Philippe Loubaton

A subspace algorithm for certain blind identification problems

The problem of blind identification of p-inputs/q-outputs FIR transfer functions is addressed. Existing subspace identification methods derived for p=1 are first reformulated. In particular, the links between the noise subspace of a certain covariance matrix of the output signals (on which subspace methods build on) and certain rational subspaces associated with the transfer function to be identified are elucidated. Based on these relations, we study the behavior of the subspace method in the case where the order of the transfer function is overestimated. Next, an asymptotic performance analysis of this estimation method is carried out. Consistency and asymptotical normality of the estimates is established. A closed-form expression for the asymptotic covariance of the estimates is given. Numerical simulations and investigations are presented to demonstrate the potential of the subspace method. Finally, we take advantage of our new reformulation to discuss the extension of the subspace method to the case p>1. We show where the difficulties lie, and we briefly indicate how to solve the corresponding problems. The possible connections with classical approaches for MA model estimations are also outlined.

Deterministic equivalents for certain functionals of large random matrices.

Consider a

Subspace-based techniques for blind separation of convolutive mixtures with temporally correlated sources

N\times n

On subspace methods for blind identification of single-input multiple-output FIR systems

random matrix

On the Capacity Achieving Covariance Matrix for Rician MIMO Channels: An Asymptotic Approach

Y_n

Blind identification of MIMO-FIR systems: a generalized linear prediction approach

where the entries are independent but not identically distributed (matrices with a variance profile) Consider now a deterministic

Separation of a class of convolutive mixtures: a contrast function approach

N\times n

Improved Subspace Estimation for Multivariate Observations of High Dimension: The Deterministic Signals Case

matrix

A CLT FOR INFORMATION-THEORETIC STATISTICS OF GRAM RANDOM MATRICES WITH A GIVEN VARIANCE PROFILE

A_n

Performance analysis of blind carrier frequency offset estimators for noncircular transmissions through frequency-selective channels

whose columns and rows are uniformly bounded for the Euclidean norm. Let