Many common adaptive beamforming methods are based on a sample matrix inversion (SMI). The schemes can be applied in two ways. The sample covariance matrices are either computed over preambles, or the sample basis for the SMI and the target of the beamforming are identical. A vector space representation provides insight into the classic SMI-based beamforming variants, and enables elegant derivations of the well-known second-order statistical properties of the output signals. Moreover, the vector space representation is helpful in the definition of appropriate interfaces between beamfoming and soft-decision signal decoding in receivers aiming at adaptive cochannel interference mitigation. It turns out that the performance of standard receivers incorporating SMI-based beamforming on short signal intervals and decoding of BICM (bit-interleaved coded modulation) signals can be significantly improved by proper interface design.
Multidimensional Vector Space Representation for Convergent Evolution and Molecular Phylogeny
