Pseudo-Inverse vs Generalized Inverse for C-RAN Downlink Precoding

This paper tackles the problem of zero-forcing (ZF) precoding for the downlink of centralized radio-access networks operating in a cell-free fashion. While the customary workhorse of ZF precoding is the channel pseudo-inverse, because of the separate power constraint at each participating access point, the pseudo-inverse is not optimum. Rather, it can be improved upon by other inverses that allow conveying stronger signals (or, equivalently, consuming less power) while respecting the same ZF conditions. Motivated by the enormous disparity in computational cost between simple pseudo-inversion and general inversion, we ascertain the performance disadvantage of the former in a wide range of conditions. The welcome conclusion is that pseudo-inversion is close-to-optimum for all operational regimes of interest.