In embodiments, apparatuses, methods, and storage media may be described for reducing the overhead associated with the transmission of channel training signals from an eNodeB (eNB) of a wireless network. Specifically, the eNB may receive feedback from a user equipment (UE) regarding the received signal energy of a first and second beamformed signal produced with a first and second beamforming vector, respectively. The eNB may identify, based on the feedback of the received signal energy, a signal subspace and a null subspace. The eNB may then transmit a channel training signal to the signal subspace.