Weighted sum-rate maximization using weighted MMSE for MIMO-BC beamforming design

Abstract

This paper studies linear transmit filter design for Weighted Sum-Rate (WSR) maximization in the Multiple Input Multiple Output Broadcast Channel (MIMO-BC). The problem of finding the optimal transmit filter is non-convex and intractable to solve using low complexity methods. Motivated by recent results highlighting the relationship between mutual information and Minimum Mean Square Error (MMSE), this paper establishes a relationship between weighted sum-rate and weighted MMSE in the MIMO-BC. The relationship is used to propose a low complexity algorithm for finding a local weighted sum-rate optimum based on alternating optimization. Numerical results studying sum-rate show that the proposed algorithm achieves high performance with few iterations.

MIMO broadcast channels with Gaussian CSIT and application to location based CSIT

“…This leads to the same Lagrange multiplier expression obtained in [7] on the basis of a heuristic that was introduced in [12] as was pointed out in [13].…”

“…The W SR(g) is a non-convex and complicated function of g. Inspired by [7], we introduced in [8], [9] an augmented cost function, the Weighted Sum MSE, W SM SE(g, f , w)…”

Sum-rate maximization in the multicell MIMO broadcast channel with interference coordination

“…Specifically, an iterative algorithm was proposed in [3] to solve the Karush-KuhnTucker conditions of the non-convex WSR maximization problem. Another solution approach to the nonconvex WSR maximization problem is to transform it into a minimization of the weighted mean squared error (WMMSE) problem [4], [10], [11]. The WMMSE problem then can be solved by iteratively optimizing the weight matrices, the MMSE precoders, and the MMSE decoders [10].…”

“…Another solution approach to the nonconvex WSR maximization problem is to transform it into a minimization of the weighted mean squared error (WMMSE) problem [4], [10], [11]. The WMMSE problem then can be solved by iteratively optimizing the weight matrices, the MMSE precoders, and the MMSE decoders [10]. Thus, by establishing the equivalence between the WSR maximization problem and the WMMSE minimization problem, a locally optimal solution to the former can be found from the solution of the latter.…”

“…In this section, we examine the second approach to solve this nonconvex problem by transforming it into a matrix-weighted sum-MSE minimization problem. Following the approach proposed in [4], [10], we develop a WMMSE-based algorithm for the multicell MIMO-BC with DPC. The newly developed algorithm will be referred to as the DPC-WMMSE algorithm, in order to avoid the confusion with the original WMMSE algorithm for the case of linear precoding in [4].…”