  Part I of this two-part paper focused on the formulation of percentile
problems, complexity analysis, and development of power control algorithms via
the quadratic fractional transform (QFT) and logarithmic fractional transform
(LFT) for sum-least-qth-percentile (SLqP) rate maximization problems. In this
second part, we first tackle the significantly more challenging problems of
optimizing SLqP rate via beamforming in a multiuser, multiple-input
multiple-output (MU- MIMO) network to maximize cell-edge throughput. To this
end, we first propose an adaptation of the QFT algorithm presented in Part I
that enables optimization of the complex-valued multidimensional beamforming
weights for the SLqP rate utility function. We also introduce a new class of
problems which we term as sum-greatest-qth-percentile weighted mean squared
error (SGqP-WMSE) minimization. We show that this class subsumes the well-known
sum-weighted mean squared error (WMMSE) minimization and max-WMSE minimization
problems. We demonstrate an equivalence between this class of problems and the
SLqP rate maximization problems, and show that this correspondence can be
exploited to obtain stationary-point solutions for the aforementioned
beamforming problem. Next, we develop extensions for the QFT and LFT algorithms
from Part I to optimize ergodic long-term average or ergodic SLqP utility.
Finally, we also consider related problems which can be solved using the
proposed techniques, including hybrid utility functions targeting optimization
at specific subsets of users within cellular networks.
