On the effects of Gaussian channel estimation errors on the capacity of adaptive transmission with space-time block coding

In this paper, we derive general closed-form expressions for the Shannon capacity achieved by orthogonal space-time block coding (STBC) over Rayleigh fading channels under adaptive transmission and channel estimation errors. Adaptive transmission can be performed on a frame-by-frame basis provided that a channel state information (CSI), consisting of the SNR level as estimated by the receiver, is fed back to the transmitter, thereby allowing for different compromises between the achievable capacity and the corresponding implementation complexity. The closed-form capacity formulae, derived for different power and rate allocation policies, are expressed in terms of the number of transmit and receive antennas, the code-rate of the STBC mapping, the average SNR per receive antenna, and a single parameter capturing Gaussian channel estimation errors. Numerical results showing the effects of the estimation errors on the capacity of STBC subject to the adaptive transmission policies under consideration are provided.