Signal Correlation Matrix Research Articles

Independent vector analysis using subband and subspace nonlinearity

Independent vector analysis (IVA) is a recently proposed technique, an application of which is to solve the frequency domain blind source separation problem. Compared with the traditional complex-valued independent component analysis plus permutation correction approach, the largest advantage of IVA is that the permutation problem is directly addressed by IVA rather than resorting to the use of an ad hoc permutation resolving algorithm after a separation of the sources in multiple frequency bands. In this article, two updates for IVA are presented. First, a novel subband construction method is introduced, IVA will be conducted in subbands from high frequency to low frequency rather than in the full frequency band, the fact that the inter-frequency dependencies in subbands are stronger allows a more efficient approach to the permutation problem. Second, to improve robustness and against noise, the IVA nonlinearity is calculated only in the signal subspace, which is defined by the eigenvector associated with the largest eigenvalue of the signal correlation matrix. Different experiments were carried out on a software suite developed by us, and dramatic performance improvements were observed using the proposed methods. Lastly, as an example of real-world application, IVA with the proposed updates was used to separate vibration components from high-speed train noise data.

Joint Space-Time Parameter Estimation for Multicarrier CDMA Systems

This paper addresses the problem of joint space-time parameter estimation for multicarrier code-division multiple-access (MC-CDMA) systems in the presence of multipath propagation. We propose a novel preprocessing technique termed as subcarrier smoothing (SCS) to decorrelate the coherency of the multipath signals. The basic idea behind the SCS is to restore the rank of the signal correlation matrix by averaging the space-time covariance matrices associated with each subcarrier. Unlike the other existing preprocessing techniques, such as spatial smoothing, the SCS preprocessing is not limited to any specific array geometry and does not decrease the array aperture.

Blind speech separation for robots with intelligent human-machine interaction

Speech recognition rate will deteriorate greatly in human-machine interaction when the speaker’s speech mixes with a bystander’s voice. This paper proposes a time-frequency approach for Blind Source Seperation (BSS) for intelligent Human-Machine Interaction(HMI). Main idea of the algorithm is to simultaneously diagonalize the correlation matrix of the pre-whitened signals at different time delays for every frequency bins in time-frequency domain. The prososed method has two merits: (1) fast convergence speed; (2) high signal to interference ratio of the separated signals. Numerical evaluations are used to compare the performance of the proposed algorithm with two other deconvolution algorithms. An efficient algorithm to resolve permutation ambiguity is also proposed in this paper. The algorithm proposed saves more than 10% of computational time with properly selected parameters and achieves good performances for both simulated convolutive mixtures and real room recorded speeches.

Taylor polynomial expansion based waveform correlation cancellation for bistatic MIMO radar localization

A Taylor polynomial expansion (TPE) based waveform decorrelation algorithm with low complexity is proposed to cancel the effects of auto-correlation and cross-correlation of transmit waveform of multiple-input multiple-output (MIMO) radar in the receiver. Cayley–Hamilton theorem is first used to expand the direct matrix inversion to the form of polynomial matrix. And then, Taylor series is used to simplify the calculation of the polynomial matrix. Furthermore, a simplified method is proposed to select the normalized factor by exploiting the special properties of signal correlation matrix, where the convergence performance for the approximation error of the TPE decorrelator is also analyzed. Finally, the performance of waveform correlation cancellation is verified by applying it to bistatic MIMO radar multi-target localization. Simulation results demonstrate the effectiveness of the proposed algorithm.

A cooperation index based on the Rényi entropy of correlation matrix spectrum

We propose an index to measure cooperation among different time-series based on the Rényi entropy of the eigenvalues of the signal correlation matrix and an optimization step. The index could be considered as a generalization of a previously known index, based instead on the Shannon entropy. The extension to Rényi entropy and the optimization step allow a better use of the information conveyed by the correlation matrix, especially when dealing with a small number of signals.

Generalized eigenvector problem for Hermitian Toeplitz matrices and its application to beamforming

The generalized eigenvector problem (GEP) for Hermitian Toeplitz matrices is studied and some properties related to its eigenvectors and the associated eigenfilters are derived. Zero locations of the eigenfilters are also investigated and all of the results are applied to the maximum SINR (signal-to-interference-plus-noise ratio) beamforming problem based on ULAs (uniform linear arrays), since maximizing output SINR can be formulated as a generalized eigenvector problem where the matrix pair consisting of the desired signal correlation matrix and interference plus noise correlation matrix. Theoretical analysis based on a three-element ULA is provided, supported by simulations.

Time delay estimation of UWB radar signals backscattered from a wall

Estimating the basic characteristics of a wall is especially important in the field of through-wall radar imaging. In this article, we focus on the time delay estimation of signals measured by an ultra-wideband short-pulse radar. We describe the essential signal preprocessing steps, which are applied before a subspace super-resolution method is used to estimate the time delays of overlapping pulses backscattered from the wall. The signal correlation matrix is estimated using only one snapshot of the measured data, and the algorithm can operate in real time. In addition, to resolve closely spaced correlated echoes, we apply an improved spatial smoothing method. The performance of our algorithm is verified by simulations, and we also present the measurement results for two real brick walls. © 2011 Wiley Periodicals, Inc. Microwave Opt Technol Lett 53:1444–1450, 2011; View this article online at wileyonlinelibrary.com. DOI 10.1002/mop.25985

High-accuracy direction finding in multipath environment with short-wave antenna arrays comprising a small number of elements

A method for short-wave multipath direction finding is considered. The method allows high-accuracy determination of the directions of arrival and the amplitudes of a priori unknown arriving signals through the use of an antenna array comprising a small number of independent receiving elements with narrow-bandwidth filters placed at their inputs. An algorithm based on eigenvector decomposition of the correlation matrix of the complex signals arriving at the inputs of the radiating elements in each subband; separation of the eigenvectors into signal vectors and noise vectors; determination of the receiving-antenna eigenpatterns from the obtained vectors; and substantiation of the functional equation that allows, with the antenna eigenpatterns taken into account, the signals’ amplitudes and angles of arrival of the signals to be determined, is proposed. The results of a numerical simulation, which confirm the high accuracy of direction finding by the proposed method, are presented.

PERFORMANCE ANALYSIS OF ANTENNA ARRAY BEAMFORMERS WITH MUTUAL COUPLING EFFECTS

Antenna array beamformers sufier from performance deterioration in the presence of mutual coupling (MC) between array sensors. In this paper, we present a theoretical analysis in terms of the output signal-to-interference-plus-noise ratio (SINR) for the performance of antenna array beamformers under MC efiects. Based on the model of a distortion matrix to encapsulate the MC efiects, a closed-form expression for the SINR is derived that is shown to accurately predict the SINR obtained in simulations. This theoretical formula is valid for any distortion matrix estimated from collected measurement data. The SINR formulas provide insights into the in∞uence of the MC efiects on the performances of the linearly constrained minimum variance (LCMV) beamformer and the eigenspace-based (ESB) beamformer. It is shown that the ESB beamformer outperforms the LCMV beamformer under MC efiects. Moreover, we derive the formulas for computing the eigenvalues of signal correlation matrix under MC efiects. Simulation results are presented for conflrming the validity of the theoretical results.

Asymptotically optimal low-complexity SC-FDE in data-like co-channel interference

In this paper, the design of a low-complexity linear equalizer is considered for single-carrier (SC) block transmission in the presence of inter-symbol interference (ISI) and data-like co-channel interference (CCI). Unlike the linear minimum mean-squared error (LMMSE) frequency-domain equalizer (FDE) designed to suppress ISI only, the LMMSE FDE suffers from high computational complexity due to the CCI component in the signal correlation matrix. Motivated by the fact that the double Fourier transform of the autocorrelation function of a wide-sense cyclostationary process consists of impulse fences with equal spacing, a low-complexity FDE is proposed that approximates the frequency-domain correlation matrix of the CCI plus noise by a block matrix with diagonal blocks. It is shown that the proposed FDE is asymptotically optimal in the sense that the average mean-squared error (MSE) converges to that of the LMMSE FDE as the block length tends to infinity. It is also shown that the proposed FDE is more numerically stable than the LMMSE FDE when the receive filter is matched to the transmit filter and its output is over-sampled to better capture the cyclostationarity of the CCI. Discussions and numerical results include SC block transmission systems with unique word instead of cyclic prefix, and systems with multiple receive antennas.

Wideband cyclic music algorithms: A frequency-domain approach

In this paper, we propose two spectral cyclic MUSIC DOA estimation algorithms for wideband cyclostationary signals: the wideband spectral cyclic conjugateMUSIC (WSCCM) algorithm and the extended wideband spectral cyclicMUSIC (EWSCM) algorithm. The proposed algorithms can be applied to estimate the spectral cyclic conjugate correlation matrix and the extended spectral cyclic correlation matrix of wideband cyclostationary signals. The presented algorithms do not require any knowledge of the optimal time lag parameter, which appears in the similar algorithms in time domain. In the proposed algorithms, the DOAs are estimated at each spectral component of the selected frequency band for a cyclic frequency of interest. This can be used to form the azimuth cyclic frequency diagram, similar to the azimuth frequency diagram in wideband direction-finding systems. Some simulation results are provided to confirm the theoretical findings.

Linear prediction based semiblind channel estimation for multiuser OFDM with insufficient guard interval

To meet the demand of high data rate transmissions for multimedia wireless communications, orthogonal frequency division multiplexing (OFDM) systems in conjunction with multiple-input multiple-output (MIMO) signal processing have been considered one of the central techniques in advanced wireless communications. In the paper, two semiblind channel estimation algorithms are proposed for the uplink multiuser OFDM systems with insufficient guard interval, in contrast to sufficient guard interval assumed in most of the prior works. A zero-padding OFDM system, which zero-pads rather than cyclicly prefixing each block, is considered in this paper. By utilizing the relation between the linear prediction error filters (LPEFs) of the received signal with multiple prediction orders and the transmitted data sequence, the first proposed algorithm, namely the multistage LP (MLP) based algorithm, can estimate the MIMO channel coefficients, with only a single pilot OFDM block used. To reduce the sensitivity of the proposed algorithms to the channel order overestimation, it is proposed to implement the LPEFs with a QR-decomposition based approach. This QRdecomposition based approach alternatively computes the LPEFs without direct inversion of the received signal correlation matrix, thus exhibiting robustness against channel order overestimation. Some simulation results are presented to demonstrate the effectiveness and robustness of the proposed algorithms.

Comparison and analysis of equalization techniques for the time-varying underwater acoustic channel.

It has long been accepted that adapting a decision feedback equalizer in a time‐varying environment by first estimating the channel impulse response and using this estimate to calculate equalizer tap coefficients results in better performance than is achieved by directly adjusting the equalizer taps. There are several empirical demonstrations in the literature, [Shukla and Turner, IEE Proc.‐Commun. 138, 525–543 (1991)], but the explanations for the performance difference are varied and none uses analytical arguments. Analysis shows that at high signal‐to‐noise ratio (SNR) for time varying channels, the taps of the feed‐forward equalizer fluctuate more rapidly than do the taps of the channel impulse response and using channel estimate based adaptation is more effective. The largest changes in the equalizer coefficients occur when the input signal correlation matrix has a large condition number. At low SNR the matrix is better conditioned and the performance gap disappears. These results assume that the del...

Perfect Blind-Channel Shortening for Multicarrier Systems

In multicarrier systems, when the order of a channel impulse response is larger than the length of the cyclic prefix (CP), there is a significant performance degradation due to interblock interference (IBI). This paper proposes a blind-channel shortening method in which the equalizer parameter vector is formed by the noise subspace of the received signal correlation matrix so that the output power is maximized. The proposed method can not only shorten the effective channel impulse response to within the CP length but also maximize the output signal-to-interference-and-noise ratio while eliminating the IBI. We point out that the performance depends on the choice of a decision delay and propose a simple method for determining the appropriate delay. We propose both a batch algorithm and an adaptive algorithm and show by simulation that they are superior to the conventional algorithms.

Estimation of the Number of Partial Discharge Sources Using Multichannel Blind Deconvolution of Electromagnetic Waves

We propose a method to estimate the number of partial discharge sources in multipath environment using the multichannel blind deconvolution method called the super-exponential deflation method. Blind deconvolution is a method of recovering transmitted signals from only observed signals without any a priori knowledge of the source signals. The deflation approach can extract a source signal which is non-Gaussian from the observed signals one by one. The deflation approach is repeated until all non-Gaussian signals are extracted, in which case the input signals become close to Gaussian noise. The eigenvalues of the spatial correlation matrix of the input signals indicate whether the input signals are Gaussian noise or not. Thus, the proposed method estimates the number of PD sources by repeating the deflation approach and analyzing the eigenvalues.

Blind despreading of short-code DS-CDMA signals in asynchronous multi-user systems

The problem of blind synchronization and despreading of multiple asynchronous short-code direct-sequence code division multiple access signals is addressed in this paper. A novel algorithm applicable in asynchronous multi-user systems is proposed in which no prior knowledge of the used spreading codes is needed. The algorithm exploits the structure of the signal correlation matrix and estimates the timing offsets and spreading codes in an iterative manner, thereby improving existing methods so that also sources with nearly equal timing offsets can be estimated. Simulation examples demonstrate that nearly ideal processing gain is obtained already at a very low signal-to-noise ratio (SNR) in an AWGN channel. The algorithm can be used in interference cancellation as well as in non-cooperative applications such as spectrum monitoring, emitter localization and electronic intelligence. As an example, high-resolution DOA estimation of spread spectrum signals at low SNR is demonstrated.

Singular spectrum analysis applied to ultrasonic detection and imaging of brachytherapy seeds

Ultrasound-guided brachytherapy using titanium-shelled radioactive seeds is a popular, effective means of treating prostate cancer. Unfortunately, implantation using needles inserted transperitoneally causes gland movement and distortion, which often results in seed misplacement and dosimetry errors. If actual seed locations could be determined in the operating room, then corrections to dosimetry errors could be made immediately. However, seed specularity, shadowing, and tissue clutter make imaging seeds difficult using conventional ultrasound. Singular spectrum analysis (SSA) shows promise for reliably imaging radioactive seeds implanted in the prostate and enabling additional corrective implantations to be made in the operating room. SSA utilizes eigenvalues derived from the diagonalized correlation matrix of envelope-detected radio-frequency echo signals to yield a P value indicative of the likelihood of a seed-specific repetitive signal. We demonstrated the potential of SSA for seed detection and imaging and illustrated the trade-off considerations for optimization of SSA in clinical applications using simulations assessing performance as a function of different levels of noise and the presence of repetitive signals with various repetition periods; experiments in an ideal scattering environment; and experiments using seeds implanted in beef.

Real-time adaptive clutter rejection filtering in color flow imaging using power method iterations

We propose a new algorithm for real-time, adaptive-clutter-rejection filtering in ultrasound color flow imaging (CFI) and related techniques. The algorithm is based on regression filtering using eigenvectors of the signal correlation matrix as a basis for representing clutter, a method that previously has been considered too computationally demanding for real-time processing in general CFI applications. The data acquisition and processing scheme introduced allows for a more localized sampling of the clutter statistics and, therefore, an improved clutter attenuation for lower filter orders. By using the iterative power method technique, the dominant eigenvalues and corresponding eigenvectors of the correlation matrix can be estimated efficiently, rendering real-time operation feasible on desktop computers. A new adaptive filter order algorithm is proposed that successfully estimates the proper dimension of the clutter basis, previously one of the major drawbacks of this clutter-rejection technique. The filter algorithm performance and computational demands has been compared to that of conventional clutter filters. Examples have been included which confirms that, by adapting the clutter-rejection filter to estimates of the clutter-signal statistics, improved attenuation of the clutter signal can be achieved in normal as well as more excessive cases of tissue movement and acceleration.

New blind frequency offset estimator for OFDM systems over frequency selective fading channels

In this paper, a blind frequency offset estimator for orthogonal frequency division multiplexing (OFDM) systems over frequency selective fading channels based on modeling the unknown channel fading gains as deterministic variables is proposed. In this estimator, the received time domain OFDM samples are first partitioned into subsets, in which neighboring samples are uncorrelated, leading to a tri-diagonal signal correlation matrix for each subset. The ML cost functions from each of the subsets are combined to perform frequency offset estimation. Simulation results show that the proposed frequency offset estimator achieves better performance than the estimators reported in [J.-J. Van De Beek, M. Sandell, P.O. Borjesson, ML estimation of time and frequency offset in OFDM systems, IEEE Trans. Signal Process. 45 (July 1997) 1800–1805] and [X. Ma, G.B. Giannakis, S. Barbarossa, Non-data-aided frequency-offset and channel estimation in OFDM: and related block transmission, IEEE ICC’01, June 2001, pp. 1866–1870]. Moreover, although the power delay profile needs to be known in deriving the proposed estimator, simulation and analytical results show that the performance of the proposed estimator is not sensitive to variation in the power delay profile.

Asymptotic spectral efficiency of multiuser multisignature CDMA in frequency-selective channels

This paper presents an asymptotic analysis of multisignature code-division multiple access (CDMA) in the presence of frequency-selective channels. We characterize the sum spectral efficiency and spectral efficiency regions for both the optimal and linear minimum mean-squared error (MMSE) multiuser receivers. Both independent and identically distributed (i.i.d). signatures and isometric signatures, which are orthogonal at each transmitter, are considered. Our results are asymptotic as the number of signatures per user and processing gain both tend to infinity with fixed ratio. The spectral efficiency of the MMSE receiver is determined from the asymptotic output signal-to-interference-plus noise ratio (SINR). For isometric signatures, our results rely on approximating certain covariance matrices with unitarily invariant matrices that are asymptotically free. This approximation is shown to be very accurate through comparison with both simulation and an "incremental-signature" analysis, which can be used to compute asymptotic moments. Also, a novel proof of the convergence of the empirical spectral distribution of the signal correlation matrix is presented. From these results, we derive the optimal coding-spreading tradeoff, which maximizes the MMSE spectral efficiency, for the case of a single user with multiple i.i.d. signatures. Simulation studies demonstrate that the asymptotic results accurately predict the performance of finite-size systems of interest. The resulting expressions are used to highlight and infer properties of the multisignature CDMA system, including the benefit of orthogonal relative to i.i.d. signatures, and the tradeoff between spectral efficiency and the versatility of providing a variable data rate service through multiple signatures