  We study the generalized degrees-of-freedom (GDoF) of cellular networks under
finite precision channel state information at the transmitters (CSIT). We
consider downlink settings modeled by the interfering broadcast channel (IBC)
under no multi-cell cooperation, and the overloaded
multiple-input-single-output broadcast channel (MISO-BC) under full multi-cell
cooperation. We focus on three regimes of interest: the mc-TIN regime, where a
scheme based on treating inter-cell interference as noise (mc-TIN) was shown to
be GDoF optimal for the IBC; the mc-CTIN regime, where the GDoF region
achievable by mc-TIN is convex without the need for time-sharing; and the
mc-SLS regime which extends a previously identified regime, where a simple
layered superposition (SLS) scheme is optimal for the 3-transmitter-3-user
MISO-BC, to overloaded cellular-type networks with more users than
transmitters. We first show that the optimality of mc-TIN for the IBC extends
to the entire mc-CTIN regime when CSIT is limited to finite precision. The
converse proof of this result relies on a new application of aligned images
bounds. We then extend the IBC converse proof to the counterpart overloaded
MISO-BC, obtained by enabling full transmitter cooperation. This, in turn, is
utilized to show that a multi-cell variant of the SLS scheme is optimal in the
mc-SLS regime under full multi-cell cooperation, albeit only for 2-cell
networks. The overwhelming combinatorial complexity of the GDoF region stands
in the way of extending this result to larger networks. Alternatively, we
appeal to extremal network analysis, recently introduced by Chan et al., and
study the GDoF gain of multi-cell cooperation over mc-TIN in the three regimes
of interest. We show that this extremal GDoF gain is bounded by small constants
in the mc-TIN and mc-CTIN regimes, yet scales logarithmically with the number
of cells in the mc-SLS regime.
