Extremal Network Theory and Robust GDoF Gain of Multi-Cell Cooperation over Multi-Cell TIN

We study the fundamental limits of multi-cell cooperation in downlink cellular networks under the assumption of finite precision channel state information at the transmitters (CSIT). By appealing to extremal network theory, recently introduced by Chan et al. [1], we characterize the extremal GDoF gain of multi-cell cooperation over non-cooperative multi-cell TIN in three weak inter-cell interference regimes: the mc-TIN regime, where multi-cell TIN is GDoF optimal under no cooperation; the mc-CTIN regime, where the GDoF region achieved through multi-cell TIN is convex without the need for time-sharing; and the mc-SLS regime, where a cooperative scheme based on simple layered superposition was shown to be optimal in small networks. We show that the extremal GDoF gain is bounded by a constant factor in the mc-TIN and mc-CTIN regimes, and scales logarithmically with the number of cells in the mc-SLS regime. The analysis is enabled by a new cooperative outer bound for cellular networks based on the aligned images approach.