective channel estimation techniques may have to be studied. In this paper, novel channel estimation algorithms using adaptive techniques such as Kalman and least mean square (LMS) filters are proposed in a channel model with temporal and spatial correlation.