  Recent investigations have shown sum capacity results within a constant
bit-gap for several channel models, e.g. the two-user Gaussian interference
channel (G-IC), k-user G-IC or the Gaussian X-channel. This has motivated
investigations of interference-limited multi-user channels, for example, the
Gaussian interfering multiple access channel (G-IMAC). Networks with
interference usually require the use of interference alignment (IA) as a
technique to achieve the upper bounds of a network. A promising approach in
view of constant-gap capacity results is a special form of IA called
signal-scale alignment, which works for time-invariant, frequency-flat,
single-antenna networks. However, until now, results were limited to the
many-to-one interference channel and the Gaussian X-channel. To make progress
on this front, we investigate signal-scale IA schemes for the G-IMAC and aim to
show a constant-gap capacity result for the G-IMAC. We derive a constant-gap
sum capacity approximation for the lower triangular deterministic (LTD)-IMAC
and see that the LTD model can overcome difficulties of the linear
deterministic model. We show that the schemes can be translated to the Gaussian
IMAC and that they achieve capacity within a constant gap. We show that
multi-user gain is possible in the whole regime and provide a new look at
cellular interference channels.
