Wireless communication apparatus and beam control method

1. A wireless communication apparatus comprising:

a plurality of antenna elements configured to output a first beam and a second beam, based on a weighting vector representing weighting with respect to at least one of a gain and a phase; and

a processor configured to perform a process including

deriving a weighting vector corresponding to a maximum eigen value of a matrix obtained by subtracting, from a first matrix representing an output power of a main lobe of the first beam, a matrix obtained by multiplying a second matrix representing an output power of a side lobe of the first beam to a reduction ratio for reducing the output power of the side lobe of the first beam interfering with a main lobe of the second beam,

determining whether or not a power ratio of the output power of the main lobe of the first beam, obtained by multiplying the weighting vector and a complex conjugate transpose of the weighting vector to the first matrix, with respect to the output power of the side lobe of the first beam, obtained by multiplying the weighting vector and the complex conjugate transpose of the weighting vector to the second matrix, is greater than a maximum Signal-to-Interference Ratio (SIR) SIR max , and

extracting the weighting vector when determining determines that the power ratio is not larger than the maximum SIR max .

2. The wireless communication apparatus as claimed in claim 1 , wherein the deriving the weighting vector obtains an initial value of a weighting vector corresponding to a maximum eigen value of a matrix obtained by subtracting, from the first matrix, a matrix obtained by multiplying the second matrix to an initial value of the reduction ratio,

and wherein the processor performs the process further including

deriving a power ratio of an initial value of the output power of the main lobe of the first beam, obtained by multiplying the initial value of the weighting vector and a complex conjugate transpose of the initial value of the weighting vector to the first matrix, with respect to an initial value of the output power of the side lobe of the first beam, obtained by multiplying the initial value of the weighting vector and the initial value of the complex conjugate transpose of the initial value of the weighting vector to the second matrix, and

performing a first process to derive an increased reduction ratio by increasing the reduction ratio by a predetermined ratio, and

wherein the deriving the weighting vector performs a second process to obtain a weighting vector corresponding to a maximum eigen value of a matrix obtained by subtracting, from the first matrix representing the output power of the main lobe of the first beam, a matrix obtained by multiplying the second matrix to the increased reduction ratio, and

wherein the determining performs a third process to determine whether or not a power ratio of the output power of the main lobe of the first beam, obtained by multiplying the weighting vector that is obtained using the increased reduction ratio, and a complex conjugate transpose thereof, to the first matrix, with respect to the output power of the side lobe of the first beam, obtained by multiplying the weighting vector that is obtained using the increased reduction ratio, and the complex conjugate transpose thereof, to the second matrix.

3. The wireless communication apparatus as claimed in claim 2 , wherein the processor performs the process further including

updating the maximum SIR max to the power ratio derived by the deriving the power ratio when the derived power ratio is greater than the maximum SIR max ,

wherein the first process of the performing, the second process of the deriving the weighting vector, and the third process of the determining are repeated when the updating updates the maximum SIR max to the power ratio derived by the deriving the power ratio.

4. The wireless communication apparatus as claimed in claim 3 , wherein the processor performs the process further including

computing a maximum power at which the first beam is outputtable under a predetermined constraint, and

deriving a tolerable ratio with which a reduction of the maximum power is tolerable for the output power of the main lobe of the first beam,

wherein the determining determines whether or not the output power of the main lobe of the first beam obtained by multiplying the weighting vector, obtained using the increased reduction ratio, and the complex conjugate transpose thereof, to the first matrix, is larger than a power obtained by multiplying the tolerable ratio to the maximum power, and performs the third process, and

wherein the updating updates the maximum SIR max when the determining determines that the output power of the main lobe of the first beam obtained by multiplying the weighting vector, obtained using the increased reduction ratio, and the complex conjugate transpose thereof, to the first matrix, is larger than the power obtained by multiplying the tolerable ratio to the maximum power, and the power ratio is determined to be larger than the maximum SIR max in the third process.

5. The wireless communication apparatus as claimed in claim 4 , wherein the predetermined constraint under which the computing computes the maximum power is a maximum distance reachable by the main lobe of the first beam.

6. The wireless communication apparatus as claimed in claim 1 , wherein the deriving the weighting vector derives the weighting vector under a constraint that a sum of squares of the weighting vectors is constant.

7. The wireless communication apparatus as claimed in claim 1 , wherein the deriving the weighting vector derives the weighting vector under a constraint that each weighting coefficient of the weighting vector is less than or equal to a constant value.

8. A beam control method for a wireless communication apparatus having computer, and a plurality of antenna elements configured to output a first beam and a second beam, based on a weighting vector representing weighting with respect to at least one of a gain and a phase, the beam forming method comprising:

deriving, by the computer, a weighting vector corresponding to a maximum eigen value of a matrix obtained by subtracting, from a first matrix representing an output power of a main lobe of the first beam, a matrix obtained by multiplying a second matrix representing an output power of a side lobe of the first beam to a reduction ratio for reducing the output power of the side lobe of the first beam interfering with a main lobe of the second beam;

determining, by the computer, whether or not a power ratio of the output power of the main lobe of the first beam, obtained by multiplying the weighting vector and a complex conjugate transpose of the weighting vector to the first matrix, with respect to the output power of the side lobe of the first beam, obtained by multiplying the weighting vector and the complex conjugate transpose of the weighting vector to the second matrix, is greater than a maximum Signal-to-Interference Ratio (SIR) SIR max ; and

extracting, by the computer, the weighting vector when determining determines that the power ratio is not larger than the maximum SIR max .

9. The beam forming method as claimed in claim 8 , wherein the deriving the weighting vector obtains an initial value of a weighting vector corresponding to a maximum eigen value of a matrix obtained by subtracting, from the first matrix, a matrix obtained by multiplying the second matrix to an initial value of the reduction ratio,

the beam forming method further comprising:

deriving, by the computer, a power ratio of an initial value of the output power of the main lobe of the first beam, obtained by multiplying the initial value of the weighting vector and a complex conjugate transpose of the initial value of the weighting vector to the first matrix, with respect to an initial value of the output power of the side lobe of the first beam, obtained by multiplying the initial value of the weighting vector and the initial value of the complex conjugate transpose of the initial value of the weighting vector to the second matrix, and

performing, by the computer, a first process to derive an increased reduction ratio by increasing the reduction ratio by a predetermined ratio, and

wherein the deriving the weighting vector performs a second process to obtain a weighting vector corresponding to a maximum eigen value of a matrix obtained by subtracting, from the first matrix representing the output power of the main lobe of the first beam, a matrix obtained by multiplying the second matrix to the increased reduction ratio, and

wherein the determining performs a third process to determine whether or not a power ratio of the output power of the main lobe of the first beam, obtained by multiplying the weighting vector that is obtained using the increased reduction ratio, and a complex conjugate transpose thereof, to the first matrix, with respect to the output power of the side lobe of the first beam, obtained by multiplying the weighting vector that is obtained using the increased reduction ratio, and the complex conjugate transpose thereof, to the second matrix.

10. The beam forming method as claimed in claim 9 , further comprising:

updating, by the computer, the maximum SIR max to the power ratio derived by the deriving the power ratio when the derived power ratio is greater than the maximum SIR max ,

wherein the first process of the performing, the second process of the deriving the weighting vector, and the third process of the determining are repeated when the updating updates the maximum SIR max to the power ratio derived by the deriving the power ratio.

11. The beam forming method as claimed in claim 10 , further comprising:

computing, by the computer, a maximum power at which the first beam is outputtable under a predetermined constraint, and

deriving, by the computer, a tolerable ratio with which a reduction of the maximum power is tolerable for the output power of the main lobe of the first beam,

wherein the determining determines whether or not the output power of the main lobe of the first beam obtained by multiplying the weighting vector, obtained using the increased reduction ratio, and the complex conjugate transpose thereof, to the first matrix, is larger than a power obtained by multiplying the tolerable ratio to the maximum power, and performs the third process, and

wherein the updating updates the maximum SIR max when the determining determines that the output power of the main lobe of the first beam obtained by multiplying the weighting vector, obtained using the increased reduction ratio, and the complex conjugate transpose thereof, to the first matrix, is larger than the power obtained by multiplying the tolerable ratio to the maximum power, and the power ratio is determined to be larger than the maximum SIR max in the third process.

12. The beam forming method as claimed in claim 11 , wherein the predetermined constraint under which the computing computes the maximum power is a maximum distance reachable by the main lobe of the first beam.

13. The beam forming method as claimed in claim 8 , wherein the deriving the weighting vector derives the weighting vector under a constraint that a sum of squares of the weighting vectors is constant.

14. The beam forming method as claimed in claim 8 , wherein the deriving the weighting vector derives the weighting vector under a constraint that each weighting coefficient of the weighting vector is less than or equal to a constant value.