# US 10,481,242 B2 · Method for joint antenna-array calibration and direction of arrival estimation for automotive applications

> Agents: this data is available as JSON from the patentgrep API and MCP server — see https://patentgrep.com/llms.txt

- Number: US 10,481,242 B2
- Document ID: US10481242B2
- Status: Granted
- Kind: B2
- Application number: 15/145,091
- Filed: 2016-05-03
- Published: 2017-03-30
- Granted: 2019-11-19
- Earliest claimed: 2015-09-25
- Assignees: Texas Instruments Incorporated
- Applicants: Texas Instruments Incorporated
- Inventors: Muhammad Zubair Ikram; Murtaza Ali
- Web page: https://patentgrep.com/patent/US10481242B2

## CPC

- G01S 7/4004: {of parts of a radar system}
- G01S 3/023: {Monitoring or calibrating}
- G01S 7/4026: {Antenna boresight}
- G01S 19/235: {Calibration of receiver components}
- G01S 13/931: of land vehicles
- G01S 2013/0245: {Radar with phased array antenna}
- G01S: RADIO DIRECTION-FINDING; RADIO NAVIGATION; DETERMINING DISTANCE OR VELOCITY BY USE OF RADIO WAVES; LOCATING OR PRESENCE-DETECTING BY USE OF THE REFLECTION OR RERADIATION OF RADIO WAVES; ANALOGOUS ARRANGEMENTS USING OTHER WAVES

## Abstract

This invention is present an iterative method for joint antenna array calibration and direction of arrival estimation using millimeter-wave (mm-Wave) radar. The calibration compensates for array coupling, phase, and gain errors and does not require any training data. This method is well suited for applications where multiple antenna elements are packaged in a chip and where offline calibration is either expensive or is not possible. This invention is also effective when the array coupling is a function of direction of arriving waves from the object. It is also applicable to any two-dimensional array shape. Real experiment results demonstrate the viability of the algorithm using real data collected from a four-element array.

## Claims

### Claim 1

A method comprising:
determining, for a radar system having an antenna array with L antenna elements, an initial array response to K objects within a field of view of the radar system, wherein L is an integer ≥1, K is an integer ≥2, and 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;
determining a covariance matrix based on the initial array response;
performing eigen-decomposition of the covariance matrix to determine an updated DOA estimate for each of the K objects;
updating the third matrix based at least partially on the updated DOA estimates;
updating 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;
updating 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
using the updated first matrix and the updated second matrix when processing signals received by the antenna array to determine additional direction of arrival (DOA) estimates for each of the K objects.

### Claim 2 (depends on 1)

The method of claim 1, wherein the second matrix is a diagonal matrix and wherein the initial values based on the gain value and the phase value of each of the L antenna elements are arranged as diagonal elements of the second matrix.

### Claim 3 (depends on 1)

The method of claim 1, wherein:
the first matrix has dimensions L×L;
the second matrix has dimensions L×L;
the third matrix has dimensions L×K; and
the fourth matrix is a column vector having K elements.

### Claim 4 (depends on 1)

The method of claim 1, wherein the initial coupling matrix is an identity matrix.

### Claim 5 (depends on 1)

The method of claim 1, wherein the updated DOA estimate for each of the K objects includes a first component that is an azimuth direction of arrival for the object and a second component that is an elevation direction of arrival for the object.

### Claim 6 (depends on 1)

The method of claim 1, wherein each updated DOA estimate includes:
an azimuth direction of arrival for a respective one of the K objects;
an elevation direction of arrival for the respective one of the K objects; and
an eigenvalue of the covariance matrix.

### Claim 7 (depends on 1)

The method of claim 1, wherein using the updated first matrix and the updated second matrix when processing signals received by the antenna array to determine additional direction of arrival (DOA) estimates for each of the K objects results in reduced biasing error in the additional direction of arrival (DOA) estimates.

### Claim 8 (depends on 1)

The method of claim 1, wherein the L antenna elements of the antenna array are arranged in a two-dimensional arrangement with at least two of the L antenna elements being arranged in a first direction and at least one other of the L antenna elements being arranged in a manner that is orthogonal to the first direction.

### Claim 9 (depends on 1)

The method of claim 1, wherein the radar system is a millimeter-wave radar system.

### Claim 10

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.

### Claim 11 (depends on 10)

The system of claim 10, wherein the second matrix is a diagonal matrix and wherein the initial values based on the gain value and the phase value of each of the L antenna elements are arranged as diagonal elements of the second matrix.

### Claim 12 (depends on 10)

The system of claim 10, wherein:
the first matrix has dimensions L×L;
the second matrix has dimensions L×L;
the third matrix has dimensions L×K; and
the fourth matrix is a column vector having K elements.

### Claim 13 (depends on 10)

The system of claim 10, wherein the initial coupling matrix is an identity matrix.

### Claim 14 (depends on 10)

The system of claim 10, wherein each updated DOA estimate includes:
an azimuth direction of arrival for a respective one of the K objects;
an elevation direction of arrival for the respective one of the K objects; and
an eigenvalue of the covariance matrix.

### Claim 15 (depends on 10)

The system of claim 10, wherein using the updated first matrix and the updated second matrix when processing signals received by the antenna array to determine additional direction of arrival (DOA) estimates for each of the K objects results in reduced biasing error in the additional direction of arrival (DOA) estimates.

### Claim 16 (depends on 10)

The system of claim 10, wherein the L antenna elements of the antenna array are arranged in a two-dimensional arrangement with at least two of the L antenna elements being arranged in a first direction and at least one other of the L antenna elements being arranged in a manner that is orthogonal to the first direction.

### Claim 17 (depends on 10)

The system of claim 10, wherein the antenna array is part of a millimeter-wave radar system.

### Claim 18 (depends on 10)

The system of claim 10, wherein the system is an advanced driver assistance system (ADAS).

### Claim 19

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.