Blind system identification using minimum noise subspace (original) (raw)

A cumulant matrix subspace algorithm for blind single FIR channel identification

IEEE Transactions on Signal Processing, 2001

Blind identification of discrete-time single-user FIR channels with nonminimum phase is studied here. Exploiting higher order cumulants of output signals of unknown channels, a new closed-form solution to the FIR channel impulse response is derived. The algorithm is simple and fast. It relies only on nullspace decomposition of some cumulant matrices. This method neither involves the difficult task of iterative global minimization of nonunimodal cost functions, nor does it require overparametrization, which poses consistency difficulties. It can be used either as the final channel estimate or as a good initial point in nonlinear cumulant matching techniques. The application of this identification method is broad and not limited to the use of any fixed-order cumulants. Its application in identifying data communication systems shows great potential and promise. Zhi Ding (M'87-SM'95) was born in Harbin, China. He received the B.Eng. degree from the Department of Wireless Engineering, Nanjing Institute of Technology, Nanjing, China, in July 1982, the M.A.Sc. degree from the

A deterministic approach to blind identification of multi-channel FIR systems

1994

Conventional blind channel identification algorithms are based on channel outputs and the knowledge of the probabilistic model of a channel input. In some practical applications, however, the input statistical model may not be known, or there may not be sufficient data to obtain accurate enough estimates of certain statistics. We consider the system input to be an unknown deterministic signal and study the problem of blind identification of a channel which can be decomposed into multichannel FIR systems driven by a input signal. A new deterministic blind identification algorithm based solely on the system outputs are proposed. Necessary and sufficient identifiability conditions concerning the channel and the deterministic input signal are also presented

An Efficient Subspace Method for the Blind Identification of Multichannel FIR Systems

IEEE Transactions on Signal Processing, 2008

We present a novel method for the blind identification of linear, single-input multiple-output (SIMO) finite- impulse-response (FIR) systems, based on second-order statistics. Our approach, called the truncated transfer matrix method (TTM) proceeds in two major steps: first, the SVD analysis of the lagged covariance matrix gives the subspace of the clipped system transfer matrix and second, the block-Toeplitz structure of the transfer matrix gives extra constraints that allow us to reconstruct the matrix through the solution of a linear system of equations. The proposed TTM method is analytical (no optimization procedure involved), and it is robust to noise. We find that the method comes with an increased computational cost but it significantly outperforms state of the art second-order methods in low signal-to-noise ratio (SNR) situations.

Blind and semi-blind maximum likelihood methods for FIR multichannel identification

1998

We investigate Maximum Likelihood (ML) methods for blind and semi-blind estimation of multiple FIR channels. Two blind Deterministic ML (DML) strategies are presented. In the first one, we propose to modify the Iterative Quadratic ML (IQML) algorithm in order to "denoise" it and hence obtain consistent channel estimates. The second strategy, called Pseudo-Quadratic ML (PQML), is naturally asymptotically denoised. Links between these two approaches are established and their global convergence is proved. Furthermore, we propose semi-blind ML techniques combining PQML with two different training sequence estimation methods and compare their performance. These semi-blind techniques, exploiting the presence of known symbols, outperform their blind version. They also allow channel estimation in situations where blind and training sequence methods fail separately. Simulations are presented to demonstrate the performance of all the proposed algorithms, and comparisons between them are discussed in a blind and/or semi-blind context.

Adaptive multi-channel least mean square and Newton algorithms for blind channel identification

Signal Processing, 2002

The problem of identifying a single-input multiple-output FIR system without a training signal, the so-called blind system identiÿcation, is addressed and two multi-channel adaptive approaches, least mean square and Newton algorithms, are proposed. In contrast to the existing batch blind channel identiÿcation schemes, the proposed algorithms construct an error signal based on the cross relations between di erent channels in a novel, systematic way. The corresponding cost (error) function is easy to manipulate and facilitates the use of adaptive ÿltering methods for an e cient blind channel identiÿcation scheme. It is theoretically shown and empirically demonstrated by numerical studies that the proposed algorithms converge in the mean to the desired channel impulse responses for an identiÿable system.

A sequential subspace method for blind identification of general FIR MIMO channels

IEEE Transactions on Signal Processing, 2005

This correspondence addresses the problem of blindly identifying multiple input multiple output (MIMO) finite impulse response (FIR) channels without the conventional assumption of identical column degrees. A subspace-based algorithm is developed that identifies the channel's columns sequentially from the lowest degree columns to the highest degree ones. Compared with the previous generalized subspace method by Gorokhov and Loubaton, the new method is simpler and more accurate.

Fast maximum likelihood for blind identification of multiple FIR channels

IEEE Transactions on Signal Processing, 1996

This paper develops a fast maximum likelihood method for estimating the impulse responses of multiple FIR channels driven by an arbitrary unknown input. The resulting method consists of two iterative steps, where each step minimizes a quadratic function. The two-step maximum likelihood (TSML) method is shown to be high-SNR efficient, i.e., attaining the CramCr-Rao lower bound (CRB) at high SNR. The TSML method exploits a novel orthogonal complement matrix of the generalized Sylvester matrix. Simulations show that the TSML method significantly outperforms the cross-relation (CR) method and the subspace (SS) method and attains the CRB over a wide range of SNR. This paper also studies a Fisher information (FI) matrix to reveal the identifiability of the M-channel system. A strong connection between the FI-based identifiability and the CR-based identifiability is established. I. INTRODUCTION LIND identification of multiple FIR channels is an im-B portant problem arising in many areas including mobile communications, multisensor signal analysis, and multisensor image restoration. Although for some applications the unknown (or inaccessible) input to the FIR channels is known to have certain statistical or/and algebraic characteristics, for some others the unknown input could be virtually arbitrary such as nonstationary, non-Gaussian, and colored. Even in mobile communications, when a fast varying channel needs to be identified within a very short period of time, any known statistical characteristics (such as whiteness) of the unknown input becomes hardly useful since a too-short data sequence cannot yield a reliable statistical average. Therefore, under certain practical conditions, the input has to be assumed to be virtually arbitrary. Note that if a system is time invariant during a period when a long enough data sequence is available and a priori statistical information about its input is reliable, then the statistics of the input should be exploited. Examples of using statistical knowledge .of the input include the second-order statistic (SOS)-based methods [3]-[5], [32] and the higher order statistics (H0S)-based methods [6]-[8]. However, this paper addresses the situation where the available data sequence is relatively short or the system is fast varying.

Structure-Based Subspace Method for Multichannel Blind System Identification

IEEE Signal Processing Letters

In this work, a novel subspace-based method for blind identification of multichannel finite impulse response (FIR) systems is presented. Here, we exploit directly the impeded Toeplitz channel structure in the signal linear model to build a quadratic form whose minimization leads to the desired channel estimation up to a scalar factor. This method can be extended to estimate any predefined linear structure, e.g. Hankel, that is usually encountered in linear systems. Simulation findings are provided to highlight the appealing advantages of the new structure-based subspace (SSS) method over the standard subspace (SS) method in certain adverse identification scenarii.

A blind multichannel identification algorithm robust to order overestimation

IEEE Transactions on Signal Processing, 2002

Active research in blind single input multiple output (SIMO) channel identification has led to a variety of second-order statistics-based algorithms, particularly the subspace (SS) and the linear prediction (LP) approaches. The SS algorithm shows good performance when the channel output is corrupted by noise and available for a finite time duration. However, its performance is subject to exact knowledge of the channel order, which is not guaranteed by current order detection techniques. On the other hand, the linear prediction algorithm is sensitive to observation noise, whereas its robustness to channel order overestimation is not always verified when the channel statistics are estimated. We propose a new second-order statistics-based blind channel identification algorithm that is truly robust to channel order overestimation, i.e., it is able to accurately estimate the channel impulse response from a finite number of noisy channel measurements when the assumed order is arbitrarily greater than the exact channel order. Another interesting feature is that the identification performance can be enhanced by increasing a certain smoothing factor. Moreover, the proposed algorithm proves to clearly outperform the LP algorithm. These facts are justified theoretically and verified through simulations.

Wireless Channel Blind Identification Using a Generic Adaptive FIR Architecture

In wireless channels there are Non-idealities that cause distortion to the mobile signal such as long distance, multipath and the noise that the channel added to the transmitted signal. This paper utilizes adaptive filtering techniques to solve this channel distortion. Consequently, an adaptive FIR blind identification architecture is developed using four adaptive algorithms to estimate wireless time invariant as well as time varying channels. The four adaptive algorithms are least mean square (LMS), normalized least square (NLMS), recursive least square (RLS) and affine projection algorithm (AFP). The results shows that the RLS outperforms other algorithm in wireless time-invariant channel with least mean square error of (0.0116), and AFA outperforms other algorithms in wireless time-variant channel with least square error of (0.433) and fastest convergence rate. The implications of this wireless channel identification architecture are feasible in detecting next-generation 5G channels and underwater acoustic channel to provide the channel information for further signal processing. Keywords: least mean square (LMS), normalized least square (NLMS), recursive least square (RLS), affine projection algorithm (AFP), finite impulse response (FIR), wireless channel, adaptive identification architecture, wireless underwater channel, 5G channel.