Over-the-air self calibration for phased array antennas

An apparatus for calibrating antenna elements of phased array antennas comprising:

• a plurality of periodically spaced antenna elements included in an antenna lattice, the plurality of periodically spaced antenna elements comprising a first antenna element, a second antenna element, a third antenna element, and a fourth antenna element;
• and
• one or more calibration components configured to:
• obtain a first mutual coupling measurement associated with a first OTA signal path between the first antenna element and the second antenna element;
• obtain a second mutual coupling measurement associated with a second OTA signal path between the third antenna element and the second antenna element;
• obtain a third mutual coupling measurement associated with a third OTA signal path between the first antenna element and the fourth antenna element, wherein the third OTA signal path is reciprocal to the second OTA signal path;
• obtain a fourth mutual coupling measurement associated with a fourth OTA signal path between the third antenna element and the fourth antenna element;
• and
• determine, based on the first mutual coupling measurement, the second mutual coupling measurement, the third mutual coupling measurement, and the fourth mutual coupling measurement, at least one of a phase correction factor or a gain correction factor between a complex gain of the first antenna element and a complex gain of the third antenna element.

A method of calibrating antenna elements for phased array antennas comprising:

• obtaining a first plurality of mutual coupling measurements, wherein each mutual coupling measurement of the first plurality of mutual coupling measurements corresponds to a respective OTA signal path associated with a first geometric relationship between pairs of antenna elements of an antenna lattice, wherein the antenna lattice comprises a plurality of periodically spaced antenna elements including the pairs of antenna elements;
• and
• obtaining a second plurality of mutual coupling measurements, wherein each mutual coupling measurement of the second plurality of mutual coupling measurements corresponds to a respective OTA signal path associated with a second geometric relationship between pairs of antenna elements of the antenna lattice, wherein the second geometric relationship is reciprocal to the first geometric relationship;
• and
• determining, based on the first plurality of mutual coupling measurements and the second plurality of mutual coupling measurements at least one of a phase correction factor or a gain correction factor between a complex gain of a first antenna element of the plurality of periodically spaced antenna elements and a complex gain of a second antenna element of the plurality of periodically spaced antenna elements.