Linear transmitter design for the MISO compound channel with interference

We consider the problem of linear transmitter design in multiple input single output (MISO) compound channels with interference. The motivation for this channel model is communication in MISO broadcast channels with partial channel state information (CSI). Since the compound capacity is unknown for this model, we consider optimal linear transmit methods for maximizing the data rate. We provide efficient numerical solutions with and without perfect CSI. We then discuss the optimality of beamforming and the existence of a saddle point in the compound channel.