  Hybrid analog-digital (AD) beamforming structure is a very attractive
solution to build low cost massive multiple-input multiple-output (MIMO)
systems. Typically these systems use a set of fixed beams for transmission and
reception to avoid the need to obtain channel state information at transmitter
(CSIT) for each antenna element individually. However, such a method can not
fully exploit the potential of hybrid AD beamforming systems. Alternatively,
CSIT can be estimated by assuming a model for the propagation channel, whereas
this model is only validated in millimeter-wave (mmWave) band thanks to its
poor scattering nature. In this paper, we focus on time division duplex (TDD)
systems with hybrid beamforming structure and propose a reciprocity calibration
scheme that allows to acquire full CSIT. Different to existing CSIT acquisition
methods, our approach does not require any assumption on the channel model and
can, in theory, estimate the CSIT up to an arbitrary small error.
