On Linear Channel - based Noise Subspace Parameterizations for Blind Multichannel Identi cation

| In a multichannel context, the problem of blind estimation of the channel can be parameterized either by the channel impulse response or by the noisefree multivariate prediction error lter and the rst vector coe cient 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. In the rst part of this paper, we begin with the resaons due to which secondorder-statistics-based estimation techniques give accurate channel estimates. In the second part, we focus on the di erent 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 speci c parameterization, which is minimal in terms of the number of rows, leads to span the overall noise subspace.