Radar system with sparse primary array and dense auxiliary array

1. A radar system comprising one or more processors configured to:

determine, based on electromagnetic (EM) energy that is received at a primary subarray of an antenna array, first potential angles of one or more objects that are reflecting the EM energy to the antenna array, the primary subarray comprising multiple first antenna elements;

determine, based on the EM energy that is received at an auxiliary subarray of the antenna array, second potential angles of the one or more objects, the auxiliary subarray comprising multiple second antenna elements, the second antenna elements having a smaller spacing than the first antenna elements; and

determine, based on the first potential angles and the second potential angles, at least one respective angle associated with each of the one or more objects by:

generating, based on the EM energy that is respectively received at the primary subarray and the auxiliary subarray, fast Fourier transform (FFT) spectrum magnitudes for the primary subarray and the auxiliary subarray using a FFT with a pre-defined window;

normalizing and aligning the FFT spectrum magnitudes for the primary subarray and the auxiliary subarray;

identifying, based on the normalized and aligned FFT spectrum magnitudes, primary spectrum peaks and auxiliary spectrum peaks;

filtering out, based on at least one of a magnitude or slope, unqualified spectrum peaks from among the primary spectrum peaks and the auxiliary spectrum peaks; and

outputting non-filtered spectrum peaks from among the primary spectrum peaks and the auxiliary spectrum peaks as the at least one respective angle associated with each of the one or more objects.

2. The radar system of claim 1 , wherein the primary spectrum peaks and auxiliary spectrum peaks are identified as peaks from the normalized and aligned FFT spectrum magnitudes that are above a threshold value.

3. The radar system of claim 2 , wherein the threshold value is inversely proportional to a signal-to-noise ratio of the EM energy received at the auxiliary subarray.

4. The radar system of claim 1 , wherein in determining the at least one respective angle associated with each of the one or more objects, the one or more processors are further configured to:

generate unfolded potential angles by unfolding the first potential angles to multiple intervals;

filter the unfolded first potential angles from the FFT spectrum magnitudes for the auxiliary subarray to construct an angle dictionary; and

determine, using an L1-minimization-based function on the EM energy that is received at the auxiliary subarray and the angle dictionary, non-zero elements in a selection vector, the non-zero elements in the selection vector representing the at least one respective angle associated with each of the one or more objects.

5. The radar system of claim 1 , wherein the primary subarray and the auxiliary subarray are uniform linear arrays, wherein the antenna elements of the uniform linear arrays are equally spaced.

6. The radar system of claim 1 , wherein the primary subarray is positioned in an azimuth direction, and the auxiliary subarray is positioned in line with the primary subarray in the same azimuth direction.

7. The radar system of claim 1 , wherein the primary subarray and the auxiliary subarray are positioned in an azimuth direction, and the auxiliary subarray is positioned with an elevation offset from the primary subarray.

8. The radar system of claim 1 , wherein the primary subarray and the auxiliary subarray are positioned in an azimuth direction, and the auxiliary subarray overlaps with at least a portion of the primary subarray.

9. The radar system of claim 1 , wherein a quantity of the first antenna elements is greater than a quantity of the second antenna elements.

10. The radar system of claim 1 , wherein a ratio of a spacing of the first antenna elements to a spacing of the second antenna elements is approximately equal to an integer.

11. The radar system of claim 10 , wherein the integer is an exponential of two.

12. The radar system of claim 1 , wherein the radar system is configured to be installed on an automobile.

13. A method comprising:

determining, based on electromagnetic (EM) energy that is received at a primary subarray of an antenna array, first potential angles of one or more objects that are reflecting the EM energy to the antenna array, the primary subarray comprising multiple first antenna elements;

determining, based on the EM energy that is received at an auxiliary subarray of the antenna array, second potential angles of the one or more objects, the auxiliary subarray comprising multiple second antenna elements, the second antenna elements having a smaller spacing than the first antenna elements; and

determining, based on the first potential angles and the second potential angles, at least one respective angle associated with each of the one or more objects by:

generating, based on the EM energy that is respectively received at the primary subarray and the auxiliary subarray, fast Fourier transform (FFT) spectrum magnitudes for the primary subarray and the auxiliary subarray using a FFT with a pre-defined window;

normalizing and aligning the FFT spectrum magnitudes for the primary subarray and the auxiliary subarray;

identifying, based on the normalized and aligned FFT spectrum magnitudes, primary spectrum peaks and auxiliary spectrum peaks;

filtering out, based on at least one of a magnitude or slope, unqualified spectrum peaks from among the primary spectrum peaks and the auxiliary spectrum peaks; and

outputting non-filtered spectrum peaks from among the primary spectrum peaks and the auxiliary spectrum peaks as the at least one respective angle associated with each of the one or more objects.

14. The method of claim 13 , wherein the primary spectrum peaks and auxiliary spectrum peaks are identified as peaks from the normalized and aligned FFT spectrum magnitudes that are above a threshold value.

15. The method of claim 14 , wherein the threshold value is inversely proportional to a signal-to-noise ratio of the EM energy received at the auxiliary subarray.

16. The method of claim 13 , wherein determining the at least one respective angle associated with each of the one or more objects further comprises:

generating unfolded potential angles by unfolding the first potential angles to multiple intervals;

filtering the unfolded first potential angles from the FFT spectrum magnitudes for the auxiliary subarray to construct an angle dictionary; and

determining, using an L1-minimization-based function on the EM energy that is received at the auxiliary subarray and the angle dictionary, non-zero elements in a selection vector, the non-zero elements in the selection vector representing the at least one respective angle associated with each of the one or more objects.

17. Non-transitory computer-readable storage media comprising computer-executable instructions that, when executed, cause a processor of a radar system to:

determine, based on electromagnetic (EM) energy that is received at a primary subarray of an antenna array, first potential angles of one or more objects that are reflecting the EM energy to the antenna array, the primary subarray comprising multiple first antenna elements;

determine, based on the EM energy that is received at an auxiliary subarray of the antenna array, second potential angles of the one or more objects, the auxiliary subarray comprising multiple second antenna elements, the second antenna elements having a smaller spacing than the first antenna elements; and

determine, based on the first potential angles and the second potential angles, at least one respective angle associated with each of the one or more objects by:

generating, based on the EM energy that is respectively received at the primary subarray and the auxiliary subarray, fast Fourier transform (FFT) spectrum magnitudes for the primary subarray and the auxiliary subarray using a FFT with a pre-defined window;

normalizing and aligning the FFT spectrum magnitudes for the primary subarray and the auxiliary subarray;

identifying, based on the normalized and aligned FFT spectrum magnitudes, primary spectrum peaks and auxiliary spectrum peaks;

filtering out, based on at least one of a magnitude or slope, unqualified spectrum peaks from among the primary spectrum peaks and the auxiliary spectrum peaks; and

outputting non-filtered spectrum peaks from among the primary spectrum peaks and the auxiliary spectrum peaks as the at least one respective angle associated with each of the one or more objects.

18. The non-transitory computer-readable storage media of claim 17 , wherein the primary spectrum peaks and auxiliary spectrum peaks are identified as peaks from the normalized and aligned FFT spectrum magnitudes that are above a threshold value.

19. The non-transitory computer-readable storage media of claim 18 , wherein the threshold value is inversely proportional to a signal-to-noise ratio of the EM energy received at the auxiliary subarray.

20. The non-transitory computer-readable storage media of claim 17 , wherein in determining the at least one respective angle associated with each of the one or more objects, the computer-readable storage media comprises additional computer-executable instructions that, when executed, further cause the processor to:

generate unfolded potential angles by unfolding the first potential angles to multiple intervals;

filter the unfolded first potential angles from the FFT spectrum magnitudes for the auxiliary subarray to construct an angle dictionary; and

determine, using an L1-minimization-based function on the EM energy that is received at the auxiliary subarray and the angle dictionary, non-zero elements in a selection vector, the non-zero elements in the selection vector representing the at least one respective angle associated with each of the one or more objects.