Despite the simplicity of the scheme of treating interference as noise (TIN), it was shown to be sum-capacity optimal in the Gaussian interference channel (IC) with very-weak (noisy) interference. In this paper, the 2-user IC is altered by introducing an additional transmitter that wants to communicate with one of the receivers of the IC.The resulting network thus consists of a point-to-point channel interfering with a multiple access channel (MAC) and is denoted PIMAC. The sum-capacity of the PIMAC is studied with main focus on the optimality of TIN. It turns out that TIN in its naive variant, where all transmitters are active and both receivers use TIN for decoding, is not the best choice for the PIMAC. In fact, a scheme that combines both time division multiple access and TIN (TDMA-TIN) strictly outperforms the naive-TIN scheme. Furthermore, it is shown that in some regimes, TDMA-TIN achieves the sum-capacity for the deterministic PIMAC and the sum-capacity within a constant gap for the Gaussian PIMAC. Additionally, it is shown that, even for very-weak interference, there are some regimes where a combination of interference alignment with power control and treating interference as noise at the receiver side outperforms TDMA-TIN. As a consequence, on the one hand treating interference as noise in a cellular uplink is approximately optimal in certain regimes. On the other hand those regimes cannot be simply described by the strength of interference.
I. INTRODUCTIONCommunicating nodes in most communication systems existing nowadays have several practical constraints.One such constraint is the limited computational capability of the communicating nodes. This limitation demands communication schemes which do not have a high complexity, and consequently, power consumption. However, communication over networks where concurrent transmissions take place (interference networks) challenges the transmitters and the receivers with additional complexity, namely, the complexity of interference management.This paper is a revised and extended version of the Intern. ITG Workshop on Smart Antennas (WSA) paper [1] in March, 2012.