Systems and methods for generating independent transmit and receive calibration matrices for MIMO radar systems

1 . A method comprising:

receiving, with at least one processor, a full calibration matrix for a multiple-input multiple-output (MIMO) radar system having N physical transmit channels, M physical receive channels, and N×M virtual transmit-receive channels, the full calibration matrix being an NM×NM complex matrix of calibration values previously generated based on chamber measurement data for the MIMO radar system;

determining, with the at least one processor, a transmit calibration matrix and a receive calibration matrix based on the full calibration matrix, the transmit calibration matrix being an N×N complex matrix of calibration values for the MIMO radar system and the receive calibration matrix being an M×M complex matrix of calibration values for the MIMO radar system; and

communicating, with the at least one processor, the transmit calibration matrix and the receive calibration matrix to the MIMO radar system;

wherein the MIMO radar system uses the calibration values of the transmit calibration matrix and receive calibration matrix to compensate antenna responses to adjust for physical characteristics of the MIMO radar system while performing at least one of ranging and detection of an object in an environment of the MIMO radar system.

2 . The method of claim 1 , wherein determining, with the at least one processor, the transmit calibration matrix and the receive calibration matrix includes using singular value decomposition of a permuted version of the full calibration matrix to determine a one-dimensional N×N array corresponding to a vector version of the transmit calibration matrix and a one-dimensional M×M array corresponding to a vector version of the receive calibration matrix and reforming the one-dimensional N×N array and the one-dimensional M×M array into the transmit calibration matrix and the receive calibration matrix, respectively.

3 . The method of claim 1 , wherein the MIMO radar system is installed in a vehicle and the communicating, with the at least one processor, the transmit calibration matrix and the receive calibration matrix to the MIMO radar system includes wirelessly communicating the transmit calibration matrix and the receive calibration matrix to the MIMO radar system.

4 . The method of claim 1 , wherein the full calibration matrix is previously stored in a memory of the MIMO radar system during manufacture of the MIMO radar system and, upon receiving the transmit calibration matrix and the receive calibration matrix, the MIMO radar system removes the full calibration matrix from the memory of the MIMO radar system and stores the transmit calibration matrix and the receive calibration matrix in the memory of the MIMO radar system.

5 . The method of claim 1 , wherein the determining, with the at least one processor, the transmit calibration matrix and the receive calibration matrix is performed based on a nearest Kronecker product (NKP) problem that includes minimizing the following function with respect to the transmit calibration matrix and the receive calibration matrix:

f

⁡

(

C

t

,

C

r

)

=



C

-

C

t

⊗

C

r



F

wherein C is the full calibration matrix, C t is the transmit calibration matrix, and C r is the receive calibration matrix.

6 . The method of claim 1 , wherein the physical characteristics of the MIMO radar system include at least one of mutual coupling of transmit/receive components of the MIMO radar system, differences in transmission and receive circuitry of the MIMO radar system, and differences in transmission and receive line lengths for each of the N physical transmit channels and the M physical receive channels.

7 . A system comprising at least one processor and memory configured to:

receive a full calibration matrix for a multiple-input multiple-output (MIMO) radar system having N physical transmit channels, M physical receive channels, and N×M virtual transmit-receive channels, the full calibration matrix being an NM×NM complex matrix of calibration values previously generated based on chamber measurement data for the MIMO radar system;

determine a transmit calibration matrix and a receive calibration matrix based on the full calibration matrix, the transmit calibration matrix being an N×N complex matrix of calibration values for the MIMO radar system and the receive calibration matrix being an M×M complex matrix of calibration values for the MIMO radar system; and

communicate the transmit calibration matrix and the receive calibration matrix to the MIMO radar system;

wherein the MIMO radar system uses the calibration values of the transmit calibration matrix and receive calibration matrix to compensate antenna responses to adjust for physical characteristics of the MIMO radar system while performing at least one of ranging and detection of an object in an environment of the MIMO radar system.

8 . The system of claim 7 , wherein the at least one processor and memory are configured to determine the transmit calibration matrix and the receive calibration matrix by using singular value decomposition of a permuted version of the full calibration matrix to determine a one-dimensional N×N array corresponding to a vector version of the transmit calibration matrix and a one-dimensional M×M array corresponding to a vector version of the receive calibration matrix and reforming the one-dimensional N×N array and the one-dimensional M×M array into the transmit calibration matrix and the receive calibration matrix, respectively.

9 . The system of claim 7 , wherein the MIMO radar system is installed in a vehicle and the at least one processor and memory are configured to communicate the transmit calibration matrix and the receive calibration matrix to the MIMO radar system by wirelessly communicating the transmit calibration matrix and the receive calibration matrix to the MIMO radar system.

10 . The system of claim 7 , wherein the full calibration matrix is previously stored in a memory of the MIMO radar system during manufacture of the MIMO radar system and, upon receiving the transmit calibration matrix and the receive calibration matrix, the MIMO radar system removes the full calibration matrix from the memory of the MIMO radar system and stores the transmit calibration matrix and the receive calibration matrix in the memory of the MIMO radar system.

11 . The system of claim 7 , wherein the at least one processor and memory are configured to determine the transmit calibration matrix and the receive calibration matrix based on a nearest Kronecker product (NKP) problem that includes minimizing the following function with respect to the transmit calibration matrix and the receive calibration matrix:

f

⁡

(

C

t

,

C

r

)

=



C

-

C

t

⊗

C

r



F

wherein C is the full calibration matrix, C t is the transmit calibration matrix, and C r is the receive calibration matrix.

12 . The system of claim 7 , wherein the physical characteristics of the MIMO radar system include at least one of mutual coupling of transmit/receive components of the MIMO radar system, differences in transmission and receive circuitry of the MIMO radar system, and differences in transmission and receive line lengths for each of the N physical transmit channels and the M physical receive channels.

13 . A method of updating calibration data stored in a memory of a multiple-input multiple-output (MIMO) radar system having N physical transmit channels, M physical receive channels, and N×M virtual transmit-receive channels, the calibration data including a full calibration matrix, the full calibration matrix being an NM×NM complex matrix of calibration values previously generated based on chamber measurement data for the MIMO radar system, the method comprising:

receiving, with at least one processor, the full calibration matrix for MIMO radar system;

determining, with the at least one processor, a transmit calibration matrix and a receive calibration matrix based on the full calibration matrix, the transmit calibration matrix being an N×N complex matrix of calibration values for the MIMO radar system and the receive calibration matrix being an M×M complex matrix of calibration values for the MIMO radar system;

communicating, with the at least one processor, the transmit calibration matrix and the receive calibration matrix to the MIMO radar system; and

communicating, with the at least one processor, updated operating code that configures the MIMO radar system to perform calibration using the transmit calibration matrix and the receive calibration matrix to the MIMO radar system;

wherein:

the MIMO radar system uses the calibration values of the transmit calibration matrix and receive calibration matrix to compensate antenna responses to adjust for physical characteristics of the MIMO radar system while performing at least one of ranging and detection of an object in an environment of the MIMO radar system;

in response to receiving the transmit calibration matrix and the receive calibration matrix, the MIMO radar system is configured to remove the full calibration matrix from the calibration data stored in the memory and to store the transmit calibration matrix and the receive calibration matrix in the memory; and

in response to receiving the updated operating code, the MIMO radar system is configured to install the updated operation code to perform calibration using the transmit calibration matrix and the receive calibration matrix to the MIMO radar system.

14 . The method of claim 13 , wherein determining, with the at least one processor, the transmit calibration matrix and the receive calibration matrix is performed by using singular value decomposition of a permuted version of the full calibration matrix to determine a one-dimensional N×N array corresponding to a vector version of the transmit calibration matrix and a one-dimensional M×M array corresponding to a vector version of the receive calibration matrix and reforming the one-dimensional N×N array and the one-dimensional M×M array into the transmit calibration matrix and the receive calibration matrix, respectively.

15 . The method of claim 13 , wherein the MIMO radar system is installed in a vehicle and the communicating, with the at least one processor, the transmit calibration matrix and the receive calibration matrix to the MIMO radar system includes wirelessly communicating the transmit calibration matrix and the receive calibration matrix to the MIMO radar system.

16 . The method of claim 13 , wherein the determining, with the at least one processor, the transmit calibration matrix and the receive calibration matrix is performed based on a nearest Kronecker product (NKP) problem that includes minimizing the following function with respect to the transmit calibration matrix and the receive calibration matrix:

f

⁡

(

C

t

,

C

r

)

=



C

-

C

t

⊗

C

r



F

wherein C is the full calibration matrix, C t is the transmit calibration matrix, and C r is the receive calibration matrix.

17 . The method of claim 13 , wherein the physical characteristics of the MIMO radar system include at least one of mutual coupling of transmit/receive components of the MIMO radar system, differences in transmission and receive circuitry of the MIMO radar system, and differences in transmission and receive line lengths for each of the N physical transmit channels and the M physical receive channels.