  In general, the zero-forcing (ZF) precoding suffers from a severe receive
signal-to-noise ratio (SNR) degradation in the high interference regime.
However, recent evidences from realistic measurements demonstrated that
millimeter wave (mmWave) systems are mainly noise-limited as high gain antennas
behave as spatial filters to the interference signal. This makes ZF precoding
equally attractive as that of other linear precoding counterparts. Considering
ZF precoding, this paper aims to derive a lower bound on the sum-rate achieved
by a decremental beam selection (BS) algorithm in a beamspace MIMO (B-MIMO)
system operating at mmWave frequencies. This bound relates Frobenious norms of
precoding matrices of full and reduced dimensional (i.e. after BS) B-MIMO
systems through a deterministic square-hyperbolic function. Note that, both ZF
precoding and decremental BS are not new concepts. However, the derived
sum-rate bound provides a new insight to the topic. Given a particular full
dimensional B-MIMO channel, the presented bound can be used to understand
limits of BS algorithms.
