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

TL;DR

This paper shows that minimizing sum-MSE in multiuser downlink leads to identical power allocations in downlink and virtual uplink, simplifying the design of transceiver algorithms.

Contribution

It extends uplink-downlink duality results by proving optimality conditions that ensure identical power allocations, simplifying existing iterative transceiver algorithms.

Findings

Optimal virtual uplink power allocation implies identical downlink power allocation.

Simplifies iterative transceiver design algorithms.

Extends duality theory for multiuser MIMO systems.

Abstract

In the multiuser downlink, power allocation for linear precoders that minimize the sum of mean squared errors under a sum power constraint is a non-convex problem. Many existing algorithms solve an equivalent convex problem in the virtual uplink and apply a transformation based on uplink-downlink duality to find a downlink solution. 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. We thus extend the known duality results and, importantly, simplify the existing algorithms used for iterative transceiver design.