  Hybrid beamforming provides a promising solution to achieve high data rate
transmission at millimeter waves. Implementing hybrid beamforming at a
transceiver based on available channel state information is a common solution.
However, many reference methods ignore the complexity of channel estimation for
large antenna arrays or subsequent steps, such as the singular value
decomposition of a channel matrix. To this end, we present a low-complexity
scheme that exploits implicit channel knowledge to facilitate the design of
hybrid beamforming for frequency-selective fading channels. The implicit
channel knowledge can be interpreted as couplings between all possible pairs of
analog beamforming vectors at the transmitter and receiver over the surrounding
channel. Instead of calculating mutual information between large antenna
arrays, we focus on small-size coupling matrices between beam patterns selected
by using appropriate key parameters as performance indicators. This converts
the complicated hybrid beamforming problem to a much simpler one: it amounts to
collecting different sets of the large-power coupling coefficients to construct
multiple alternatives for an effective channel matrix. Then, the set yielding
the largest Frobenius norm (or the largest absolute value of the determinant)
of the effective channel provides the solution to the hybrid beamforming
problem. It turns out that the proposed method does not require information on
MIMO channel and can be simply implemented by the received correlated pilot
signals that are supposed to be used for channel estimation.
