Optimal BeamFormers (BFs) that maximize the Weighted Sum Rate
(WSR) for a Multiple-Input Multiple-Output (MIMO) interference
broadcast channel (IBC) remains an important research area. Under
practical scenarios, the problem is compounded by the fact that only
partial channel state information at the transmitter (CSIT) is available.
Hence, a typical choice of the optimization metric is the Expected
Weighted Sum Rate (EWSR). However, the presence of the
expectation operator makes the optimization a daunting task. On the
other hand, for the particular, but significant, special case of massive
MIMO (MaMIMO), the EWSR converges to Expected Signal covariance
Expected Interference covariance based WSR (ESEI-WSR)
and this metric is more amenable to optimization. Recently, [1] considered
a multi-user Multiple-Input Single-Output (MISO) scenario
and proposed approximating the EWSR by ESEI-WSR. They then
derived a constant bound for this approximation. This paper performs
a refined analysis of the gap between EWSR and ESEI-WSR
criteria for finite antenna dimensions.