Many practical systems employ a feedback channel to convey the channel state information to the transmitter.The capacity of the feedback channels is usually limited to a few bits per frame. We design feedback based transmission schemes for multiple transmit antenna systems in this work. The important contribution of this work is a design criterion for the construction of optimal beamformers with a constraint on the rate of the feedback channel. Beamforming schemes also lead to reduced complexity compared to space time coding schemes at the cost of a few bits of feedback.