Spectral efficiency evaluation of generalized selection combiners (GSC) over slow fading with estimation errors

In this paper we derive closed-form expressions for the single-user capacity of generalized selection combiners (GSC) system, taking into account the effect of imperfect channel estimation at the receiver. The channel considered is a slowly varying spatially independent flat Rayleigh fading channel. The complex channel estimate and the actual channel are modelled as jointly Gaussian random variables with a correlation that depends on the estimation quality. Two adaptive transmission schemes are analyzed: 1) optimal power and rate adaptation; and 2) constant power with optimal rate adaptation, including derivation of an upper bound and asymptotically tight approximations at high and low SNR regions. Our numerical results show the effect of Gaussian channel estimation error on the achievable spectral efficiency.