  Signal-to-interference plus noise ratio (SINR) and rate fairness in a system
are substantial quality-of-service (QoS) metrics. The acclaimed SINR
maximization (max-SINR) algorithm does not achieve fairness between user's
streams, i.e., sub-stream fairness is not achieved. To this end, we propose a
distributed power control algorithm to render sub-stream fairness in the
system. Sub-stream fairness is a less restrictive design metric than stream
fairness (i.e., fairness between all streams) thus sum-rate degradation is
milder. Algorithmic parameters can significantly differentiate the results of
numerical algorithms. A complete picture for comparison of algorithms can only
be depicted by varying these parameters. For example, a predetermined iteration
number or a negligible increment in the sum-rate can be the stopping criteria
of an algorithm. While the distributed interference alignment (DIA) can
reasonably achieve sub-stream fairness for the later, the imbalance between
sub-streams increases as the preset iteration number decreases. Thus comparison
of max-SINR and DIA with a low preset iteration number can only depict a part
of the picture. We analyze such important parameters and their effects on SINR
and rate metrics to exhibit numerical correctness in executing the benchmarks.
Finally, we propose group filtering schemes that jointly design the streams of
a user in contrast to max-SINR scheme that designs each stream of a user
separately.
