Communication systems, methods, and non-transitory computer-readable storage devices using orbital angular momentum beams

1. A method comprising:

determining a set of phase-shifting values based on a parameter-value set of a set of antenna-misalignment parameters between a transmitting antenna array and a receiving antenna array, the set of antenna-misalignment parameters comprising one or more antenna-misalignment parameters and the parameter-value set comprising one or more values of the one or more antenna-misalignment parameters, the receiving antenna array comprising a plurality of receiving antennas each receiving a copy of an orbital angular momentum (OAM) beam from the transmitting antenna array;

shifting phases of the received copies of the OAM beam using the set of determined phase-shifting values to obtain a plurality of phase-shifted copies of the OAM beam; and

detecting the signal by combining the plurality of phase-shifted copies of the OAM beam.

2. The method of claim 1 , wherein said shifting the phases of the received copies of the OAM beam using the set of determined phase-shifting values comprises:

shifting the phases of the received copies of the OAM beam using the set of determined phase-shifting values in an analog domain and/or in a radio-frequency (RF) band.

3. The method of claim 1 , wherein said detecting the signal by combining the plurality of phase-shifted copies of the OAM beam comprises:

converting the plurality of phase-shifted copies of the OAM beam to a baseband; and

extracting the signal from the converted copies of the OAM beam using a successive interference cancellation (SIC) method.

4. The method of claim 1 , wherein the set of antenna-misalignment parameters comprises: a non-parallel angle ϕ between the transmitting antenna array and the receiving antenna array, or a combination of an off-axis distance r and an off-axis angle θ between the transmitting antenna array and the receiving antenna array.

5. The method of claim 1 , wherein said determining the set of phase-shifting values comprises:

determining a misaligned channel H based on the parameter-value set;

determining an augmented channel matrix Ĥ being an aggregation of a combined channel matrix H and a covariance matrix of an additive noise, the combined channel matrix H combining the misaligned channel H and a transmitting BF matrix;

calculating a set of unit-magnitude values based on the augmented channel matrix Ĥ; and

determining the set of phase-shifting values as phases of the set of unit-magnitude values.

6. The method of claim 5 , wherein said determining the set of phase-shifting values as phases of the set of unit-magnitude values comprises:

quantizing the phases of the set of unit-magnitude values to a predefined number of bits; and

determining the set of phase-shifting values as the quantized phases.

7. The method of claim 5 , wherein said determining the set of unit-magnitude elements based on the augmented channel matrix Ĥ comprises:

decomposing the augmented channel matrix Ĥ using a sorted QR (SQR) decomposition method to obtain an orthogonal matrix {circumflex over (Q)}=[Q 1 T , Q 2 T ] T with Q 1 being the upper portion of {circumflex over (Q)} having a same number of rows as the combined channel matrix H;

partitioning the orthogonal matrix {circumflex over (Q)} to the summation of two matrices {circumflex over (Q)} A and {circumflex over (Q)} B having unit-magnitude elements;

retrieving a portion Q A1 of {circumflex over (Q)} A having a same size as Q 1 ;

retrieving a portion Q B1 of {circumflex over (Q)} B having a same size as Q 1 ; and

using elements of Q A1 and Q B1 as the set of unit-magnitude values.

8. The method of claim 1 , wherein said determining the set of phase-shifting values comprises:

selecting the set of phase-shifting values from a beamforming (BF) codebook based on the parameter-value set.

9. The method of claim 8 , wherein the BF codebook is constructed by:

determining one or more ranges for the one or more antenna-misalignment parameters;

obtaining a plurality of possible parameter-value sets within the one or more ranges;

for each possible parameter-value set of the plurality of parameter-value sets,

determining a misaligned channel H based on the possible parameter-value set,

determining an augmented channel matrix Ĥ being an aggregation of a combined channel matrix H and an independent and a covariance matrix of an additive noise, the combined channel matrix H combining the misaligned channel H and a transmitting BF matrix,

determining a set of unit-magnitude values based on the augmented channel matrix Ĥ,

determining a set of possible phase-shifting values as phases of the set of unit-magnitude values, and

adding the set of possible phase-shifting values to the BF codebook.

10. The method of claim 9 , wherein said determining the set of possible phase-shifting values further comprises:

quantizing the phases of the set of unit-magnitude values to a predefined number of bits; and

determining the set of possible phase-shifting values as the quantized phases.

11. The method of claim 9 , wherein said determining the set of unit-magnitude elements based on the augmented channel matrix Ĥ comprises:

decomposing the augmented channel matrix Ĥ using a sorted QR (SQR) decomposition method to obtain an orthogonal matrix {circumflex over (Q)}=[Q 1 T , Q 2 T ] T with Q 1 being the upper portion of {circumflex over (Q)} having a same number of rows as the combined channel matrix H;

partitioning the orthogonal matrix {circumflex over (Q)} to the summation of two matrices {circumflex over (Q)} A and {circumflex over (Q)} B having unit-magnitude elements;

retrieving a portion Q A1 of {circumflex over (Q)} A having a same size as Q 1 ;

retrieving a portion Q B1 of {circumflex over (Q)} B having a same size as Q 1 ; and

using elements of Q A1 and Q B1 as the set of unit-magnitude values.

12. An apparatus comprising:

at least one processor for:

determining a set of phase-shifting values based on a parameter-value set of a set of antenna-misalignment parameters between a transmitting antenna array and a receiving antenna array, the set of antenna-misalignment parameters comprising one or more antenna-misalignment parameters and the parameter-value set comprising one or more values of the one or more antenna-misalignment parameters, the receiving antenna array comprising a plurality of receiving antennas each receiving a copy of an orbital angular momentum (OAM) beam from the transmitting antenna array;

shifting phases of the received copies of the OAM beam using the set of determined phase-shifting values to obtain a plurality of phase-shifted copies of the OAM beam; and

detecting the signal by combining the plurality of phase-shifted copies of the OAM beam.

13. The apparatus of claim 12 , wherein the set of antenna-misalignment parameters comprises: a non-parallel angle ϕ between the transmitting antenna array and the receiving antenna array, or a combination of an off-axis distance r and an off-axis angle θ between the transmitting antenna array and the receiving antenna array.

14. The apparatus of claim 12 , wherein said determining the set of phase-shifting values comprises:

selecting the set of phase-shifting values from a beamforming (BF) codebook based on the parameter-value set.

15. The apparatus of claim 14 , wherein the BF codebook is constructed by:

determining one or more ranges for the one or more antenna-misalignment parameters;

obtaining a plurality of possible parameter-value sets within the one or more ranges;

for each possible parameter-value set of the plurality of parameter-value sets,

determining a misaligned channel H based on the possible parameter-value set,

determining an augmented channel matrix Ĥ being an aggregation of a combined channel matrix H and a covariance matrix of an additive noise, the combined channel matrix H combining the misaligned channel H and a transmitting BF matrix,

determining a set of unit-magnitude values based on the augmented channel matrix Ĥ,

determining a set of possible phase-shifting values as phases of the set of unit-magnitude values, and

adding the set of possible phase-shifting values to the BF codebook.

16. The apparatus of claim 15 , wherein said determining the set of possible phase-shifting values further comprises:

quantizing the phases of the set of unit-magnitude values to a predefined number of bits; and

determining the set of possible phase-shifting values as the quantized phases.

17. The apparatus of claim 15 , wherein said determining the set of unit-magnitude elements based on the augmented channel matrix Ĥ comprises:

decomposing the augmented channel matrix Ĥ using a sorted QR (SQR) decomposition method to obtain an orthogonal matrix {circumflex over (Q)}=[Q 1 T , Q 2 T ] T with Q 1 being the upper portion of {circumflex over (Q)} having a same number of rows as the combined channel matrix H;

partitioning the orthogonal matrix {circumflex over (Q)} to the summation of two matrices {circumflex over (Q)} A and {circumflex over (Q)} B having unit-magnitude elements;

retrieving a portion Q A1 of {circumflex over (Q)} A having a same size as Q 1 ;

retrieving a portion Q B1 of {circumflex over (Q)} B having a same size as Q 1 ; and

using elements of Q A1 and Q B1 as the set of unit-magnitude values.

18. One or more non-transitory computer-readable storage devices comprising computer-executable instructions for constructing a BF codebook, wherein the instructions, when executed, cause a processing structure to perform actions comprising:

determining one or more ranges for the one or more antenna-misalignment parameters;

obtaining a plurality of possible parameter-value sets within the one or more ranges;

for each possible parameter-value set of the plurality of parameter-value sets,

determining a misaligned channel H based on the possible parameter-value set,

determining an augmented channel matrix Ĥ being an aggregation of a combined channel matrix H and a covariance matrix of an additive noise, the combined channel matrix H combining the misaligned channel H and a transmitting BF matrix,

determining a set of unit-magnitude values based on the augmented channel matrix Ĥ,

determining a set of possible phase-shifting values as phases of the set of unit-magnitude values, and

adding the set of possible phase-shifting values to the BF codebook.

19. The one or more non-transitory computer-readable storage devices of claim 18 , wherein said determining the set of possible phase-shifting values further comprises:

quantizing the phases of the set of unit-magnitude values to a predefined number of bits; and

determining the set of possible phase-shifting values as the quantized phases.

20. The one or more non-transitory computer-readable storage devices of claim 18 , wherein said determining the set of unit-magnitude elements based on the augmented channel matrix Ĥ comprises:

decomposing the augmented channel matrix Ĥ using a sorted QR (SQR) decomposition method to obtain an orthogonal matrix {circumflex over (Q)}=[Q 1 T , Q 2 T ] T with Q 1 being the upper portion of {circumflex over (Q)} having a same number of rows as the combined channel matrix H;

partitioning the orthogonal matrix {circumflex over (Q)} to the summation of two matrices {circumflex over (Q)} A and {circumflex over (Q)} B having unit-magnitude elements;

retrieving a portion Q A1 of {circumflex over (Q)} A having a same size as Q 1 ;

retrieving a portion Q B1 of {circumflex over (Q)} B having a same size as Q 1 ; and

using elements of Q A1 and Q B1 as the set of unit-magnitude values.