Offset-Based Beamforming: A New Approach to Robust Downlink Transmission
Abstract
The design of a set of beamformers for the multiuser multiple-input
single-output (MISO) downlink that provides the receivers with prespecified
levels of quality-of-service (QoS) can be quite challenging when the channel
state information is not perfectly known at the base station. The constraint of
having the SINR meet or exceed a given threshold with high probability is
intractable in general, which results in problems that are fundamentally hard
to solve. In this paper, we will develop a high quality approximation of the
SINR outage constraint that, along with a semidefinite relaxation, enables us
to formulate the beamformer design problem as a convex optimization problem
that can be efficiently solved. For systems in which the uncertainty size is
small, a further approximation yields algorithms based on iterative evaluations
of closed-form expressions that have substantially lower computational cost.
Since finding the beamforming directions incurs most of the computational load
of these algorithms, analogous power loading algorithms for predefined
beamforming directions are developed and their performance is shown to be close
to optimal. When the system contains a large number of antennas, the proposed
power loading can be obtained at a computational cost that grows only linearly
in the number of antennas. The proposed power loading algorithm provides an
explicit relationship between the outage probability required and the power
consumed, which allows us to precisely control the power consumption, and
automatically identifies users who are consuming most of the power resources.
The flexibility of the proposed approach is illustrated by developing a power
loading technique that minimizes an average notion of outage.