Asymptotic performance analysis of channel inversion under CSI imperfections

In multiantenna downlink, linear precoders like channel inversion (CI) are more desirable than their nonlinear counterparts due to their reduced complexity. However, to harness the full capabilities of multiuser multiantenna downlink, the availability of perfect channel state information (CSI) at base station (BS) is mandatory. Since from the practical point of view, this is an optimistic assumption, in this paper, we evaluate the asymptotic performance of CI under a generalized CSI mismatch model where the variance of the channel estimation error depends on the signal-to-noise ratio (SNR). In this case, we quantify novel bounds regarding the asymptotic mean loss in sum rate and achievable degrees of freedom (DoF) by deriving the received signal-to-interference-plus-noise ratio (SINR) of each user. It is shown that, for example, the achievable DoF is directly related to the SNR exponent of the channel estimation error variance. In other words, if the intention is to keep the asymptotic mean loss in sum rate bounded, the variance of the channel estimation error must at least scale with the inverse of SNR. Also an asymptotic gap to capacity for analog feedback is derived.