A Quasi-Symmetric Model for the Two-Way MIMO Communication Channel

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 symmetric scalar product, respectively.