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

Hybrid beamforming provides a promising solution to achieve high data rate transmission at millimeter waves. To implement the hybrid beamforming at the transceiver, a common solution is to decouple the transmitter and receiver functions and then optimize them separately based on given channel state information. However, many references ignore the complexity of the high-dimensional channel estimation problem or the effort for the subsequent step of computing the singular value decomposition of a large channel matrix. To this end, we present a low-complexity scheme that exploits implicit channel knowledge to facilitate the design of hybrid beamforming for frequencyselective fading channels. The implicit channel knowledge can be interpreted as a coupling of the channel and all pairs of possible analog beamforming vectors at the transmitter and receiver, and it is obtained by receiving the transmitted pilots. Based on the received pilots, different effective channel matrices are constructed in the sense that the matrix elements are essentially the coupling coefficients. Instead of calculating mutual information, we use the Frobenius norm of the effective channel as a key parameter of the hybrid beamforming gain. As a result, the complicated hybrid beamforming problem becomes a much simpler one: it amounts to trying different sets of the large-power received pilots to construct multiple alternatives for the effective channel matrix. Then, the set yielding the largest Frobenius norm provides the solution to the hybrid beamforming problem.