Given a uniform linear array (ULA) with $\mathit{M}$ sensors, most rooting-based direction of arrival (DOA) estimators used to solve polynomials with high degree $2(\mathit{M}-1)$ for source DOAs, which is time-consuming with large ULAs. In this paper, we propose a novel polynomial deflation method which can be generally used for all coefficient-symmetric rooting-based DOA estimators, e.g., root-MUSIC, unitary root-MUSIC (U-root-MUSIC), real-valued root-MUSIC (RV-root-MUSIC), etc. We prove that for $\mathit{L}<\mathit{M}$ sources, the greatest common divisor (GCD) of original polynomial and its derivative contains DOA information and has reduced degree about $\mathit{L}$. Therefore, DOA can be obtained by GCD directly. Numerical simulations are conducted to demonstrate that with significantly reduced complexity, such a GCD method can provide satisfactory performance close to the Cram$\acute{\text{e}}$r-Rao Lower Bound (CRLB).

给定一个均匀线性阵列 (ULA) $\mathit{米}$ 传感器，大多数基于生根的到达方向 (DOA) 估计器用于求解高阶多项式 $2(\mathit{米}-1)$对于源 DOA，这对于大型 ULA 来说非常耗时。在本文中，我们提出了一种新的多项式紧缩方法，该方法通常可用于所有基于系数对称根的 DOA 估计器，例如 root-MUSIC、酉根-MUSIC（U-root-MUSIC）、实值根- MUSIC (RV-root-MUSIC) 等。我们证明对于$\mathit{升}<\mathit{米}$ 源，原始多项式及其导数的最大公约数（GCD）包含 DOA 信息，并降低了约 $\mathit{升}$. 因此，可以直接通过 GCD 获得 DOA。进行数值模拟以证明在显着降低复杂性的情况下，这种 GCD 方法可以提供接近 Cram 的令人满意的性能$\acute{\text{电子}}$r-Rao 下限 (CRLB)。