Techniques for calculating the array factor of a phased array antenna

1 . A wireless device comprising:

a phased array antenna comprising a plurality of antenna elements, wherein the plurality of antenna elements are organized in a two-dimensional planar array;

digital beam forming (DBF) circuitry coupled to the phased array antenna;

a processing device operatively coupled to the DBF circuitry; and

a memory device operatively coupled to the processing device, wherein the memory device stores instructions that, when executed by the processing device, cause the processing device to perform operations comprising:

receiving input comprising an azimuth angle value and an elevation angle value;

receiving a first value that specifies a distance between a first element and a second element of the plurality of antenna elements in a first dimension, a second value that specifies a wavelength associated with an operating frequency of the phased array antenna, a third value that specifies a first sampling frequency in the first dimension, a fourth value that specifies a distance between the first element and the second element of the plurality of antenna elements in a second dimension, and a fifth value that specifies a second sampling frequency in the second dimension, wherein the first value and the fourth value define an inter-element distance between the first element and the second element;

defining a first set of coordinate values using the first, second, and third values, wherein the first set of coordinate values are representative of a first relationship between the elevation angle value and the azimuth angle value, and wherein the first set of coordinate values correspond to a first dimension of a first coordinate space;

defining a second set of coordinate values using the second, fourth, and fifth values, wherein the second set of coordinate values are representative of a second relationship between the elevation angle value and the azimuth angle value, and wherein the second set of coordinate values correspond to a second dimension of the first coordinate space;

defining a set of amplitudes, wherein each amplitude of the set of amplitudes is based on the third value, the fifth value, an excitation amplitude of a respective one of the plurality of antenna elements, and an excitation phase of the respective one of the plurality of antenna elements;

determining a spatial positioning of a third phantom element within the two-dimensional planar array, wherein the third phantom element has a zero amplitude, wherein the spatial positioning is determined to be between the first element and the second element such that a third distance, defined between the first element and the third phantom element or the second element and the third phantom element, is less than the inter-element distance; and

determining first array factor values for the phased array antenna in the first coordinate space by computing a two-dimensional inverse Fast Fourier Transform (IFFT) using the set of amplitudes, the zero amplitude and the spatial positioning of the third phantom element, the first set of coordinate values, and the second set of coordinate values, wherein the first array factor values are determined without the elevation angle value or the azimuth angle value.

2 . The wireless device of claim 1 , wherein the processing device is further to perform operations comprising:

determining second array factor values for the phased array antenna by performing a two-dimensional spline interpolation on the first array factor values at points in the first coordinate space corresponding to the plurality of antenna elements, wherein each of the second array factor values comprises a first component representing a magnitude to be applied at the respective one of the plurality of antenna elements and a second component representing a phase or delay to be applied at the respective one of the plurality of antenna elements; and

sending the second array factor values to the DBF circuitry that causes the phased array antenna to steer a radiation beam using the second array factor values, wherein the first set of coordinate values depend on the third value and a first ratio of the second value divided by the first value, wherein the second set of coordinate values depend on the fifth value and a second ratio of the second value divided by the fourth value.

3 . The wireless device of claim 1 , wherein the first array factor values corresponding to negative coordinate values of the first set of coordinate values and the second set of coordinate values are computed using a periodicity of the two-dimensional IFFT.

4 . The wireless device of claim 1 , wherein the processing device is further to perform operations comprising:

receiving additional input comprising vi) a sixth value that specifies a third sampling frequency that is higher than the first sampling frequency, and vii) a seventh value that specifies a fourth sampling frequency that is higher than the second sampling frequency;

defining a second set of amplitudes of the two-dimensional IFFT, each amplitude of the second set of amplitudes being based on the sixth value, the seventh value, the excitation amplitude of the respective one of the plurality of antenna elements, and the excitation phase of the respective one of the plurality of antenna elements;

determining third array factor values for the phased array antenna in the first coordinate space by computing the two-dimensional IFFT of the second set of amplitudes in the first coordinate space using the first set of coordinate values and the second set of coordinate values;

determining fourth array factor values for the phased array antenna by performing a two-dimensional spline interpolation on the third array factor values at points in the first coordinate space, wherein each of the fourth array factor values comprises a first component representing a magnitude to be applied at the respective one of the plurality of antenna elements and a second component representing a phase or delay to be applied at the respective one of the plurality of antenna elements; and

sending the fourth array factor values to the DBF circuitry that causes the phased array antenna to steer a radiation beam using the fourth array factor values.

5 . The wireless device of claim 1 , wherein the processing device is further to perform operations comprising:

multiplying the first array factor values by a first skew value based on an offset starting position of the two-dimensional planar array from an origin in a first dimension; and

multiplying the first array factor values by a second skew value based on an offset starting position of the two-dimensional planar array from the origin in a second dimension.

6 . The wireless device of claim 1 , wherein the two-dimensional planar array comprises a custom grid for which the plurality of antenna elements are placed at a user-defined angle from a horizontal axis.

7 . The wireless device of claim 1 , wherein the processing device is further to perform operations comprising:

determining spatial positionings of a plurality of third phantom elements within the two-dimensional planar array, wherein each third phantom element of the plurality of third phantom elements has a zero amplitude; and

including the plurality of third phantom elements within the two-dimensional planar array.

8 . A computing system comprising:

a processing device; and

a memory device operatively coupled to the processing device, wherein the memory device stores instructions that, when executed by the processing device, cause the processing device to perform operations comprising:

receiving input comprising an azimuth angle value and an elevation angle value;

receiving a first value that specifies a distance between a first element and a second element of a plurality of antenna elements organized in a two-dimensional planar array in a first dimension of a phased array antenna, a second value that specifies a wavelength associated with an operating frequency of the phased array antenna, a third value that specifies a first sampling frequency in the first dimension, a fourth value that specifies a distance between a first element and a second element of the plurality of antenna elements in a second dimension, and a fifth value that specifies a second sampling frequency in the second dimension, wherein the first value and the fourth value define an inter-element distance between the first element and the second element;

defining a first set of coordinate values using the first, second, and third values, wherein the first set of coordinate values are representative of a first relationship between the elevation angle value and the azimuth angle value, and wherein a first dimension of a first coordinate space corresponds to the first set of coordinate values;

defining a second set of coordinate values using the second, fourth, and fifth values, wherein the second set of coordinate values are representative of a second relationship between the elevation angle value and the azimuth angle value, and wherein a second dimension of the first coordinate space corresponds to the second set of coordinate values;

defining a set of amplitudes, wherein each amplitude of the set of amplitudes is based on the third value, the fifth value, an excitation amplitude of a respective one of the plurality of antenna elements, and an excitation phase of the respective one of the plurality of antenna elements;

determining a spatial positioning of a third phantom element within the two-dimensional planar array, wherein the third phantom element has a zero amplitude, wherein the spatial positioning is determined to be between the first element and the second element such that a third distance, defined between the first element and the third phantom element or the second element and the third phantom element, is less than the inter-element distance; and

determining first array factor values for the phased array antenna by computing a two-dimensional inverse Fast Fourier Transform (IFFT) using the set of amplitudes, the zero amplitude and the spatial positioning of the third phantom element, the first set of coordinate values, and the second set of coordinate values, wherein the first array factor values are determined without the elevation angle value or the azimuth angle value.

9 . The computing system of claim 8 , wherein the processing device is further to perform operations comprising:

determining second array factor values for the phased array antenna by performing a two-dimensional spline interpolation on the first array factor values at points in the first coordinate space corresponding to a plurality of antenna elements of the phased array antenna, wherein each of the second array factor values comprises a first component representing a magnitude to be applied at the respective one of the plurality of antenna elements and a second component representing a phase or delay to be applied at the respective one of the plurality of antenna elements; and

sending the second array factor values to digital beam forming (DBF) circuitry that causes the phased array antenna to steer a radiation beam using the second array factor values, wherein the first coordinate set of values depend on the third value and a first ratio of the second value divided by the first value, wherein the second set of coordinate values depend variable depends on the fifth value and a second ratio of the second value divided by the fourth value.

10 . The computing system of claim 8 , wherein the first array factor values corresponding to negative coordinate values of the first and second sets of coordinate values are computed using a periodicity of a one-dimensional inverse Fast Fourier Transform (IFFT).

11 . The computing system of claim 8 , wherein the processing device is further to perform operations comprising:

receiving additional input comprising vi) a sixth value that specifies a third sampling frequency that is higher than the first sampling frequency, and vii) a seventh value that specifies a fourth sampling frequency that is higher than the second sampling frequency;

defining a second set of amplitudes of the two-dimensional IFFT, each amplitude of the second set of amplitudes being based on the sixth value, the seventh value, the excitation amplitude of the respective one of a plurality of antenna elements of the phased array antenna, and the excitation phase of the respective one of the plurality of antenna elements;

determining third array factor values for the phased array antenna in the first coordinate space by computing the two-dimensional IFFT of the second set of amplitudes in the first coordinate space using the first and second sets of coordinate values;

determining fourth array factor values for the phased array antenna by performing a two-dimensional spline interpolation on the third array factor values at points in the first coordinate space, wherein each of the fourth array factor values comprises a first component representing a magnitude to be applied at the respective one of the plurality of antenna elements and a second component representing a phase or delay to be applied at the respective one of the plurality of antenna elements; and

sending the fourth array factor values to digital beam forming (DBF) circuitry that causes the phased array antenna to steer a radiation beam using the fourth array factor values.

12 . The computing system of claim 8 , wherein the phased array antenna comprises a plurality of antenna elements organized in a two-dimensional planar array, wherein the processing device is further to perform operations comprising:

multiplying the first array factor values by a first skew value based on an offset starting position of the two-dimensional planar array from an origin in a first dimension; and

multiplying the first array factor values by a second skew value based on an offset starting position of the two-dimensional planar array from the origin in a second dimension.

13 . The computing system of claim 8 , wherein the phased array antenna comprises a plurality of antenna elements organized in a two-dimensional planar array, wherein the two-dimensional planar array comprises a custom grid for which the plurality of antenna elements are placed at a user-defined angle from a horizontal axis.

14 . The computing system of claim 8 , wherein the processing device is further to perform operations comprising:

determining spatial positionings of a plurality of third phantom elements within the two-dimensional planar array, wherein each third phantom element of the plurality of third phantom elements has a zero amplitude; and

including the plurality of third phantom elements within the two-dimensional planar array.

15 . The computing system of claim 8 , wherein the computing system is coupled to digital beam forming (DBF) circuitry, wherein the DBF circuitry is coupled to a plurality of antenna elements of the phased array antenna, wherein the plurality of antenna elements are organized in a two-dimensional array, wherein the two-dimensional array is at least one of a planar array or a circular array.

16 . A method of operating a wireless device, the method comprising:

receiving input comprising an azimuth angle value and an elevation angle value, wherein the azimuth angle value and the elevation angle value are associated with digital beam forming (DBF) circuitry coupled to a phased array antenna comprising a plurality of antenna elements organized in a two-dimensional planar array;

receiving a first value that specifies a distance between a first element and a second element of the plurality of antenna elements in a first dimension, a second value that specifies a wavelength associated with an operating frequency of the phased array antenna, a third value that specifies a first sampling frequency in the first dimension, a fourth value that specifies a distance between the first element and the second element of the plurality of antenna elements in a second dimension, and a fifth value that specifies a second sampling frequency in the second dimension, wherein the first value and the fourth value define an inter-element distance between the first element and the second element;

defining a first set of coordinate values using the first, second, and third values, wherein the first set of coordinate values are representative of a first relationship between the elevation angle value and the azimuth angle value, and wherein the first set of coordinate values correspond to a first dimension of a first coordinate space;

defining a second set of coordinate values using the second, fourth, and fifth values, wherein the second set of coordinate values are representative of a second relationship between the elevation angle value and the azimuth angle value, and wherein the second set of coordinate values correspond to a second dimension of the first coordinate space;

defining a set of amplitudes, wherein each amplitude of the set of amplitudes is based on the third value, the fifth value, an excitation amplitude of a respective one of the plurality of antenna elements, and an excitation phase of the respective one of the plurality of antenna elements;

determining a spatial positioning of a third phantom element within the two-dimensional planar array, wherein the third phantom element has a zero amplitude, wherein the spatial positioning is determined to be between the first element and the second element such that a third distance, defined between the first element and the third phantom element or the second element and the third phantom element, is less than the inter-element distance; and

determining first array factor values for the phased array antenna in the first coordinate space by computing a two-dimensional inverse Fast Fourier Transform (IFFT) using the set of amplitudes, the zero amplitude and the spatial positioning of the third phantom element, the first set of coordinate values, and the second set of coordinate values, and wherein the first array factor values are determined without the elevation angle value or the azimuth angle value.

17 . The method of claim 16 , further comprising:

determining second array factor values for the phased array antenna by performing a two-dimensional spline interpolation on the first array factor values at points in the first coordinate space corresponding to the plurality of antenna elements, wherein each of the second array factor values comprises a first component representing a magnitude to be applied at the respective one of the plurality of antenna elements and a second component representing a phase or delay to be applied at the respective one of the plurality of antenna elements; and

sending the second array factor values to the DBF circuitry that causes the phased array antenna to steer a radiation beam using the second array factor values, wherein the first set of coordinate values depend on the third value and a first ratio of the second value divided by the first value, wherein the second set of coordinate values depend on the fifth value and a second ratio of the second value divided by the fourth value.

18 . The method of claim 16 , further comprising:

receiving additional input comprising vi) a sixth value that specifies a third sampling frequency that is higher than the first sampling frequency, and vii) a seventh value that specifies a fourth sampling frequency that is higher than the second sampling frequency;

defining a second set of amplitudes of the two-dimensional IFFT, each amplitude of the second set of amplitudes being based on the sixth value, the seventh value, the excitation amplitude of the respective one of the plurality of antenna elements, and the excitation phase of the respective one of the plurality of antenna elements;

determining third array factor values for the phased array antenna in the first coordinate space by computing the two-dimensional IFFT of the second set of amplitudes in the first coordinate space using the first and second sets of coordinate values;

determining fourth array factor values for the phased array antenna by performing a two-dimensional spline interpolation on the third array factor values at points in the first coordinate space, wherein each of the fourth array factor values comprises a first component representing a magnitude to be applied at the respective one of the plurality of antenna elements and a second component representing a phase or delay to be applied at the respective one of the plurality of antenna elements; and

sending the fourth array factor values to the DBF circuitry that causes the phased array antenna to steer a radiation beam using the fourth array factor values.

19 . The method of claim 16 , further comprising computing, using a periodicity of a one-dimensional IFFT, a portion of the first array factor values that correspond to negative coordinate values of the first and second sets of coordinate values.