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.
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