High-precision fast direction-of-arrival estimation method for planar array

The proposed high-precision fast direction-of-arrival estimation method for planar array includes two steps, and the expression of the result includes two items:

1) a 2-stage grid search approach over the 2-dimensional spectrum is applied to obtain a quick coarse estimation of DOA. In the first stage, the 2D discretized spectrum is obtained with relatively large search steps on large spatial search range, to obtain the coarse estimations of signal directions; in the second stage, the search range is reduced to only a small spectrum region centered at the coarse estimation obtained in the first stage and search steps are smaller, thus obtaining refined estimations of signal directions, which is also the first item of the final expression.

2) the high-precision estimation is achieved on the basis of the quadratic surface fitting method. Assume that the refined spatial spectrum is a quadratic surface and has a corresponding fitting function with six coefficients. Nine points of the spectrum are selected (as shown in Fig. 2), and the coefficients can be determined by the least square method. Afterwards, the derivatives of the surface fitting function are zeros which should be solved, leading to the second item of the final expression.

Simulation results verified the effectiveness of the proposed method. In simulation, the uniform planar array is of 10 × 10 antenna elements with half-wavelength antenna element spacing along both the horizontal and vertical directions. Three independent signal sources with equal signal-to-noise ratio (SNR) are from three different directions. The additive white Gaussian noise is considered. The root mean square error is as the estimation metric and 200 independent Monte Carlo simulations are carried out. The proposed method is assessed and compared with other three kinds of MUSIC methods. From results shown in Figs. 3 and 4, it is found that the performance of the proposed method is much better than the conventional DOA estimation methods for planar array.