Multiple-input Multiple-output Channel Estimation Research Articles

Sparse Bayesian Learning-Aided Joint Sparse Channel Estimation and ML Sequence Detection in Space-Time Trellis Coded MIMO-OFDM Systems

Sparse Bayesian learning (SBL)-based approximately sparse channel estimation schemes are conceived for space-time trellis coded (STTC) multiple-input multiple-output (MIMO) orthogonal frequency division multiplexing (OFDM) systems relying on trellis-based encoding and decoding over the data subcarriers. First, a pilot-aided channel estimation scheme is developed employing the multiple response extension of SBL (MSBL) framework. Subsequently, a novel data-aided joint channel estimation and data decoding framework relying on optimal maximum likelihood sequence detection (MLSD) is intrinsically amalgamated with our powerful EM-based MSBL algorithm. Explicitly, an MSBL-based MIMO channel estimate is gleaned in the E-step followed by a novel modified path-metric-based Viterbi decoder in the M-step. Our theoretical analysis characterizes the performance of the proposed schemes in terms of the associated frame error rate (FER) upper bounds by explicitly considering the effect of estimation errors along with evaluating the product measure of the STTC under consideration. Finally, our simulation results are complemented by the Bayesian Cramer-Rao bound (BCRB), the associated complexity analysis and the performance of the proposed schemes for validating the theoretical bounds.

Quasi-Static and Time-Selective Channel Estimation for Block-Sparse Millimeter Wave Hybrid MIMO Systems: Sparse Bayesian Learning (SBL) Based Approaches

This paper develops schemes for block-sparse channel estimation in millimeter wave (mmWave) multiple-input multiple-output (MIMO) systems that exploit the spatial sparsity inherent in such channels. Initially, a novel sparse Bayesian learning (SBL) based block-sparse channel estimation technique is developed for a mmWave hybrid MIMO system with multiple measurement vectors, which overcomes the shortcomings of the existing orthogonal matching pursuit-based framework. This is subsequently extended to a temporally correlated block-sparse mmWave MIMO channel. Further, an online recursive hierarchical Bayesian Kalman Filter is developed for the estimation of a time-selective mmWave MIMO channel. Bayesian Cramer–Rao bounds are also derived for the proposed static and time-selective mmWave MIMO channel estimation schemes followed by precoder/combiner design employing the SBL-based imperfect channel estimates. Simulation results are presented to demonstrate the improved performance of the proposed SBL-based channel estimation techniques in comparison to the popular OMP-based scheme proposed recently.

Leveraging the Restricted Isometry Property: Improved Low-Rank Subspace Decomposition for Hybrid Millimeter-Wave Systems

Communication at millimeter wave frequencies will be one of the essential new technologies in 5G. Acquiring an accurate channel estimate is the key to facilitate advanced millimeter wave hybrid multiple-input multiple-output (MIMO) precoding techniques. Millimeter wave MIMO channel estimation, however, suffers from a considerably increased channel use overhead. This happens due to the limited number of radio frequency (RF) chains that prevent the digital baseband from directly accessing the signal at each antenna. To address this issue, recent research has focused on adaptive closed-loop and two-way channel estimation techniques. In this paper, unlike the prior approaches, we study a non-adaptive, hence rather simple, open-loop millimeter wave MIMO channel estimation technique. We present a simple random design of channel subspace sampling signals and show that they obey the restricted isometry property (RIP) with high probability. We then formulate the channel estimation as a low-rank subspace decomposition problem and, based on the RIP, show that the proposed framework reveals resilience to a low signal-to-noise ratio. It is revealed that the required number of channel uses ensuring a bounded estimation error is linearly proportional to the degrees of freedom of the channel, whereas it converges to a constant value if the number of RF chains can grow proportionally to the channel dimension while keeping the channel rank fixed. In particular, we show that the tighter the RIP characterization the lower the channel estimation error is. We also devise an iterative technique that effectively finds a suboptimal but stationary solution to the formulated problem. The proposed technique is shown to have improved channel estimation accuracy with a low channel use overhead as compared to that of previous closed-loop and two-way adaptation techniques.

Reduced-complexity Krylov subspace methods for large-scale MIMO channel estimation

Large-scale multiple-input multiple-output (MIMO) system has been intensively studied for wireless communications. Channel estimation is one of the challenges in large-scale MIMO. Direct implementation of the minimum mean squared error (MMSE) channel estimator has a cubic computational complexity due to the operation of matrix inverse. Iterative Krylov subspace methods can be applied to reduce the complexity to quadratic, which is dominated by the matrix-vector products involved. In this paper, we apply conjugate gradient (CG) method and preconditioning to improve the convergence rate and reduce complexity. The computational complexities are analyzed, showing that the preconditioned CG (PCG) schemes have significantly lower complexities compared to several alternative Krylov subspace schemes.

Channel Estimation for Millimeter-Wave MIMO Communications With Lens Antenna Arrays

Millimeter-wave (mmWave) communication is a promising technology for future wireless communication systems. By utilizing the advanced lens antenna arrays, a mmWave lens multiple-input multiple-output (MIMO) system significantly reduces the number of radio-frequency (RF) chains required, and thus, achieves cost-effective implementation. In this paper, we propose a novel channel estimation scheme for the mmWave lens MIMO system with limited RF chains. The proposed scheme is applicable for the general mmWave MIMO communications, regardless of narrow-band or wide-band, time-division-duplexing or frequency-division-duplexing operations. By exploiting the energy-focusing property of lens arrays, jointly with the multipath sparsity of mmWave channels, the proposed channel estimation scheme requires only low-complexity two-way energy-based antenna selections and reduced-size MIMO channel estimation. Numerical results show that under limited RF chains and taking the channel training overhead and imperfect estimation into account, the proposed lens MIMO system achieves significantly higher throughput compared to the more complex benchmark system with the conventional uniform planar array and MIMO-orthogonal-frequency-division-multiplexing-based transmissions.

Limited Feedback Channel Estimation in Massive MIMO With Non-Uniform Directional Dictionaries

Channel state information (CSI) at the base station (BS) is crucial to achieve beamforming and multiplexing gains in multiple-input multiple-output (MIMO) systems. State-of-the-art limited feedback schemes require feedback overhead that scales linearly with the number of BS antennas, which is prohibitive for 5G massive MIMO. This paper proposes novel limited feedback algorithms that lift this burden by exploiting the inherent sparsity in double-directional MIMO channel representation using overcomplete dictionaries. These dictionaries are associated with angle of arrival and angle of departure that specifically account for antenna directivity patterns at both ends of the link. The proposed algorithms achieve satisfactory channel estimation accuracy using a small number of feedback bits, even when the number of transmit antennas at the BS is large-making them ideal for 5G massive MIMO. Judicious simulations reveal that they outperform a number of popular feedback schemes and underscore the importance of using angle dictionaries matching the given antenna directivity patterns, as opposed to uniform dictionaries. The proposed algorithms are lightweight in terms of computation, especially on the user equipment side, making them ideal for actual deployment in 5G systems.

Pilot Assisted Channel Estimation in MIMO-STBC Systems over Time-Varying Fading Channels- A Review

this paper, challenge about the condition of channel state info (CSI) in multiple-input multiple-output (MIMO) systems supported space time block codes (STBC) over slow time- varying Rayleigh attenuation channels are addressed. We develop a novel MIMO control assessment algorithmic rule that adopts a pilot symbol assisted modulation (PSAM) which has been proved to be effective for attenuation channels. In this approach, pilot symbols are periodically inserted into the information stream that's sent through the orthogonal STBC encoder. At the receiver, we propose a simple MIMO channel estimation methodology before getting used by STBC decoder. Simulation results indicate that the proposed pilot- assisted MIMO conception provides accurate channel estimates. The impact of Doppler frequency on performance scheme is also investigated by simulation. Keywords-input- multiple-output (MIMO), pilot assisted systems, rate distortion. Channel Estimation.

Compressed Sensing of Sparse Multipath MIMO Channels with Superimposed Training Sequence

Recent advances in multiple-input multiple-output (MIMO) systems have renewed the interests of researchers to further explore this area for addressing various dynamic challenges of emerging radio communication networks. Various measurement campaigns reported recently in the literature show that physical multipath MIMO channels exhibit sparse impulse response structure in various outdoor radio propagation environments. Therefore, a comprehensive physical description of sparse multipath MIMO channels is presented in first part of this paper. Superimposing a training sequence (low power, periodic) over the information sequence offers an improvement in the spectral efficiency by avoiding the use of dedicated time/frequency slots for the training sequence, which is unlike the traditional schemes. The main contribution of this paper includes three superimposed training (SiT) sequence based channel estimation techniques for sparse multipath MIMO channels. The proposed techniques exploit the compressed sensing theory and prior available knowledge of channel's sparsity. The proposed sparse MIMO channel estimation techniques are named as, SiT based compressed channel sensing (SiT-CCS), SiT based hardlimit thresholding with CCS (SiT-ThCCS), and SiT training based match pursuit (SiT-MP). Bit error rate (BER) and normalized channel mean square error are used as metrics for the simulation analysis to gauge the performance of proposed techniques. A comparison of the proposed schemes with a notable first order statistics based SiT least squares (SiT-LS) estimation technique is presented to establish the improvements achieved by the proposed schemes. For sparse multipath time-invariant MIMO communication channels, it is observed that SiT-CCS, SiT-MP, and SiT-ThCCS can provide an improvement up to 2, 3.5, and 5.2 dB in the MSE at signal to noise ratio (SNR) of 12 dB when compared to SiT-LS, respectively. Moreover, for $$\mathrm {BER}=10^{-1.9}$$BER=10-1.9, the proposed SiT-CCS, SiT-MP, and SiT-ThCCS, compared to SiT-LS, can offer a gain of about 1, 2.5, and 3.5 dB in the SNR, respectively. The performance gain in MSE and BER is observed to improve with an increase in the channel sparsity.

Improvement of Complexity and Performance of Least Square Based Channel Estimation in MIMO System

<p>Multiple-input multiple-output (MIMO) systems play a vital role in fourth generation wireless systems to provide advanced data rate. In this paper, a better performance and reduced complexity channel estimation method is proposed for MIMO systems based on matrix factorization. This technique is applied on training based least squares (LS) channel estimation using STBC for performance improvement. Simulation results indicate that the proposed method not only alleviates the performance of MIMO channel estimation but also significantly reduces the complexity caused by matrix inversion. The performance evaluations are validated through computer simulations using MATLAB in terms of bit error rate (BER) for modified LS with LS and MMSE channel estimation techniques. Simulation results show that the BER performance and complexity of the proposed method clearly outperforms the conventional LS channel estimation method.</p><p><em>Journal of Advanced College of Engineering and Management, Vol. 1, 2015</em>, pp. 11-24</p>

Iterative MIMO Detection and Channel Estimation Using Joint Superimposed and Pilot-Aided Training

This paper presents a novel iterative detection and channel estimation scheme that combines the effort of superimposed training (ST) and pilot-aided training (PAT) for multiple-input multiple-output (MIMO) flat fading channels. The proposed method, hereafter known as joint mean removal ST and PAT (MRST-PAT), implements an iterative detection and channel estimation that achieves the performance of data-dependent ST (DDST) algorithm, with the difference that the data arithmetic cyclic mean is estimated and removed from data at the receiver’s end. It is demonstrated that this iterative and cooperative detection and channel estimator algorithm surpasses the effects of data detection identifiability condition that DDST has shown when higher orders of modulation are used. Theoretical performance of the MRST-PAT scheme is provided and corroborated by numerical simulations. In addition, the performance comparison between the proposed method and different MIMO channel estimation techniques is analyzed. The joint effort between ST and PAT shows that MRST-PAT is a solid candidate in communications systems for multiamplitude constellations in Rayleigh fading channels, while achieving high-throughput data rates with manageable complexity and bit-error rate (BER) as a figure of merit.

Low‐complexity large‐scale multiple‐input multiple‐output channel estimation using affine combination of sparse least mean square filters

Large-scale multiple-input multiple-output (MIMO) system is considered one of promising technologies to realise next-generation wireless communication system (5G). So far, channel estimation problem is a big obstacle to develop large-scale MIMO system design due to high computational complexity and curse of dimensionality, which are caused by the long delay spread as well as a large number of antennas. Hence, devising any low-complexity channel estimation method could promote the successful development of the large-scale MIMO system. Due to the fact that, large-scale MIMO channels often exhibit sparse or/and cluster-sparse structure, in this study, the authors propose an effective low-complexity large-scale MIMO channel estimation method by using affine combination of sparse adaptive filtering filters. First, problem formulation and standard affine combination of adaptive least mean square (LMS) filters are introduced. Then they propose an effective affine combination method with two sparse LMS filters and design an approximate optimum affine combiner according to stochastic gradient search method. Later, to verify the proposed algorithm for large-scale MIMO channel estimation, both theoretical analysis and numerical simulations are provided to confirm effectiveness of the proposed algorithm which can achieve better estimation performance than the traditional methods.

Succesive Co-Channel Interference Cancellation

In this work, a successive four-stage interference cancellation model to unwrap and remove two co-channel interference signals is introduced and successfully tested. This model utilizes the second order statistics of the co-channel interference signals in an interference limited communication environment for interference cancelation. In this model, interferers and the signal of interest (SOI) are considered as multiple inputs of a multiple-input multiple-output (MIMO) system. Therefore, MIMO equalizers and blind MIMO channel estimator are employed for the corresponding tasks. At any stage of equalization in this model, a single signal is equalized and recovered. Later, a replica of the captured signal is cancelled from the received signal mixture. The remaining signal is fed to the next stage for equalization. The benefit of using this scheme is mainly improving the quality of the SOI by re-equalizing after interferers are completely removed. In the results section, 16 dB interference cancellation gain is shown where interferers are as strong as signal (SIR=0) and SNR is 30 dB. A Rayleigh fading (iid) channel is used for simulation.

Two-Tier Channel Estimation Aided Near-Capacity MIMO Transceivers Relying on Norm-Based Joint Transmit and Receive Antenna Selection

We propose a norm-based joint transmit and receive antenna selection (NBJTRAS) aided near-capacity multiple-input–multiple-output (MIMO) system relying on the assistance of a novel two-tier channel estimation scheme. Specifically, a rough estimate of the full MIMO channel is first generated using a low-complexity, low-training-overhead minimum mean square error based channel estimator, which relies on reusing a modest number of radio frequency (RF) chains. NBJTRAS is then carried out based on this initial full MIMO channel estimate. The NBJTRAS aided MIMO system is capable of significantly outperforming conventional MIMO systems equipped with the same modest number of RF chains while dispensing with the idealized simplifying assumption of having perfectly known channel state information (CSI). Moreover, the initial subset channel estimate associated with the selected subset MIMO channel matrix is then used for activating a powerful semi-blind joint channel estimation and turbo detector–decoder, in which the channel estimate is refined by a novel block-of-bits selection based soft-decision aided channel estimator (BBSB-SDACE) embedded in the iterative detection and decoding process. The joint channel estimation and turbo detection–decoding scheme operating with the aid of the proposed BBSB-SDACE channel estimator is capable of approaching the performance of the near-capacity maximum-likelihood (ML) turbo transceiver associated with perfect CSI. This is achieved without increasing the complexity of the ML turbo detection and decoding process.

Low-Complexity Polynomial Channel Estimation in Large-Scale MIMO With Arbitrary Statistics

This paper considers pilot-based channel estimation in large-scale multiple-input multiple-output (MIMO) communication systems, also known as massive MIMO, where there are hundreds of antennas at one side of the link. Motivated by the fact that computational complexity is one of the main challenges in such systems, a set of low-complexity Bayesian channel estimators, coined Polynomial ExpAnsion CHannel (PEACH) estimators, are introduced for arbitrary channel and interference statistics. While the conventional minimum mean square error (MMSE) estimator has cubic complexity in the dimension of the covariance matrices, due to an inversion operation, our proposed estimators significantly reduce this to square complexity by approximating the inverse by a L-degree matrix polynomial. The coefficients of the polynomial are optimized to minimize the mean square error (MSE) of the estimate. We show numerically that near-optimal MSEs are achieved with low polynomial degrees. We also derive the exact computational complexity of the proposed estimators, in terms of the floating-point operations (FLOPs), by which we prove that the proposed estimators outperform the conventional estimators in large-scale MIMO systems of practical dimensions while providing a reasonable MSEs. Moreover, we show that L needs not scale with the system dimensions to maintain a certain normalized MSE. By analyzing different interference scenarios, we observe that the relative MSE loss of using the low-complexity PEACH estimators is smaller in realistic scenarios with pilot contamination. On the other hand, PEACH estimators are not well suited for noise-limited scenarios with high pilot power; therefore, we also introduce the low-complexity diagonalized estimator that performs well in this regime. Finally, we ...

Structured compressive sensing based superimposed pilot design in downlink large‐scale MIMO systems

Large-scale multiple-input multiple-output (MIMO) with high spectrum and energy efficiency is a very promising key technology for future 5G wireless communications. For large-scale MIMO systems, accurate channel state information (CSI) acquisition is a challenging problem, especially when each user has to distinguish and estimate numerous channels coming from a large number of transmit antennas in the downlink. Unlike the conventional orthogonal pilots whose pilot overhead prohibitively increases with the number of transmit antennas, we propose a spectrum-efficient superimposed pilot design for downlink large-scale MIMO scenarios, where frequency-domain pilots of different transmit antennas occupy the completely same subcarriers in the freqency domain. Meanwhile, spatial-temporal common sparsity of large-scale MIMO channels motivates us to exploit the emerging theory of structured compressive sensing (CS) for reliable MIMO channel estimation, which is realized by the proposed structured subspace pursuit (SSP) algorithm to simultaneously recover multiple channels with low pilot overhead. Simulation results demonstrate that the proposed scheme performs well and can approach the performance bound.

Ultrahigh capacity 2 × 2 MIMO RoF system at 60 GHz employing single-sideband single-carrier modulation

This article proposes and experimentally demonstrates a radio-over-fiber system employing single-sideband single-carrier (SSB-SC) modulation at 60GHz. SSB-SC modulation has a lower peak-to-average-power ratio than orthogonal frequency division multiplex (OFDM) modulation; therefore, the SSB-SC signals provide superior nonlinear tolerance, compared to OFDM signals. Moreover, multiple-input multiple-output (MIMO) technology was used extensively to enhance spectral efficiency. A least-mean-square-based equalizer was implemented, including MIMO channel estimation, frequency response equalization, and I/Q imbalance compensation to recover the MIMO signals. Thus, using 2×2 MIMO technology and 64-QAM SSB-SC signals, we achieved the highest data rate of 84Gbps with 12 bit/s/Hz spectral efficiency using the 7-GHz license-free band at 60GHz.

Variable is better than invariable: sparse VSS-NLMS algorithms with application to adaptive MIMO channel estimation.

Channel estimation problem is one of the key technical issues in sparse frequency-selective fading multiple-input multiple-output (MIMO) communication systems using orthogonal frequency division multiplexing (OFDM) scheme. To estimate sparse MIMO channels, sparse invariable step-size normalized least mean square (ISS-NLMS) algorithms were applied to adaptive sparse channel estimation (ACSE). It is well known that step-size is a critical parameter which controls three aspects: algorithm stability, estimation performance, and computational cost. However, traditional methods are vulnerable to cause estimation performance loss because ISS cannot balance the three aspects simultaneously. In this paper, we propose two stable sparse variable step-size NLMS (VSS-NLMS) algorithms to improve the accuracy of MIMO channel estimators. First, ASCE is formulated in MIMO-OFDM systems. Second, different sparse penalties are introduced to VSS-NLMS algorithm for ASCE. In addition, difference between sparse ISS-NLMS algorithms and sparse VSS-NLMS ones is explained and their lower bounds are also derived. At last, to verify the effectiveness of the proposed algorithms for ASCE, several selected simulation results are shown to prove that the proposed sparse VSS-NLMS algorithms can achieve better estimation performance than the conventional methods via mean square error (MSE) and bit error rate (BER) metrics.

Research of Improved Algorithm for MIMO Channel Estimation

We introduced an improved singular value decomposition (SVD) channel estimation algorithm for multiple-input multiple-output (MIMO) wireless communication system. The algorithm is supposed to solve the issue that the channel estimation result is not accurate when the training sequences have some 0 elements. The improvement is also applicable in the other channel estimation algorithms. We made some comparisons between the linear least squares (LS) and the linear minimum mean square error (LMMSE) channel estimation, the traditional singular value decomposition and the improved SVD algorithm to demonstrate the efficiency. Results show that the proposed improved SVD algorithm has better performance in mean square error (MSE) and bit error rate (BER) of channel estimation and the estimated values approach the actual channel state.

Training sequence design for MIMO channels: an application-oriented approach

In this paper, the problem of training optimization for estimating a multiple-input multiple-output (MIMO) flat fading channel in the presence of spatially and temporally correlated Gaussian noise is studied in an application-oriented setup. So far, the problem of MIMO channel estimation has mostly been treated within the context of minimizing the mean square error (MSE) of the channel estimate subject to various constraints, such as an upper bound on the available training energy. We introduce a more general framework for the task of training sequence design in MIMO systems, which can treat not only the minimization of channel estimator’s MSE but also the optimization of a final performance metric of interest related to the use of the channel estimate in the communication system. First, we show that the proposed framework can be used to minimize the training energy budget subject to a quality constraint on the MSE of the channel estimator. A deterministic version of the 'dual’ problem is also provided. We then focus on four specific applications, where the training sequence can be optimized with respect to the classical channel estimation MSE, a weighted channel estimation MSE and the MSE of the equalization error due to the use of an equalizer at the receiver or an appropriate linear precoder at the transmitter. In this way, the intended use of the channel estimate is explicitly accounted for. The superiority of the proposed designs over existing methods is demonstrated via numerical simulations.

Subspace techniques for multidimensional model order selection in colored noise

R-dimensional (R-D) harmonic retrieval (HR) in colored noise, where R≥2, is required in numerous applications including radar, sonar, mobile communications, multiple-input multiple-output channel estimation and nuclear magnetic resonance spectroscopy. Tensor-based subspace approaches to R-D HR such as R-D unitary ESPRIT and R-D MUSIC provide super-resolution performance. However, they require the prior knowledge of the number of signals. The matrix based (1-D) ESTimation ERror (ESTER) is subspace based detection method that is robust against colored noise. To estimate the number of signals from R-D measurements corrupted by colored noise, we propose two R-D extensions of the 1-D ESTER by means of the higher-order singular value decomposition. The first R-D ESTER combines R shift invariance equations each applied in one dimension. It inherits and enhances the robustness of the 1-D ESTER against colored noise, and outperforms the state-of-the-art R-D order selection rules particularly in strongly correlated colored noise environment. The second R-D scheme is developed based on the tensor shift invariance equation. It performs best over a wide range of low-to-moderate noise correlation levels, but poorly for high noise correlation levels showing a weakened robustness to colored noise. Compared with the existing R-D ESTER scheme, both proposals are able to identify much more signals when the spatial dimension lengths are distinct.