Spectral efficiency of maximum ratio combining (MRC) over slow fading with estimation errors

In this paper, we derive closed-form expressions for capacity statistics of the maximal ratio combining (MRC) system, taking into account the effect of imperfect channel estimation at the receiver. The channel considered is a slowly varying flat Rayleigh fading that is also spatially independent. The combiner weights are assumed to be affected by Gaussian errors at the receiver. In particular, we derive the moment generating function (MGF), complementary cumulative distribution function (CDF) and the probability density function (PDF) of the capacity. Furthermore, we derive closed-form expressions for the system capacity when employing different adaptive transmission schemes such as (1) optimal power and rate adaptation (opra); (2) constant power with optimal rate adaptation (ora); and (3) channel inversion with fixed rate (cifr). Analytical results show accurately the impact of the channel estimation error on the achievable spectral efficiency.