  Stream fairness, fairness between all streams in the system, is a more
restrictive condition than sub-stream fairness, fairness between all streams of
each user. Thus sub-stream fairness alleviates utility loss as well as
complexity and overhead compared to stream fairness. Moreover, depending on
algorithmic parameters, conventional algorithms including distributed
interference alignment (DIA) may not provide sub-stream fairness, and generate
sub-streams with poor signal-to-interference plus noise ratios (SINRs), thus
with poor bit error rates (BERs). To this end, we propose a distributed power
control algorithm to render sub-stream fairness in the system, and establish
initiatory connections between sub-stream SINRs, BERs, and rates. Algorithms
have particular responses to parameters. In the paper, important algorithmic
parameters are analyzed to exhibit numerical correctness in benchmarking. The
distinction between separate filtering schemes that design each stream of a
user separately and group filtering schemes that jointly design the streams of
a user is also underscored in the paper. Finally, the power control law used in
the proposed algorithm is proven to linearly converge to a unique fixed-point,
and the algorithm is shown to achieve feasible SINR targets.
