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Second order blind equalization: the band limited case

Most of the second order based fractionally sampled blind equalizers are known to perform poorly in the context of band-limited signals. In this paper, we analyse the behaviour of the subspace method in the particular context of band-limited signals. As it is well known, the subspace channel estimate is obtained as the eigenvector associated to the eigenvalue 0 of a certain positive quadratic form Q. We show that apart from 0, Q has quite small eigenvalues, and that this induces poor statistical performance. More importantly, we characterize the numerical kernel of Q, and show that it contains vectors constructed from certain spheroidal wave sequences. From this, we deduce that the subspace method does not allow to estimate accurately the transfer function of the channel on a certain frequency interval.