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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.

Hybrid Beamforming Based on Implicit Channel State Information for Millimeter Wave Links