Interference Alignment and a Noisy Interference Regime for Many-to-One Interference Channels

We study the capacity of discrete memoryless many-to-one interference channels, i.e., K user interference channels where only one receiver faces interference. For a class of many-to-one interference channels, we identify a noisy interference regime, i.e., a regime where random coding and treating interference as noise achieves sum-capacity. Specializing our results to the Gaussian MIMO many-to-one interference channel, which is a special case of the class of channels considered, we obtain new capacity results. Firstly, while previous results characterized noisy interference regimes for many-to-one interference channels with inputs having average power constraints, we show that this remains valid for a more general class of inputs. This more general class of inputs includes the practical scenario of the inputs being restricted to fixed finite-size constellations such as PSK or QAM. Secondly, we extend noisy interference results previously studied in interference channels with single antenna nodes at all transmitters, to MIMO and parallel many-to-one interference channels. Finally, while previous results considered the Gaussian interference channel with full channel state information (CSI) at all nodes, we provide a noisy interference regime for fading Gaussian many-to-one interference channels without CSI at the transmitters. While the many-to-one interference channel requires interference alignment, which in turn requires structured codes in general, we argue that in the noisy interference regime, interference is implicitly aligned by random coding irrespective of the input distribution. As a byproduct of our study, we identify a second class of many-to-one interference channels (albeit deterministic) where random coding is optimal (though interference is not treated as noise). We attribute the optimality of random coding in this second class of channels to the resolvability of the multiple interferers at the receiver which precludes the possibility of interference alignment and hence obviates the need of structured codes.