Logarithmic-Domain Array Interpolation for Improved Direction of Arrival Estimation in Automotive Radars

Abstract

In automotive radar systems, a limited number of antenna elements are used to estimate the angle of the target. Therefore, array interpolation techniques can be used for direction of arrival (DOA) estimation to achieve high angular resolution. In general, to generate interpolated array elements from original array elements, the method of linear least squares (LLS) is used. When the LLS method is used, the amplitudes of the interpolated array elements may not be equivalent to those of the original array elements. In addition, through the transformation matrix obtained from the LLS method, the phases of the interpolated array elements are not precisely generated. Therefore, we propose an array transformation matrix that generates accurate phases for interpolated array elements to improve DOA estimation performance, while maintaining constant amplitudes of the array elements. Moreover, to enhance the effect of our interpolation method, a power calibration method for interpolated received signals is also proposed. Through the simulation, we confirm that the array interpolation accuracy and DOA estimation performance of the proposed method are improved compared to those of the conventional method. Moreover, the performance and effectiveness of our proposed method are also verified using data obtained from the commercial radar system. Because the proposed method exhibits better performance when applied to actual measurement data, it can be utilized in commercial automotive radar systems.

Keywords: array interpolation; automotive radar; direction of arrival (DOA) estimation.

Figure 1

Two types of interpolation errors from ${\mathbf{T}}^{*}$ and ${\mathbf{V}}^{*}$.

Figure 2

Normalized Bartlett pseudospectrums for two adjacent targets located at $[-{3.5}^{\circ },{2.5}^{\circ }]$.

Figure 3

Resolution probabilities versus SNR ($N=4$).

Figure 4

Root mean squared errors versus SNR ($N=4$).

Figure 5

Resolution probabilities versus the number of time samples (SNR is 10 dB).

Figure 6

Root mean squared errors versus the number of time samples (SNR is 10 dB).

Figure 7

Normalized pseudospectrums for three targets located at $[-8^{\circ },{1.5}^{\circ },{7.5}^{\circ }]$.

Figure 8

Resolution probabilities versus SNR ($N=3$).

Figure 9

Root mean squared errors versus SNR ($N=3$).

Figure 10

Resolution probabilities versus SNR ($N=5$).

Figure 11

Root mean squared errors versus SNR ($N=5$).

Figure 12

Measurement environment of two target vehicles located at $[-{1.7}^{\circ },{4.6}^{\circ }$].

Figure 13

Measurement environment of two target vehicles (expressway).