Optimum beamforming for MIMO multicasting

Baisheng Du,Xuchu Dai,Xiaodong Xu,Yi Jiang

doi:10.1186/1687-6180-2013-121

Abstract

This paper investigates the transmit (Tx) beamforming design to maximize the throughput of a multiple-input multiple-output multicast channel, where common information is sent from the base station to K users simultaneously. This so-called max-min fair beamforming problem is known to be NP-hard. When the base station is equipped with two Tx antennas, we prove that the original complex-valued beamforming problem can be transformed into a real-valued problem and the globally optimal solution can be found by exhausting at most hypothesis tests. Moreover, a prune and search algorithm (PASA) is proposed for searching the optimal beamformer with computational complexity in the worst case. When the base station has more than two Tx antennas, we develop an efficient algorithm named iterative two-dimensional optimization which converts the original beamforming problem into a series of two-antenna subproblems by iterations and hence, the beamformer is improved using PASA iteratively. Simulations results are presented to demonstrate the superior performance of the proposed algorithms.

Highlights

In the generation of wireless networks, spectrally efficient multicasting techniques are required to support applications such as web TV, online gaming, and software updates, where common messages are sent to a group of users simultaneously
The main contributions of this paper are listed below: (1) For the case that the base station (BS) has two Tx antennas, we derive that the feasible set of the signal-to-noise ratio (SNR) vector of all users is a two-dimensional ellipsoid in K -dimensional Euclidean space, where K is the number of users
We prove that the original complex-valued optimization problem can be simplified as a real-valued problem and the optimal beamforming vector can be found by exhausting CK1 + CK2 + CK3 hypothesis tests of the bottleneck users, which are defined as the users with the lowest SNR

Summary

Introduction

In the generation of wireless networks, spectrally efficient multicasting techniques are required to support applications such as web TV, online gaming, and software updates, where common messages are sent to a group of users simultaneously. For the max-min fair beamforming problem, to the best of our knowledge, previous methods are not guaranteed to obtain the globally optimal beamforming vector when the base station serves arbitrary number of users. (1) For the case that the BS has two Tx antennas, we derive that the feasible set of the SNR vector of all users is a two-dimensional ellipsoid in K -dimensional Euclidean space, where K is the number of users With this geometrical property, we prove that the original complex-valued optimization problem can be simplified as a real-valued problem and the optimal beamforming vector can be found by exhausting CK1 + CK2 + CK3 hypothesis tests of the bottleneck users, which are defined as the users with the lowest SNR. In represents an n × n identity matrix and 1n is an all-one column vector with length n, while 0n is an all-zero column vector with length n

System model and problem statement

Prune and search algorithm

The I2DO algorithm

Implementation complexity of I2DO

Conclusions