  We consider a multi-user multiple-input single-output downlink system that
provides each user with a prespecified level of quality-of-service. The base
station (BS) designs the beamformers so that each user receives a certain
signal-to-interference-and-noise ratio (SINR). In contrast to most of the
available literature in the beamforming field, we focus on the required
modifications when the system changes. We specifically study three cases: (i)
user entering the system, (ii) user leaving the system, and (iii) a change in
the SINR target. We do so in order to avoid designing the entire system from
scratch for every change in the requirements. In each of the three cases, we
describe the modifications required to the beamforming directions and the power
loading. We consider maximum ratio transmission (MRT), zero-forcing (ZF) and
the optimal beamformers. The proposed modifications provide performance that is
either exact or very close to that obtained when we redesign the entire system,
while having much lower computational cost.
