Samuli Visuri

Sign and rank covariance matrices

The robust estimation of multivariate location and shape is one of the most challenging problems in statistics and crucial in many application areas. The objective is to find highly efficient, robust, computable and affine equivariant location and covariance matrix estimates. In this paper, three different concepts of multivariate sign and rank are considered and their ability to carry information about the geometry of the underlying distribution (or data cloud) are discussed. New techniques for robust covariance matrix estimation based on different sign and rank concepts are proposed and algorithms for computing them outlined. In addition, new tools for evaluating the qualitative and quantitative robustness of a covariance estimator are proposed. The use of these tools is demonstrated on two rank-based covariance matrix estimates. Finally, to illustrate the practical importance of the problem, a signal processing example where robust covariance matrix estimates are needed is given.

Subspace-based direction-of-arrival estimation using nonparametric statistics

The problem of subspace estimation using multivariate nonparametric statistics is addressed. We introduce new high-resolution direction-of-arrival (DOA) estimation methods that have almost optimal performance in nominal conditions and are robust in the face of heavy-tailed noise. The extensions of the techniques for the case of coherent sources are considered as well. The proposed techniques are based on spatial sign and rank concepts. We show that spatial sign and rank covariance matrices can be used to obtain convergent estimates of the signal and noise subspaces. In the proofs, the noise is assumed to be spherically symmetric. Moreover, we illustrate how the number of signals may be determined using the proposed covariance matrix estimates and a robust estimator of variance. The performance of the algorithms is studied using simulations in a variety of noise conditions including noise that is not spherically symmetric. The results show that the algorithms perform near optimally in the case of Gaussian noise and highly reliably if the noise is non-Gaussian.

Blind Frequency Synchronization in OFDM via Diagonality Criterion

In this paper, we address the problem of blind carrier frequency offset (CFO) estimation in orthogonal frequency-division multiplexing (OFDM) systems in the case of frequency-selective channels. CFO destroys the orthogonality between the carriers leading to nondiagonal signal covariance matrices in frequency domain. The proposed blind method enforces a diagonal structure by minimizing the power of nondiagonal elements. Hence, the orthogonality property inherent to OFDM transmission with cyclic prefix is restored. The method is blind since it does not require a priori knowledge of the transmitted data or the channel, and does not need any virtual subcarriers. A closed-form solution is derived, which leads to accurate and computationally efficient CFO estimation in multipath fading environments. Consistency of the estimator is proved and the convergence rate as a function of the sample size is analyzed as well. To assess the large sample performance, we derive the Cramer-Rao bound (CRB) for the blind CFO estimation problem. The CRB is derived assuming a general Gaussian model for the OFDM signal, which may be applied to both circular and noncircular modulations. Finally, simulation results on CFO estimation are reported using a realistic channel model

Affine equivariant multivariate rank methods

The classical multivariate statistical methods (MANOVA, principal component analysis, multivariate multiple regression, canonical correlation, factor analysis, etc.) assume that the data come from a multivariate normal distribution and the derivations are based on the sample covariance matrix. The conventional sample covariance matrix and consequently the standard multivariate techniques based on it are, however, highly sensitive to outlying observations. In the paper a new, more robust and highly efficient, approach based on an affine equivariant rank covariance matrix is proposed and outlined. Affine equivariant multivariate rank concept is based on the multivariate Oja (Statist. Probab. Lett. 1 (1983) 327) median.

Resolving ambiguities in subspace-based blind receiver for MIMO channels

The problem of subspace based blind channel estimation in FIR-MIMO systems is addressed in this paper. In such blind MIMO methods, some ambiguities always remain. They may be expressed in a form of full rank mixing matrix. In this paper, a two-stage receiver algorithm solving these ambiguities is proposed. The FIR-MIMO model is identified first followed by equalization stage. The ambiguity remaining after the equalizer is modeled as an instantaneous MIMO system. This system is solved using independent component analysis (ICA) using the assumption that transmitted sequences is statistically independent and non-Gaussian.

Performance bound for blind CFO estimation in OFDM with real-valued constellations

In this paper, we investigate the performance of the blind carrier frequency offset (CFO) estimation method for OFDM with real-valued constellations introduced in (T. Roman et al, ICASSP, vol.4, p.IV 369-IV 372, 2004). The method is based on minimizing the total off-diagonal power of the received pseudo-covariance matrix and the resulting solution has a simple closed-form expression. To assess the large sample performance, we derive the Cramer-Rao bound (CRB) for the blind CFO estimation problem. When deriving the CRB, the transmitted OFDM modulated signal is assumed to be a Gaussian process. Since real-valued constellations are used, the received signal is non-circular. As a result, the CRB has to be derived for a non-circular Gaussian model. Simulation results highlight significant differences in performance between the complex circular and non-circular cases.

Robust subspace DOA estimation for wireless communications

This paper is concerned with array signal processing in non-Gaussian noise typical in urban and indoor radio channels. Robust and fully nonparametric high resolution algorithms for direction of arrival (DOA) estimation are presented. The algorithms are based on multivariate spatial sign and rank concepts. The performance of the algorithms is studied using simulations. The results show that almost optimal performance is obtained in wide variety of noise conditions.

Blind channel identification using robust subspace estimation

The paper introduces a robust approach to subspace based blind channel identification. The technique is based on estimating the noise subspace from the sample sign covariance matrix. The theoretical motivation for the technique is shown under the white Gaussian noise assumption. A simulation study is performed to demonstrate the robust performance of the algorithm both in Gaussian and non-Gaussian noise. The results indicate that when the noise is Gaussian, the proposed method has similar good performance as the standard subspace method. When the noise is heavy-tailed, the proposed method outperforms the conventional subspace technique.

Nonparametric statistics for DOA estimation in the presence of multipath

This paper is concerned with array signal processing in nonGaussian noise and in the presence of multipath. Robust and fully nonparametric high resolution algorithms for direction of arrival (DOA) estimation are presented. The algorithms are based on multivariate spatial sign and rank concepts. Spatial smoothing of the multivariate rank and sign based covariance matrices is employed as a preprocessing step in order to deal with coherent sources. The performance of the algorithms is studied using simulations. The results show that almost optimal performance is obtained in wide variety of different noise conditions.