An apparatus for use in transmit beamforming to a beamformee having NR receive antennas. The apparatus includes a controller configured to i) construct a partial channel matrix that describes a multiple input, multiple output (MIMO) channel between a beamformer and M receive antennas, wherein M is less than NR, and ii) generate L independent vectors using the partial channel matrix, wherein L is a rank of the partial channel matrix. When a number NS of one or more streams is greater than L, the controller is further configured to i) select the L independent vectors as steering vectors to steer L streams of the plurality of streams, and ii) select NS−L orthogonal vectors in a null space of the L independent vectors as steering vectors to steer a remainder of the streams in the plurality of streams.