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In the multiuser downlink, power allocation for linear precoders thatminimize the sum of mean squared errors under a sum power constraint is anon-convex problem. Many existing algorithms solve an equivalent convex problemin the virtual uplink and apply a transformation based on uplink-downlinkduality to find a downlink solution. In this letter, we analyze the optimalitycriteria for the power allocation subproblem in the virtual uplink, anddemonstrate that the optimal solution leads to identical power allocations inthe downlink and virtual uplink. We thus extend the known duality results and,importantly, simplify the existing algorithms used for iterative transceiverdesign.

Minimizing Sum-MSE Implies Identical Downlink and Dual Uplink Power Allocations