Subspace-based Channel Estimation Research Articles

Blind and Semi-Blind Channel Estimation/Equalization for Poisson Channels in Optical Wireless Scattering Communication Systems

The communication systems for Poisson channels require long pilot for channel estimation and may result in large percentage of overhead due to the signal-dependent noise of Poisson-distributed signal, i.e., both signal part and noise part experience random processes. In this paper, both blind and semi-blind channel estimation methods are studied to shorten the overhead and increase the transmission efficiency for Poisson channels. First, fractionally spaced equalizers are proposed based on modified constant modulus algorithm (CMA) and subspace (SS). Second, a data-aided iterative channel estimation (ICE) is designed and analyzed in terms of its asymptotic unbiasedness and convergence. The proposed methods are evaluated based on both a constant channel scenario and a varying channel scenario. Numerical simulation results show that the modified CMA has the worst bit-error rate performance but requires the lowest computational complexity. Besides, both SS based channel estimation and ICE have negligible overhead and comparable bit-error rate performances with respect to the conventional periodic pilot based channel estimation having 50% overhead.

A Spatial–Temporal Subspace-Based Compressive Channel Estimation Technique in Unknown Interference MIMO Channels

Spatial–temporal (ST) subspace-based channel estimation techniques formulated with $\ell 2$ minimum mean square error (MMSE) criterion alleviate the multi-access interference (MAI) problem when the interested signals exhibit low-rank property. However, the conventional $\ell 2$ ST subspace-based methods suffer from mean squared error (MSE) deterioration in unknown interference channels, due to the difficulty to separate the interested signals from the channel covariance matrices (CCMs) contaminated with unknown interference. As a solution to the problem, we propose a new $\ell 1$ regularized ST channel estimation algorithm by applying the expectation-maximization (EM) algorithm to iteratively examine the signal subspace and the corresponding sparse-supports. The new algorithm updates the CCM independently of the slot-dependent $\ell 1$ regularization, which enables it to correctly perform the sparse-independent component analysis (ICA) with a reasonable complexity order. Simulation results shown in this paper verify that the proposed technique significantly improves MSE performance in unknown interference MIMO channels, and hence, solves the BER floor problems from which the conventional receivers suffer.

Spatiotemporal-MIMO Channel Estimator and Beamformer for 5G

With requirements of spiraling data rates and limited spectrum availability, there is an increased interest in mm-wave beamformer-based communications for 5G. For upcoming cellular networks, the critical point is to exploit the increased number of employable antennas at both Tx and Rx to: 1) combat increased path loss; 2) tackle higher interference due to higher user density; and 3) handle multipath effects in frequency selective channels. Toward this, a multi-beam spatiotemporal superresolution beamforming framework is proposed in this paper as a promising candidate to design beampatterns that mitigate/suppress co-channel interference and deliver massive gain in the desired directions. Initially, channel and signal models suitable for the mm-wave MIMO system are presented using the manifold vectors of both Tx and Rx antenna arrays. Based on these models, a novel subspace-based channel estimator is employed, which estimates delays, directions, velocities, and fading coefficients of the desired signal paths. This information is then exploited by the proposed spatiotemporal beamformer to provide a massive array gain that combats path loss without increasing the number of antenna array elements and to be tolerant to the near-far problem in a high interference environment. The performance of the proposed channel estimator and beamformer is examined using computer simulation studies.

Channel Estimation for Massive MIMO-OFDM Systems by Tracking the Joint Angle-Delay Subspace

In this paper, we propose joint angle-delay subspace based channel estimation in single cell for broadband massive multiple-input and multiple-output (MIMO) systems employing orthogonal frequency division multiplexing (OFDM) modulation. Based on a parametric channel model, we present a new concept of the joint angle-delay subspace which can be tracked by the low-complexity low-rank adaptive filtering (LORAF) algorithm. Then, we investigate an interference-free transmission condition that the joint angle-delay subspaces of the users reusing the same pilots are non-overlapping. Since the channel statistics are usually unknown, we develop a robust minimum mean square error (MMSE) estimator under the worst precondition of pilot decontamination, considering that the joint angle-delay subspaces of the interfering users fully overlap. Furthermore, motivated by the interference-free transmission criteria, we present a novel low-complexity greedy pilot scheduling algorithm to avoid the problem of initial value sensitivity. Simulation results show that the joint angle-delay subspace can be estimated effectively, and the proposed pilot reuse scheme combined with robust MMSE channel estimation offers significant performance gains.

The Impact of Physical Channel on Performance of Subspace-Based Channel Estimation in Massive MIMO Systems

A subspace method for channel estimation has been recently proposed [1] for tackling the pilot contamination effect, which is regarded by some researchers as a bottleneck in massive MIMO systems. It was shown in [1] that if the power ratio between the desired signal and interference is kept above a certain value, the received signal spectrum splits into signal and interference eigenvalues, namely, the "pilot contamination" effect can be completely eliminated. However, [1] assumes an independently distributed (i.d.) channel, which is actually not much the case in practice. Considering this, a more sensible finite-dimensional physical channel model (i.e., a finite scattering environment, where signals impinge on the base station (BS) from a finite number of angles of arrival (AoA)) is employed in this paper. Via asymptotic spectral analysis, it is demonstrated that, compared with the i.d. channel, the physical channel imposes a penalty in the form of an increased power ratio between the useful signal and the interference. Furthermore, we demonstrate an interesting "antenna saturation" effect, i.e., when the number of the BS antennas approaches infinity, the performance under the physical channel with P AoAs is limited by and nearly the same as the performance under the i.d. channel with P receive antennas.

Using ICA to improve blind subspace-based channel estimation for OFDM system under unknown noise fields

Blind subspace-based channel estimation methods have received considerable attention for multicarrier communication systems with virtual carriers over white Gaussian noises. In this paper, orthogonal frequency division multiplexing (OFDM) system without any training symbols or any prior knowledge of the noise covariance matrix is considered under unknown noise fields. No single subspace feature extraction method outperforms others under all circumstances, but applying a dual-space feature extraction method can overcome the limits of single subspace. A robust dual-space feature extraction is put forward based on minor component analysis (MCA) and independent component analysis (ICA) to increase the channel estimate accuracy. Especially, the proposed feature extraction always starts the procedure as a pure-MCA and ends as a pure-ICA. Once the new noise basis vectors are obtained, which is as orthogonal as possible to the estimated noise basis vectors especially for highly correlated and impulse noises, the noise subspace can be reconstructed for the MCA-based estimator. Computer simulation is provided for illustrating the effectiveness of the proposed method.

Performance Analysis of Subspace Based Downlink Channel Estimation for W-CDMA Systems Using Chaotic Codes

This paper presents blind channel estimation for downlink W-CDMA system that employs chaotic codes and Walsh codes for spreading information bits of the multiple users. In a W-CDMA system, while transmitting over multipath channels, both intersymbol interference (ISI) as a result of Inter Chip Interference and multiple access interference (MAI) cannot be easily eliminated. Although it is possible to design multiuser detectors that suppress MAI and ISI, these detectors often require explicit knowledge of at least the desired users' signature waveform. Earlier work focused on a subspace based channel estimation algorithm for asynchronous CDMA systems to estimate the multiple users' symbols, where only AWGN channel was considered. In our work, we study a similar subspace-based signature waveform estimation algorithm for downlink W-CDMA systems, which use chaotic codes instead of pseudo random codes, that provide estimates of the multiuser channel by exploiting structural information of the data output at the base station. In particular, we show that the subspace of the (data+noise) matrix contains sufficient information for unique determination of channels, and hence, the signature waveforms and signal constellation. We consider Rayleigh and Rician fading channel model to quantify the multipath channel effects. Performance measures like bit error rate and root mean square error are plotted for both chaotic codes and Walsh codes under Rayleigh and Rician fading channels.

Subspace-Based Channel Estimation for MIMO-OFDM Systems With Few Received Blocks

We propose a method of obtaining the autocorrelation matrix to improve the performance of the subspace-based channel estimation method. By exploiting the circulant property of the received signal, the proposed method reduces the number of received blocks required to satisfy the persistency of excitation (POE) criterion for the input and decreases the residual error which affects the accuracy of the noise subspace. To verify the proposed method, we derive the analytical method for evaluating the POE criterion for the input. In simulation results, we demonstrate the efficiency of the proposed method.

Subspace based downlink channel estimation for W-CDMA systems

Wideband code division multiple access (W-CDMA) is a third generation (3G) mobile wireless technology that promises much higher data speeds for mobile and portable wireless devices than those which are commonly offered in todayʼs market. In W-CDMA systems transmitting over multipath channels, both Inter Symbol Interference (ISI) as a result of Inter Chip Interference (ICI) and Multiple Access Interference (MAI) cannot be easily eliminated. Although it is possible to design multiuser detectors that suppress MAI and ISI, these detectors often require explicit knowledge of at least the desired usersʼ signature waveform. Torlak and Xu (1997) [1] proposed a subspace based channel estimation algorithm for Asynchronous CDMA (A-CDMA) systems to estimate the multiple usersʼ symbols. In our work, we study a similar subspace based channel estimation scheme for downlink W-CDMA systems that provide estimates of the subchannels of multiple users by exploiting the structural information of the data output. In particular, we show that the subspace of the (data + noise) matrix contains sufficient information for unique determination of channels, and hence, the signature waveforms and signal constellation. Performance measures like Bit Error Rate (BER) and Root Mean Square Error (RMSE) are plotted for Rayleigh and Rician fading channels.

Widely Linear versus Conventional Subspace-Based Estimation of SIMO Flat-Fading Channels: Mean Squared Error Analysis

We analyze the mean-squared error (MSE) performance of widely linear (WL) and conventional subspace-based channel estimation for single-input multiple-output (SIMO) flat-fading channels employing binary phase-shift-keying (BPSK) modulation when the covariance matrix is estimated using a finite number of samples. The conventional estimator suffers from a phase ambiguity that reduces to a sign ambiguity for the WL estimator. We derive closed-form expressions for the MSE of the two estimators under four different ambiguity resolution scenarios. The first scenario is optimal resolution, which minimizes the Euclidean distance between the channel estimate and the actual channel. The second scenario assumes that a randomly chosen coefficient of the actual channel is known and the third assumes that the one with the largest magnitude is known. The fourth scenario is the more realistic case where pilot symbols are used to resolve the ambiguities. Our work demonstrates that there is a strong relationship between the accuracy of ambiguity resolution and the relative performance of WL and conventional subspace-based estimators, and shows that the less information available about the actual channel for ambiguity resolution, or the lower the accuracy of this information, the higher the performance gap in favor of the WL estimator.

Semiblind Channel Estimation for IFDMA in Case of Channels with Large Delay Spreads

Discrete Fourier Transform- (DFT-) precoded Orthogonal Frequency Division Multiple Access (OFDMA) with interleaved subcarrier allocation per user is considered which is denoted as Interleaved Frequency Division Multiple Access (IFDMA). For IFDMA, the received signal exhibits a cyclostationarity with the parameter which defines the number of allocated subcarriers per user. In previous works, we have shown that this cyclostationarity can be exploited for the application of subspace-based semiblind channel estimation to IFDMA. Nevertheless, the formerly proposed algorithm is restricted to channels with small delay spreads, meaning that the number of channel delay taps needs to be smaller than . In this paper, we introduce a new semiblind subspace-based channel estimation algorithm which identifies a subspace of the received signal that is spanned by the elements of the so-called cyclic channel impulse response. By doing so, the number of elements to be estimated is reduced and the proposed algorithm is able to cope with channels with large delay spreads.

Subspace-Based Semi-Blind Channel Estimation in Uplink OFDMA Systems

This paper presents a new approach for subspace-based semi-blind channel estimation in the uplink channel of orthogonal frequency division multiple access (OFDMA) systems. In the proposed approach, the orthogonality between the signal subspace and the noise subspace induced by the virtual carriers (VCs) is exploited to estimate the channel status of each user. The redundancy provided by the sub-carriers of the non-active users is then adopted to enhance the channel estimation performance. It is shown that while the proposed subspace-based channel estimation scheme is feasible for both sub-band and interleaved OFDMA systems, it is particularly effective for interleaved OFDMA systems due to their improved frequency diversity characteristic. In addition, a novel scheme, designated as the virtual carrier recovery (VCR) scheme, is proposed to further enhance the performance of the channel estimation process by recovering the VCs to zeros at the receiver end. The simulation results demonstrate that the VCR scheme yields a significant improvement in the channel estimation performance; particularly for the case of partially-loaded OFDMA systems. It is also shown that the proposed VCR scheme has a comparable bit error rate (BER) performance to that of the case when the receiver has perfect channel state information (CSI).

Subspace-Based Iterative Semiblind Channel Estimation for MIMO-OFDM Considering Residual Error

A new approach to subspace-based channel estimation for multiple-input-multiple-output orthogonal frequency-division multiplexing (MIMO-OFDM) systems is proposed. The proposed method exploits both the receive diversity and the statistical property of the received signal based on the iterative algorithm. To reduce the effect of residual error affecting the accuracy of the noise subspace, a measure called the Hermitian angle is introduced. In addition, the forgetting factor is used to consider a time-varying channel.

Generalized Correlation Decomposition-Based Blind Channel Estimation in DS-CDMA Systems With Unknown Wide-Sense Stationary Noise

A new blind subspace-based channel estimation technique is proposed for direct-sequence code-division multiple access (DS-CDMA) systems operating in the presence of unknown wide-sense stationary noise. Unlike most of the blind techniques developed for unknown correlated noise environments so far, the proposed algorithm is applicable to an arbitrary symbol constellation and does not require any auxiliary antennas at the receiver or any prior knowledge of the interfering user spreading codes. Our approach exploits the centro-Hermitian property of the unknown noise covariance matrix and makes use of the generalized correlation decomposition (GCD) to obtain an accurate estimate of the noise subspace and, consequently, of the user-of- interest channel vector. We also obtain optimal values of the GCD weighting matrices which maximally preserve the orthogonality of the estimated noise subspace to the actual signal subspace in the high signal-to-noise ratio (SNR) regime. It is shown that such an optimal choice of the weighting matrices transforms GCD to an extended form of the conventional canonical correlation decomposition (CCD). Simulation results further demonstrate that if such an extended CCD-based approach is used to estimate the user-of-interest channel vector, then the estimation performance can be substantially improved as compared to earlier SVD-based blind channel estimation techniques.

A Decorrelating-MRC Based Space–Time Multiuser Receiver for Time-Hopping UWB System

In this paper, we propose a two-stage linear multiuser detector (LMD) for ultra wideband (UWB) multiple single-input multi-output (M-SIMO) system and multipath fading environment. Time-hopping (TH) and antipodal pulse amplitude modulation (PAM) are employed for the multiple access system. The decorrelating detector is first employed at the front end of each receive antenna to eliminate the multi-user interference (MUI), then a set of maximum-ratio-combiners (MRC) are proceeded to maximize the signal-to-noise power ratio (SNR) for each user. Since the channel information is crucial for the Decorrelating-MRC (D-MRC) receiver, we develop a subspace-based blind M-SIMO channel estimation method. The effect of channel estimation error on system performance is extensively evaluated. It is also verified from the analytical and numerical results that by exploiting both spatial and temporal diversities, the D-MRC receiver dramatically improves system performance even without additional coding. Moreover, we demonstrate that both the D-MRC receiver and subspace-based blind channel estimator are computationally feasible and near-far resistant.

Performance of blind channel estimation algorithms for space-frequency block coded multi-carrier code division multiple access systems

The problem of blind channel estimation for downlink space-frequency block coded multi-carrier code division multiple access (SFBC MC-CDMA) schemes is considered. For these schemes, the authors first develop a system model for complex modulated signals, which reduces the multichannel estimation problem to a single-input single-output problem. Then, they present an intuitive subspace-based channel estimation method along with the corresponding necessary and sufficient conditions under which the channel estimate is unique (within a complex scalar). Their studies highlight two interesting properties of SFBC MC-CDMA systems: (i) there is no antenna order ambiguity (also known as permutation ambiguity) even though only one spreading code is assigned to each user; (ii) channel identifiability is guaranteed, regardless of the channel zeros location. They also establish the unbiasedness of the channel estimates and derive closed-form expressions for the mean-square-error of the estimates as well as the corresponding Cramer-Rao bound (CRB). In the derivation of the CRB, they suggest a novel approach which assumes the knowledge of only the spreading code of desired user. This approach results in a tighter bound than the CRB derived based on the knowledge of all users' signatures.

MIMO Capon Receiver and Channel Estimation for Space-Time Coded CDMA Systems

In this paper the code-division multiple-access (CDMA) multiple-input multiple-output (MIMO) systems with space-time block code (STBC) are investigated. Both the forward-backward averaging technique and the eigenspace: technique are proposed to enhance the system performance. Moreover, we present a subspace-based channel estimator which utilizes the space-time coding property to improve the performance of channel estimator. Then the performance analysis using the first order perturbation theory is derived. Computer simulations are given to demonstrate the effectiveness of the channel estimation and receiver design for the STBC-based CDMA systems

Subspace system identification for training-based MIMO channel estimation

The application of state-space-based subspace system identification methods to training-based estimation for quasi-static multi-input–multi-output (MIMO) frequency-selective channels is explored with the motivation for better model approximation performance. A modification of the traditional subspace methods is derived to suit the non-contiguous nature of training data in mobile communication systems. To track the time variation of the channel, a new recursive subspace-based channel estimation is proposed and demonstrated in simulation with practical MIMO channel models. The comparison between the state-space-based channel estimation algorithm and the FIR-based Recursive Least Squares algorithm shows the former is a more robust modeling approach than the latter.

Subspace-based blind channel estimation: generalization and performance analysis

In this paper, we present a systematic study of the subspace-based blind channel estimation method. We first formulate a general signal model of multiple simultaneous signals transmitted through vector channels, which can be applied to a multitude of modern digital communication systems. Based on this model, we then propose a generalized subspace-based channel estimator by minimizing a novel cost function, which incorporates the set of kernel matrices of the signals sharing the target channel via a weighted sum of projection errors. We investigate the asymptotic performance of the proposed estimator, i.e., bias, covariance, mean square error (MSE), and Cramer-Rao bound, for large numbers of independent observations. We show that the performance of the estimator can be optimized by increasing the number of kernel matrices and by using a special set of weights in the cost function. Finally, we consider the application of the proposed estimator to a downlink code division multiple access (CDMA) system operating in a frequency-selective fading channel with negligible intersymbol interference (ISI). The results of the computer simulations fully support our analytical developments.

Improved subspace-based channel estimation algorithm for DS∕CDMA systems exploiting pulse-shaping information

An improved subspace-based channel estimation algorithm for DS/CDMA system is presented. The proposed algorithm is based on the Torlak/Xu algorithm for asynchronous DS/CDMA systems. The aim is to incorporate knowledge of the pulse-shaping filter into the Torlak/Xu subspace algorithm with the objective of reducing the variance of the channel estimates. The improved algorithm is developed from a system model of a DS/CDMA system where the output is oversampled with respect to the chip rate. By oversampling the received signal, knowledge of the pulse-shaping filter is incorporated into the proposed channel estimation algorithm. It is shown that the variance of the channel estimate for the proposed subspace algorithm is less than the Torlak/Xu algorithm that does not exploit pulse-shaping filter information. A mathematical expression of the mean square error of estimation for the improved algorithm is also derived. It is shown that the analytical expression provides a good approximation of the actual mean square error for high SNR signals.