 
Summary: 1
Minimizing SumMSE Implies Identical Downlink
and Dual Uplink Power Allocations
Adam J. Tenenbaum, Student Member, IEEE, and Raviraj S. Adve, Senior Member, IEEE
AbstractMinimizing the sum of mean squared errors using
linear transceivers under a sum power constraint in the multiuser
downlink is a nonconvex problem. Existing algorithms exploit
an uplinkdownlink duality and transform the solution of a
convex problem in the virtual uplink back to the downlink.
In this letter, we analyze the optimality criteria for the power
allocation subproblem in the virtual uplink, and demonstrate
that the optimal solution leads to identical power allocations
in the downlink and virtual uplink, thus extending the known
duality results and permitting a reduction in the computational
complexity of existing algorithms.
Index TermsMIMO systems, optimization methods, least
mean square methods
I. INTRODUCTION
MINIMIZATION of the sum of mean squared errors
(sumMSE) under a sum power constraint using linear
