Imperfect CSI based two-way AF MIMO relaying of OSTBC

We consider the two-way relaying of orthogonal space time block codes (OSTBCs) with imperfect channel information. We derive a maximum likelihood (ML) decoder of OSTBC, by assuming perfect channel knowledge at both user nodes. The decoding of OSTBC data at a user terminal is performed by replacing the exact channel state information (CSI) by the estimated CSI, in the ML metric. An approximate closed-form expression for the moment generating function (m.g.f.) of the received signal-to-noise ratio at a user is derived. By using the m.g.f. expression, the analytical average error performance of the scheme is obtained for M-ary phase shift keying constellation. The diversity order of the considered scheme is analytically calculated, for certain system configurations. It is deduced by the simulations and analysis that the channel estimation does not affect the diversity order of the two-way amplify-and-forward multiple-input multiple-output relay system.