A Quasi-Symmetric Model for
the Two-Way MIMO Communication Channel
June 2007
Lang P. Withers, Jr., The MITRE Corporation
ABSTRACT
It is well-known that the wireless MIMO fading channel at
any moment in time and at any frequency is not exactly reciprocal
or symmetric. This raises the question of how the forward
and reverse channel response matrices are related. Clearly
we do not want to forfeit all symmetry and merely consider
them as two independent instances of a stochastic fading
model. Here a more general relation, called quasi-symmetry,
is proposed to relate the incoming and outgoing channel response
matrices. We also find that quasi-symmetry is equivalent
to simple relations between the complex symmetric singular
value decompositions (SVDs) of the two channel matrices.
Appropriate background is included on the two kinds of
complex linear algebra that originate from the usual conjugate-symmetric
scalar product, and the transpose-symmetric scalar
product, respectively.
Additional Search Keywords
MIMO wireless channel, reciprocity, quasi-symmetry, complex symmetric
matrices
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