Abstract:
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In numerical linear algebra, students encounter early
the iterative power method, which finds eigenvectors of a matrix
from an arbitrary starting point through repeated normalization
and multiplications by the matrix itself. In practice, more sophisticated
methods are used nowadays, threatening to make the power
method a historical and pedagogic footnote. However, in the context
of communication over a time-division duplex (TDD) multipleinput
multiple-output (MIMO) channel, the power method takes a
special position. It can be viewed as an intrinsic part of the uplink
and downlink communication switching, enabling estimation
of the eigenmodes of the channel without extra overhead. Generalizing
the method to vector subspaces, communication in the
subspaces with the best receive and transmit signal-to-noise ratio
(SNR) is made possible. In exploring this intrinsic subspace convergence
(ISC), we show that several published and new schemes can
be cast into a common framework where all members benefit from
the ISC. |