To further improve the potential of full-duplex communications, networks may employ multiple antennas at the base station or user equipment. To this end, networks that employ current radios usually deal with self-interference and multi-user interference by beamforming techniques. Although previous works investigated beamforming design to improve spectral efficiency, the fundamental question of how to split the antennas at a base station between uplink and downlink in full-duplex networks has not been investigated rigorously. This paper addresses this question by posing antenna splitting as a binary nonlinear optimization problem to minimize the sum mean squared error of the received data symbols. It is shown that this is an NP-hard problem. This combinatorial problem is dealt with by equivalent formulations, iterative convex approximations, and a binary relaxation. The proposed algorithm is guaranteed to converge to a stationary solution of the relaxed problem with much smaller complexity than exhaustive search. Numerical results indicate that the proposed solution is close to the optimal in both high and low self-interference capable scenarios, while the usually assumed antenna splitting is far from optimal. For large number of antennas, a simple antenna splitting is close to the proposed solution. This reveals that the importance of antenna splitting diminishes with the number of antennas.