Senjian An

Blind identification of FIR MIMO channels by decorrelating subchannels

We study blind identification and equalization of finite impulse response (FIR) and multi-input and multi-output (MIMO) channels driven by colored signals. We first show a sufficient condition for an FIR MIMO channel to be identifiable up to a scaling and permutation using the second-order statistics of the channel output. This condition is that the channel matrix is irreducible (but not necessarily column-reduced), and the input signals are mutually uncorrelated and of distinct power spectra. We also show that this condition is necessary in the sense that no single part of the condition can be further weakened without another part being strengthened. While the above condition is a strong result that sets a fundamental limit of blind identification, there does not yet exist a working algorithm under that condition. In the second part of this paper, we show that a method called blind identification via decorrelating subchannels (BIDS) can uniquely identify an FIR MIMO channel if a) the channel matrix is nonsingular (almost everywhere) and column-wise coprime and b) the input signals are mutually uncorrelated and of sufficiently diverse power spectra. The BIDS method requires a weaker condition on the channel matrix than that required by most existing methods for the same problem.

Group decorrelation enhanced subspace method for identifying FIR MIMO channels driven by unknown uncorrelated colored sources

Identification of finite-impulse-response (FIR) and multiple-input multiple-output (MIMO) channels driven by unknown uncorrelated colored sources is a challenging problem. In this paper, a group decorrelation enhanced subspace (GDES) method is presented. The GDES method uses the idea of subspace decomposition and signal decorrelation more effectively than the joint diagonalization enhanced subspace (JDES) method previously reported in the literature. The GDES method has a much better performance than the JDES method. The correctness of the GDES method is proved assuming that 1) the channel matrix is irreducible and column reduced and 2) the source spectral matrix has distinct diagonal functions. However, the GDES method has an inherent ability to trade off between the required condition on the channel matrix and that on the source spectral matrix. Simulations show that the GDES method yields good results even when the channel matrix is not irreducible, which is not possible at all for the JDES method.

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

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 channels columns sequentially from the lowest degree columns to the highest degree ones. Compared with the previous generalized subspace method by Gorokhov and Loubaton (1997), the new method is simpler and more accurate.

Blind identification and equalization of FIR MIMO channels by BIDS

This paper presents an algorithm of blind identification and equalization of finite-impulse-response and multiple-input and multiple-output (FIR MIMO) channels driven by colored signals. This algorithm is an improved realization of a concept referred to as blind identification via decorrelating subchannels (BIDS). This BIDS algorithm first constructs a set of decorrelators which decorrelate the output signals of subchannels, and then estimates the channel matrix using the transfer functions of the decorrelators, and finally recovers the input signals using the estimated channel matrix. This BIDS algorithm in general assumes that the channel matrix is irreducible and the input signals are mutually uncorrelated and of sufficiently diverse power spectra. However, for channel matrix identification, this BIDS algorithm only requires the channel matrix to be nonsingular (ie, full rank almost everywhere as opposed to everywhere) and column-wise coprime. Such a channel matrix may have zeros and be of non-minimum phase.

Blind identification of FIR MIMO channels by group decorrelation

We present a new method for identification of FIR MIMO channels driven by unknown, uncorrelated and colored sources. This method, belonging to the BID (blind identification by decorrelation) family, makes use of the mutual uncorrelation of the unknown sources by first decorrelating the observed signals into two uncorrelated groups. The two decorrelators are then used to estimate the channel matrix (i.e., MIMO channel transfer function matrix) up to a constant matrix. This constant matrix is finally determined using a BID method for instantaneous MIMO channels. This new method, named BID-G, is shown to be much more robust than the subspace method that requires the channel matrix to be irreducible and column-reduced.

Experimental investigation of delayed instantaneous demixer for speech enhancement

This paper presents a delayed instantaneous demixer (DID) for speech signal separation from real recordings. Based on the fact that the original signals are colored and mutually uncorrelated, a simple algorithm is derived to estimate the parameters of the demixer. This algorithm consists of two parts: a grid searching method to estimate time delays and an alternating projection method to estimate gain coefficients. Experimental result demonstrates the performance of the model and the algorithm.

Blind signal separation and blind system identification of irreducible MIMO channels

This paper deals with blind system identification of FIR MIMO (finite impulse response and multi input multi output) channels driven by colored signals. Based on second order statistics, a novel technique of blind identification is developed for irreducible MIMO channels. It requires a weaker condition on the input power spectra than some existing blind system identification methods and the computation is also reduced.

Separating colorred signals distorted by convolutive channels using diagonal constrained decorrelation

We consider the problem of separating colorred signals mixed by unknown convolutive channels. We introduce a variation of a previous approach of separating signals via decorrelation. This variation minimizes the mutual correlation among the output signals of a decorrelation matrix subject to a diagonal constraint. The diagonal constraint ensures a better quality of separation. The diagonal constraint is shown to be essential when the number of original signals is less than the number of distorted signals

Robust stability of polynomials with nonlinear dependent coefficient perturbations

The robust stability of polynomial functions of interval polynomials, which is called nested polynomial families, has been investigated by Kharitonov (1996) and it can be guaranteed by checking only fixed four vertices. This paper deals with the robust stability analysis of polynomials with nonlinear uncertainty structure. For a special class of polynomial family with nonlinear dependent coefficient perturbations, some new extreme point results are obtained. We investigate the extremality properties of the inner frequency response (IFR) set associated with uncertain Hurwitz polynomials and the relationship between the stability problem of nested polynomial families and the properties of IFR set is established.

Convex directions for nested Hurwitz polynomials

A nested polynomial family is a polynomial function of a standard polynomial family. Such families arise in stability analysis of uncertain uniform systems. This paper considers the convex direction for nested Hurwitz polynomial families. A necessary and sufficient condition is obtained for a polynomial to be such a convex direction. This condition is on the phase growth rate of the difference polynomial, and it constitutes a generalization of Rantzers phase-growth condition for convex directions of real Hurwitz polynomials.