Codebook design for beamforming in 5G and beyond mmWave systems

1. 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 the beam pattern covers a given interval in azimuth angle with a constant gain.

2. The communications system of claim 1 , wherein the beam are designed for Uniform Linear Arrays (ULA).

3. The communications system of claim 1 , wherein the beam are designed for Uniform Planar Arrays (UPA).

4. The communications system of claim 1 , wherein the beam are designed for a Twin Uniform Linear Array (TULA) antenna structure that is comprised of two Uniform Linear Arrays that are employed side by side.

5. The communications system of claim 4 , wherein a distance between the two Uniform Linear Arrays is controlled to generate an asymmetric beam pattern.

6. The communications system of claim 1 , wherein an absolute value of an m th beamforming coefficient for a beamforming codeword q is given by product of a constant factor and sinc(δ q (η+m)), wherein δ q and η are two constant values.

7. The communications system of claim 6 , wherein a smoothness and a sharpness of the beam is controlled by the constant value η.

8. The communications system of claim 4 , wherein an element of one ULA using the beamforming coefficient w has a corresponding element in the other ULA for which the beamforming coefficient is given by w=e jb , where b is a design constant and j is the square root of −1.

9. The communications system of claim 8 , wherein the design constant b controls an isolation between the beam and a beam counterpart, the isolation being a ratio of the average power of the beam over the average power of the beam counterpart.

10. 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.

11. The method of claim 10 , wherein the beam are designed for Uniform Linear Arrays (ULA).

12. The method of claim 10 , wherein the beam are designed for Uniform Planar Arrays (UPA).

13. The method of claim 10 , wherein the beam are designed for a Twin Uniform Linear Array (TULA) antenna structure that is comprised of two Uniform Linear Arrays that are employed side by side.

14. The method of claim 13 , wherein a distance between the two Uniform Linear Arrays is controlled to generate an asymmetric beam pattern.

15. The method of claim 10 , wherein an absolute value of an m th beamforming coefficient for a beamforming codeword q is given by product of a constant factor and sinc(δ q (η+m)), wherein δ q and η are two constant values.

16. The method of claim 15 , wherein a smoothness and a sharpness of the beam is controlled by the constant value η.

17. The method of claim 13 , wherein an element of one ULA using the beamforming coefficient w has a corresponding element in the other ULA for which the beamforming coefficient is given by w=e jb , where b is a design constant and j is the square root of −1.

18. The method of claim 17 , wherein the design constant b controls an isolation between the beam and a beam counterpart, the isolation being a ratio of the average power of the beam over the average power of the beam counterpart.

19. 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 m th beamforming coefficient for a beamforming codeword q is given by product of a constant factor and sinc(δ q (η+m)), wherein δ q and η are two constant values.