Does non-orthogonal spectrum sharing in the same cell improve the sum-rate of wireless operators?

We study non-orthogonal spectrum sharing to determine under what circumstances operators can gain by such sharing. To model the spectrum sharing, we use the multiple-input single-output (MISO) interference channel (IC) assuming that the operators transmit in the same band. For the baseline scenario of no sharing, we use the MISO broadcast channel (BC) assuming that the operators transmit in disjunct bands. For both the IC and BC, we give achievable (lower) and upper bounds on the maximum sum-rate. While these bounds are well-known we also propose a new fast algorithm for finding a lower bound on the sum-rate of the BC using linear beamforming. We use the bounds to numerically evaluate the potential gain of non-orthogonal spectrum sharing. In this study we assume that the operators efficiently utilize all their spatial degrees of freedom. We will see that the gains from spectrum sharing under these circumstances are limited.