Method for joint antenna-array calibration and direction of arrival estimation for automotive applications

A system comprising:

• an antenna array including L antenna elements, wherein L is an integer ≥1;
• radio frequency (RF) circuitry coupled to the antenna array;
• and
• a processor coupled to the RF circuitry and configured to execute instructions to process signals received via the antenna array to:
• determine an initial array response to K objects within a field of view of the antenna array, wherein K is an integer ≥2, and wherein the initial array response is a function of a first matrix that is an initial coupling matrix, a second matrix that includes for each of the L antenna elements an initial value based on a gain value and a phase value of the antenna element, a third matrix that includes an initial direction of arrival (DOA) estimate for each of the K objects, and a fourth matrix that includes a complex signal amplitude value for each of the K objects;
• determine a covariance matrix based on the initial array response;
• perform eigen-decomposition of the covariance matrix to determine an updated DOA estimate for each of the K objects;
• update the third matrix based at least partially on the updated DOA estimates;
• update the second matrix based at least partially on a fifth matrix that is a diagonal matrix based on the updated DOA estimates and a sixth matrix that includes eigenvectors corresponding to the covariance matrix;
• update the first matrix in accordance with a cost function that is a function of the updated second matrix, the updated third matrix, and the sixth matrix;
• and
• use the updated first matrix and the updated second matrix when processing additional signals received by the antenna array to determine additional direction of arrival (DOA) estimates for each of the K objects.

An integrated circuit comprising:

• a memory to store instructions;
• a processor coupled to the memory and configured to execute the instructions to:
• determine an initial array response to K objects within a field of view of the radar system having an antenna array with L antenna elements, wherein L is an integer greater than or equal to 1 and wherein K is an integer greater than or equal to 2, and wherein the initial array response is a function of a first matrix that is an initial coupling matrix, a second matrix that includes for each of the L antenna elements an initial value based on a gain value and a phase value of the antenna element, a third matrix that includes an initial direction of arrival (DOA) estimate for each of the K objects, and a fourth matrix that includes a complex signal amplitude value for each of the K objects;
• determine a covariance matrix based on the initial array response;
• perform eigen-decomposition of the covariance matrix to determine an updated DOA estimate for each of the K objects;
• update the third matrix based at least partially on the updated DOA estimates;
• update the second matrix based at least partially on a fifth matrix that is a diagonal matrix based on the updated DOA estimates and a sixth matrix that includes eigenvectors corresponding to the covariance matrix;
• update the first matrix in accordance with a cost function that is a function of the updated second matrix, the updated third matrix, and the sixth matrix;
• and
• use the updated first matrix and the updated second matrix when processing additional signals received by the antenna array to determine additional direction of arrival (DOA) estimates for each of the K objects.