The Capacity Region of the Wireless Ergodic Fading Interference Channel with Partial CSIT to Within One Bit

Fundamental capacity limits are studied for the two-user wireless ergodic fading IC with partial Channel State Information at the Transmitters (CSIT) where each transmitter is equipped with an arbitrary deterministic function of the channel state (this model yields a full control over how much state information is available). One of the main challenges in the analysis of fading networks, specifically multi-receiver networks including fading ICs, is to obtain efficient capacity outer bounds. In this paper, a novel capacity outer bound is established for the two-user ergodic fading IC. For this purpose, by a subtle combination of broadcast channel techniques (i.e., manipulating mutual information functions composed of vector random variables by Csiszar-Korner identity) and genie-aided techniques, first a single-letter outer bound characterized by mutual information functions including some auxiliary random variables is derived. Then, by novel arguments the derived bound is optimized over its auxiliaries only using the entropy power inequality. Besides being well-described, our outer bound is efficient from several aspects. Specifically, it is optimal for the fading IC with uniformly strong interference. Also, it is sum-rate optimal for the channel with uniformly mixed interference. More importantly, it is proved that when each transmitter has access to any amount of CSIT that includes the interference to noise ratio of its non-corresponding receiver, the outer bound differs by no more than one bit from the achievable rate region given by Han-Kobayashi scheme. This result is viewed as a natural generalization of the ETW to within one bit capacity result for the static channel to the wireless ergodic fading case.