  In this paper, we show that the signal-to-interference-plus-noise ratio
(SINR) at a base station (BS) equipped with an arbitrary physical array antenna
can be expressed as a function of two fundamental figures-of-merit (FoMs): (I)
the instantaneous effective gain (IEG), and (II) the beamforming-channel
correlation (BCC). These two FoMs are functions of the array antenna layout,
the antenna elements, the propagation channel and the applied signal processing
algorithms, and hence they are random variables (RVs) in general. We illustrate
that both FoMs provide essential insights for quality-of-service (QoS)-based
phased array design by investigating their statistics for BSs applying
full-digital (FD) zero forcing (ZF) beamforming. We evaluate various array
designs and show that arrays with higher IEGs and a reduced probability of low
BCCs can increase the ergodic sum rate and reduce the need for scheduling.
