Channel inversion and regularization revisited

In multiuser multiple-input-single-output (MISO) downlink, linear precoders like channel inversion (CI) and regularized CI (RCI) are more desirable than their nonlinear counterparts due to their reduced complexity. To achieve the full benefits of linear precoding, the availability of perfect channel state information (CSI) at base stations (BSs) is necessary. Since in practice, having access to perfect CSI is not pragmatic, in this paper, we evaluate the performance of CI and RCI under a generalized, imperfect CSI model where the variance of the channel estimation error depends on the signal-to-noise ratio (SNR) and thus covers digital and analog feedbacks as two special cases. Then, based on this imperfect CSI model, we quantify the asymptotic mean loss in sum rate and the achievable degrees of freedom (DoFs) by deriving the received signal-to-interference-plus-noise ratio (SINR) of each user. For example, it is shown that the achievable DoF is directly related to the SNR exponent of the channel estimation error variance. Also, two asymptotic gaps to capacity for the analog feedback are derived: mean loss in sum rate and power loss. In addition, we propose an adaptive RCI technique by deriving an appropriate regularization parameter as a function of the error variance and without imposing any restrictions on the number of users or antennas. It is shown that in the presence of CSI mismatch, while the comparative improvement of the standard RCI to CI becomes negligible, the adaptive RCI compensates this degraded performance of the standard RCI without introducing any extra computational complexity.