  In this paper, system design for the multi-input multi-output (MIMO) relay
broadcast channel with individual signal-to-interference-plus-noise ratio
(SINR) constraints at the mobile stations (MS) is considered. By exploring the
structure of downlink (DL) uplink (UL) duality at either the base station (BS)
or the relay station (RS), we propose two schemes of joint power allocation and
beamforming design at the BS and the RS. The problem of existence of feasible
solutions under practical power constraints at the BS and the RS with given
SINR targets is considered first. Then the problem of sum power minimization is
considered. Each design problem can be solved efficiently using optimal joint
power allocation and beamforming under the framework of convex optimization. We
also show that with subchannel pairing at the RS, the transmission power can be
reduced by channel compensation at either hop. Finally, an extension to more
general multi-hop applications is provided to further improve the power
efficiency.
