Subspace-based Methods Research Articles

Perturbation expansions of signal subspaces for long signals

Singular Spectrum Analysis and many other subspace-based methods of processing are implicitly relying on the assumption of close proximity of unperturbed and subspaces extracted by the Singular Value Decomposition of special and perturbed signal matrices. In this paper, the analysis of the main principal angle between these subspaces is performed in terms of the perturbation expansions of the corresponding orthogonal projectors. Applicable upper bounds are derived. The main attention is paid to the asymptotical case when the length of the time series tends to infinity. Results concerning conditions for convergence, rate of convergence, and the main terms of proximity are presented.

Multistage inversion algorithm for biological tissue imaging

A new inversion method for diffuse optical tomography is proposed. This is a multistage algorithm, that uses a signal subspace-based method to simplify the inverse problem and proposes a guided iterative inversion process to improve the imaging. First, subspace-based analysis is used to determine the voxels that definitely belong to the background and exclude them from further consideration. Then, the pseudo-inverse technique is applied for reconstruction. In the final stage, the reconstruction is improved iteratively by finding and excluding more voxels belonging to background. The method reduces the ill-posedness of the image reconstruction problem iteratively such that good imaging results are obtained for multiple heterogeneities having complicated geometries even in the presence of 3% additive white noise.

Prediction of Modal Parameters of Linear Time-Varying Systems

Many engineering structures, such as cranes, traffic-excited bridges, flexible mechanisms and robotic devices exhibit characteristics that vary with time and are referred to as time-varying or nonstationary. In particular, linear time-varying (LTV) systems have been often dealt with on a case-by-case basis. Many concepts and analytic methods of linear time-invariant (LTI) systems cannot be applied to LTV systems, as for example the conventional definition of modal parameters. In fact, LTV systems violate one of the assumptions of the conventional modal analysis, which is stationarity.Subspace-based identification methods, proposed in the 1970s, have been attracting much attention due to their affinity to the modern control theory, which is based on the state space model. These methods are now successfully applied to many industrial cases and may be considered reference methods for identifying LTI systems.In this paper the use of a subspace-based method for identifying LTV systems is discussed and applied to both numerical and experimental systems. More precisely a modified version of the SSI method, referred to here as ST-SSI (Short Time Stochastic Subspace Identification) is introduced as well as a method for predicting time-varying stochastic systems using the angle variation between the subspaces; the latter is able to predict the system parameter in the “near” future.

Fast Coherent Signal Subspace-Based Method for Bearing and Range of Buried Objects Estimation in the Presence of Colored Noise

In this paper, a new method for simultaneous range and bearing estimation for buried objects in the presence of an unknown colored noise is proposed. We propose a method based on multiple signal classification (MUSIC) with a new source steering vector which includes both the reflection and the refraction of wave at water-sediment interface at each sensor. The bearing and the range objects at each sensor are expressed as a function of those at the first sensor. To reduce the computational load we propose the fixed-Point algorithm, which it is faster than singular value decomposition (SVD) for MUSIC, to compute only the leading eigenvectors. A novel iterative denoising algorithm based on the noise subspace spanned by the eigenvectors associated with the smallest eigenvalues is developed when the noise spectral matrix is one unknown band matrix. The bilinear focusing operator is used to decorrelate the received wideband signals and to estimate the coherent signal subspace. The performance of the proposed algorithms is evaluated by computer simulations. Finally,we test the proposed algorithms on experimental data recorded during underwater acoustic experiments.

Face recognition method based on Gabor wavelet and common vector

The performance of subspace-based face recognition methods is easily affected by variances of lighting,pose and expression.To overcome the limitation,a novel face recognition method was proposed which combined Gabor filter and Common Vector(CV)approach.Gabor filter could better extract the local features of images because of its selectivity on scale and orientation,and it is robust to variances of lighting,pose and expression.The common vector is a linear subspace classification method,which can obtain good classification results by extracting the common property of each class training samples.The experimental results show that the proposed method can obtain good recognition results on ORL and Yale databases.

A Cross-Relation-Based Frequency-Domain Method for Blind SIMO-OFDM Channel Estimation

Single-input multiple-output (SIMO) orthogonal frequency division multiplexing (OFDM) is an appealing multi- carrier transmission technique for combating frequency-selective fading and increasing signal-to-noise ratio. To retrieve transmitted data correctly, reliable estimation of time-dispersive channels is important. This letter develops an improved cross-relation (CR) based blind SIMO-OFDM channel estimation method in the frequency domain. The significance of the proposed algorithm is twofold. First, it is highly data-efficient in that the SIMO-OFDM channels can be blindly identified using a single received data block. Second, the proposed method only requires an upper bound rather than the exact knowledge of the channel length. Simulation results show that the new method performs favorably compared to the existing CR- and subspace-based methods.

Blind Channel Identification and Equalisation in OFDM using Subspace-Based Methods

A subspace-based method is proposed for estimating the channel responses of single-input-multiple-output (SIMO) Orthogonal Frequency Division Multiplexing (OFDM) system. Our technique relies on minimum noise subspace (MNS) decomposition to obtain noise subspace in a parallel structure from a set of pairs (combinations) of system outputs that form a properly connected sequence (PCS). The developed MNS-OFDM estimator is more efficient in computation than subspace (SS)- OFDM estimator, although the former is less robust to noise than the later. To maximise the MNS-OFDM estimator performance, a symmetric version ofMNS is implemented. We present simulation results demonstrating the channel identification performance of the corresponding OFDM-based SIMO systems employ cyclic prefixing approach.

Blind Channel Estimation for Non-CP OFDM Systems Using Multiple Receive Antennas

The orthogonal frequency division multiplexing (OFDM) transmission scheme equipped with multiple receive antennas increases robustness against frequency-selective fading and combats loss in SNR. Based on the multichannel signaling property, this letter develops a frequency-domain blind channel estimator for OFDM systems without cyclic prefix (CP). With high data efficiency and low computational complexity, the proposed algorithm is able to identify the channels using a single received OFDM data block. Numerical simulations show that the proposed method performs satisfactorily with only one or very few received OFDM blocks, as compared to the existing subspace-based methods which require many more data records.

Underdetermined Blind Source Separation Based on Relaxed Sparsity Condition of Sources

Recently, Aissa-El-Bey et al. have proposed two subspace-based methods for underdetermined blind source separation (UBSS) in time-frequency (TF) domain. These methods allow multiple active sources at TF points so long as the number of active sources at any TF point is strictly less than the number of sensors, and the column vectors of the mixing matrix are pairwise linearly independent. In this correspondence, we first show that the subspace-based methods must also satisfy the condition that any M times M submatrix of the mixing matrix is of full rank. Then we present a new UBSS approach which only requires that the number of active sources at any TF point does not exceed that of sensors. An algorithm is proposed to perform the UBSS.

Subspace-Based Optimization Method in Electric Impedance Tomography

This paper extends the application of the subspace-based optimization method, which was originally proposed to solve inverse scattering problems, to two dimensional electric impedance tomography (EIT) problems with inclusions embedded in a known homogeneous background. Although the EIT problem is both physically and mathematically different from the inverse scattering problem, the EIT problem can be cast into an optimization problem whose objective function is in the same format as that of the inverse scattering problem. Numerical simulations validate the fast convergence and robustness of the proposed inverse method.

Iterative Group-Blind Multiuser Detection and Decoding With Signal Rank Estimation for Coded CDMA Systems

In this paper, a turbo receiver structure is proposed for the uplink of coded code-division multiple-access (CDMA) systems in the presence of unknown users. The proposed receiver consists of two stages following each other. The first stage performs soft interference cancellation and group-blind linear minimum mean square error (MMSE) filtering, and the second stage performs channel decoding. The proposed group-blind linear MMSE filter suppresses the residual multiple-access interference (MAI) from known users based on the spreading sequences and the channel characteristics of these users while suppressing the interference from other unknown users using a subspace-based blind method. The proposed receiver is suitable for suppressing intercell interference in heavily loaded CDMA systems. Since the knowledge of the number of unknown users is crucial for the proposed receiver structure, a novel estimator is also proposed to estimate the number of unknown users in the system by exploiting the statistical properties of the received signal. Simulation results demonstrate that the proposed estimator can provide the number of unknown users with high accuracy; in addition, the proposed group-blind receiver integrated with the new estimator can significantly outperform the conventional turbo multiuser detector in the presence of unknown users.

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.

Higher-Order SVD-Based Subspace Estimation to Improve the Parameter Estimation Accuracy in Multidimensional Harmonic Retrieval Problems

Multidimensional harmonic retrieval problems are encountered in a variety of signal processing applications including radar, sonar, communications, medical imaging, and the estimation of the parameters of the dominant multipath components from MIMO channel measurements. R-dimensional subspace-based methods, such as R-D Unitary ESPRIT, R-D RARE, or R-D MUSIC, are frequently used for this task. Since the measurement data is multidimensional, current approaches require stacking the dimensions into one highly structured matrix. However, in the conventional subspace estimation step, e.g., via an SVD of the latter matrix, this structure is not exploited. In this paper, we define a measurement tensor and estimate the signal subspace through a higher-order SVD. This allows us to exploit the structure inherent in the measurement data already in the first step of the algorithm which leads to better estimates of the signal subspace. We show how the concepts of forward-backward averaging and the mapping of centro-Hermitian matrices to real-valued matrices of the same size can be extended to tensors. As examples, we develop the R-D standard Tensor-ESPRIT and the R-D Unitary Tensor-ESPRIT algorithms. However, these new concepts can be applied to any multidimensional subspace-based parameter estimation scheme. Significant improvements of the resulting parameter estimation accuracy are achieved if there is at least one of the R dimensions, which possesses a number of sensors that is larger than the number of sources. This can already be observed in the two-dimensional case.

High-Resolution Through-the-Wall Radar Imaging Using Beamspace MUSIC

The MUSIC algorithm is a high-resolution direction finding technique which has been successfully applied to enhance radar imaging in inverse synthetic aperture radar (ISAR). Although this signal subspace-based method has proven effective when dealing with point targets and high signal-to-noise ratio (SNR), it may fail to work when directly applied to extended targets or target returns of low SNR. The Beamspace MUSIC (BS-MUSIC), in which the MUSIC algorithm is applied to multiple beams, is capable of locating spatially extended targets in low SNR environments. In this paper, we consider BS-MUSIC as an image formation method for indoor radar imaging problems and sensing through-the-wall applications. We compare BS-MUSIC performance to conventional beamforming and element-space MUSIC. Imaging results, using both synthesized and real data, demonstrate the advantages of the proposed algorithm in depicting targets behind walls.

Estimation of the Uncertainty in a Helicopter Dynamic Model Identified by the Subspace-based Method Using Bootstrap Techniques

Knowledge of the uncertainty in an identified model is of great importance, in particular for robust controller design. This paper presents a method for estimating the uncertainty in a state-space helicopter dynamical model identified from the subspace-based method using bootstrap techniques. Computer simulations are carried out to illustrate the operation and performance of the method using concatenated data sets generated from an unmanned rotorcraft model. The results obtained are in good agreement with those from conventional Monte Carlo simulations demonstrating the effectiveness of the method.

Blind channel estimation for multiple input multiple output uplink guard-band assisted code division multiple access systems with layered space frequency equalisation

Single carrier (SC) code division multiple access (CDMA) with block transmission has been shown to be more effective while utilising a low-complexity equaliser to combat frequency-selective fading channels, when compared with conventional direct sequence CDMA technology. It also has lower peak-to-average power ratio and lower frequency sensitivity compared with multicarrier CDMA. The authors propose two blind channel estimation methods for uplink multiple input multiple output SC-CDMA systems with block transmisssion-one is the subspace-based method and the other is the so-called autocorrelation contribution method (ACM). Both the methods provide close performance to the case with perfect channel knowledge at high signal-to-noise ratio (SNR) without any training data required. It is shown that ACM yields a better performance than the subspace method at a lower SNR, and a similar performance at a high SNR, with the advantages of avoiding rank determination and noise power estimation as in the subspace method. In addition, the authors integrate layered space frequency equalisation with blind channel estimation, which provides improved performance over the conventional linear equalisation, by employing successive interference cancellation.

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.

Method for direct position estimation in UWB systems

A one-step subspace-based method for direct position estimation in impulse UWB systems is proposed. The performance of the proposed method is illustrated by the results of simulations.

Decimative subspace-based parameter estimation methods of magnetic resonance spectroscopy based on prior knowledge

The method Hankel Total Least Squares (HTLS)-PK, which successfully incorporates prior knowledge of known signal poles into the method HTLS, has been proven to greatly improve the performance for parameter estimation of overlapping peaks of magnetic resonance spectroscopy (MRS) signal. In addition, decimation is also proposed as a way to increase the performance of subspace-based parameter estimation methods in the case of oversampling. Taking advantage of decimation in combination with prior knowledge to estimate the MRS signal parameters, two novel subspace-based parameter estimation methods, HTLSDSumPK and HTLSDStackPK, are presented in this paper. The experimental results and relevant analysis show that the methods HTLSDSumPK, HTLSDStackPK and HTLS-PK are slightly better than the method HTLS at low noise levels; however, the three prior-knowledge-incorporating methods, especially the method HTLSDSumPK, have much better performance than the method HTLS at high noise levels in the terms of robustness, estimated accuracy and computational complexity. Even if some inaccuracy of prior knowledge is considered, the method HTLSDSumPK also shows some advantages.

Accurate Angle-of-Arrival Estimation Method in Real System by Applying Calibration and Spatial Smoothing

Although subspace-based methods for estimating the Angle of Arrival (AOA) require a precise array response to achieve highly accurate results, it is difficult to obtain this response in practice even though the antennas are calibrated. Therefore, a method of compensating for errors in calibration is required. This paper proposes a procedure to enable precise AOA estimates to be obtained in a real system by applying array calibration and spatial smoothing preprocessing (SSP). Measured data were collected from experiments using two scenarios, i.e., in an anechoic chamber and at an open site, where a single source signal arrived at the array antenna. All measured data were then calibrated by using data obtained at 0 deg in an anechoic chamber before the AOAs were estimated. Nevertheless, errors in the array response remained after calibration because errors in the AOA estimates could still be observed. SSP was then applied to the calibrated data to obtain more accurate AOA estimates. We found that SSP can reduce the random error in an array response obtained in a real system, leading to reduced errors in AOA estimates in the observed data. To generalize the problem that SSP can reduce random perturbation in the array response, simple expressions are illustrated and verified by Monte-Carlo simulation. Random gain and phase errors in the array response are only considered in this paper and ESPRIT was used to estimate the AOAs.