A multiple input multiple output (MIMO) antenna system is implemented for communications in a wireless device. MIMO beamforming techniques are utilized to improve communications, and may be utilized in full-duplex mode. Techniques include the formation of beamforming patterns having orthogonal polarizations to one another at each communication device, but having matching polarization between transmit/receive pairs located at each respective communication device. Techniques also include the formation of beamforming patterns in a direction towards another communication device to maximize transmit power in that direction while inducing nulls in the beamforming pattern to reduce self-interference coupling via antennas configured for reception. Full-duplex communications are improved through monitoring of the self-interference coupling and adapting the beamforming patterns to reduce it. Beamforming vectors may be generated by solving a cost function that may include an additional constraint of reduction of self-interference coupling.