Degrees of freedom (DoF) of locally connected interference channels with cooperating multiple-antenna transmitters

We consider locally connected K-user MISO interference channels where each transmitter has N antennas and is connected to the receiver with the same index as well as [L/2] successively preceding receivers and [L/2] following receivers. We assume that each receiver is interested in one message, which can be available at a maximum of M transmitters. Under these assumptions, we study the available degrees of freedom as well as the optimal way to assign messages to transmitters. For the case where each message is assigned to the transmitter with the same index, we know from [1] that [KN/N+1] DoF is achievable for the considered locally connected channel using interference alignment as the number of symbol extensions goes to infinity. In this work, we show that a simple linear strategy employing zero forcing transmit beams achieves min {2MN/M(N+1)+L, 1} per user degrees of freedom. In particular, the N/N+1 per user DoF is achievable by coding over only one channel realization, for any value of M ≥ L/N+1. Moreover, we show that the proposed scheme is optimal among a class of linear strategies where each receiver is either inactive or enjoys interference-free communication. Finally, we generalize the upper bound proved for Wyner's asymmetric channel model (L = 1) in [2], and show that message assignments satisfying a local cooperation constraint are optimal for a general setting of the parameters.