On linear channel-based noise subspace parameterizations for blind multichannel identification

In a multichannel context, the problem of blind estimation of the channel can be parameterized either by the channel impulse response or by the noise-free multivariate prediction error filter and the first vector coefficient of the vector channel. The noise subspace, spanned by a set of vectors that are orthogonal to the signal subspace, can be parameterized according to different linear parameterizations. We begin with the reasons due to which second-order-statistics-based estimation techniques give accurate channel estimates. We focus on the different noise subspace parameterizations in terms of blocking equalizers and classify them. We present linear (in terms of subchannel impulse responses) noise subspace parameterizations and we prove that using a specific parameterization, which is minimal in terms of the number of rows, leads to span the overall noise subspace.