Codebook design for beamforming in 5G and beyond mmWave systems

A method for hybrid beamforming in a communications system, comprising:

• encoding, by a base station, data into a plurality of streams, each transmitted through a radio frequency chain;
• a forming a beamforming codebook comprising a set of beamforming codewords;
• and
• transmitting, by a beamformer, a given one of the plurality of streams through multiple antennas by adjusting a phase and a gain of symbols of the given one of the plurality of streams for each of the multiple antennas by using a corresponding beamforming coefficient of a given beamforming codeword chosen from the beamforming codebook,
• wherein a beam and its corresponding beamforming codeword is designed such that the mean squared error between the beam pattern generated with the given beamforming codeword and a given beam pattern is minimized, wherein the beam pattern covers a given interval in azimuth angle with a constant gain.

A communications system for hybrid beamforming, comprising:

• a base station encoding data into a plurality of streams, each transmitted through a radio frequency chain;
• a beamforming codebook comprising a set of beamforming codewords;
• and
• a beamformer transmitting a given one of the plurality of streams through multiple antennas by adjusting a phase and a gain of symbols of the given one of the plurality of streams for each of the multiple antennas by using a corresponding beamforming coefficient of a given beamforming codeword chosen from the beamforming codebook,
• wherein a beam and its corresponding beamforming codeword is designed such that the mean squared error between the beam pattern generated with the given beamforming codeword and a given beam pattern is minimized, wherein an absolute value of an mth beamforming coefficient for a beamforming codeword q is given by product of a constant factor and sinc(δq(η+m)), wherein δq and η are two constant values.