  Millimeter wave (mmW) wireless networks are capable to support multi-gigabit
data rates, by using directional communications with narrow beams. However,
existing mmW communications standards are hindered by two problems: deafness
and single link scheduling. The deafness problem, that is, a misalignment
between transmitter and receiver beams, demands a time consuming beam-searching
operation, which leads to an alignment-throughput tradeoff. Moreover, the
existing mmW standards schedule a single link in each time slot and hence do
not fully exploit the potential of mmW communications, where directional
communications allow multiple concurrent transmissions. These two problems are
addressed in this paper, where a joint beamwidth selection and power allocation
problem is formulated by an optimization problem for short range mmW networks
with the objective of maximizing effective network throughput. This
optimization problem allows establishing the fundamental alignment-throughput
tradeoff, however it is computationally complex and requires exact knowledge of
network topology, which may not be available in practice. Therefore, two
standard-compliant approximation solution algorithms are developed, which rely
on underestimation and overestimation of interference. The first one exploits
directionality to maximize the reuse of available spectrum and thereby
increases the network throughput, while imposing almost no computational
complexity. The second one is a more conservative approach that protects all
active links from harmful interference, yet enhances the network throughput by
100% compared to the existing standards. Extensive performance analysis
provides useful insights on the directionality level and the number of
concurrent transmissions that should be pursued. Interestingly, extremely
narrow beams are in general not optimal.
