Topological Interference Management: Linear Cooperation is not useful for Wyner's Networks

In this work, we study the value of cooperative transmission in wireless networks if no channel state information is available at the transmitters (no CSIT). Our focus is on large locally connected networks, where each transmitter is connected to the receiver that has the same index as well as L succeeding receivers. The cases of L=1 and L=2 represent Wyner's asymmetric and symmetric network models, respectively. The considered rate criterion is the per user Degrees of Freedom (puDoF) as the number of transmitter-receiver pairs goes to infinity. For the case when L=1, it was shown in previous work that linear cooperation schemes do not increases the puDoF value, and that the optimal scheme relies on assigning each message to a single transmitter and using orthogonal access (TDMA). Here, we extend this conclusion to the case where L=2, by proving optimality of TDMA in this case as well. We conclude by discussing whether increasing the value of L can create a value for linear cooperation schemes from a DoF perspective.