UC Irvine

Generalized degrees of freedom (GDoF) analysis of wireless networks has contributed significantly to recent advances in the fundamental understanding of their capacity. A variety of schemes have been developed that are GDoF-optimal under the assumption that the Channel State Information at Transmitter(s) (CSIT) is perfect. However, these schemes become fragile in practice because channel uncertainty is unavoidable. Motivated by the need to understand the robust information-theoretic limits of wireless networks, we explore three settings under the assumption that the CSIT is limited to finite precision, and present their GDoF characterization.First, the optimality of Treating Interference as Noise (TIN) for K-user Interference Channel under finite precision CSIT is investigated. TIN is found to be GDoF optimal by Geng et al. in a parameter regime called the "TIN regime" under perfect CSIT. Our result shows that TIN is GDoF optimal in a much larger regime, called the CTIN regime, under finite precision CSIT. Next, the GDoF of the two-user interference channel are characterized for all parameter regimes under finite precision CSIT, when a limited amount of (half-duplex or full-duplex) cooperation is allowed between the transmitters. In all cases, the number of over-the-air bits that each cooperation bit buys is shown to be equal to either 0, 1, 1/2 or 1/3. The most interesting aspect of the result is the 1/3 slope, which appears only under finite precision CSIT and strong interference, and as such has not been encountered in previous studies that invariably assumed perfect CSIT. Finally, we explore the multi-hop interference channel. We consider the sum-GDoF of the symmetric multi-hop interference channel under finite precision CSIT. The sum-GDoF value is first characterized for the 2 × 2 × 2 setting that is comprised of 2 sources, 2 relays, and 2 destinations. The result is then generalized to the 2 × 2 × · · · × 2 setting that is comprised of L hops. Remarkably, for large L, the sum-GDoF value approaches that of the one-hop broadcast channel that is obtained by full cooperation among the two transmitters of the last hop, under finite precision CSIT. Under finite precision CSIT, a combination of classical random coding schemes that are simpler and much more robust, namely a rate-splitting between decode-and-forward and amplify-and-forward, is shown to be GDoF optimal.