In this paper, we consider the problem of two-dimensional (2-D) direction of arrival (DOA) estimation for L-shaped monostatic MIMO radar with two-level nested linear array (NLA). To obtain more degrees of freedom (DOFs) than traditional nested L-shaped (NLs) MIMO radar, we propose the extensional NLs (ENLs) MIMO radar by extending all of the sensor positions in transmitter array with an identical magnification compared with NLs MIMO radar. The ENLs MIMO radar can offer $O(M_1{M}_2{N}_1{N}_2)$ DOFs with only $O(M_1+M_2+N_1+N_2)$ sensors, where $M_1(N_1)$ and $M_2(N_2)$ respectively represents the numbers of the first-level and second-level sensors of NLA in transmitter (receiver) array. Furthermore, to avoid the eigenvalue decomposition, spatial spectral search and polynomial root finding technique in spatial smoothing multiple signals classification (SS-MUSIC) and SS-ROOT-MUSIC, and to improve the estimation accuracy simultaneously, we propose a search-free iterative Taylor expansion (SF-ITE) algorithm to perform DOA estimation, which employs the Discrete Fourier transform (DFT) method to get the coarse estimation, and then utilizes the iterative Taylor expansion technique to obtain fine estimation. SF-ITE can get more precise estimation by performing iteration only once than both SS-MUSIC and SS-ROOT-MUSIC. In addition, we derive an angle-pairing procedure to help to eventually resolve more targets than the total number of sensors. Finally, simulation results are provided to validate the superiority of the ENLs MIMO radar and SF-ITE algorithm.

在本文中，我们考虑了具有两级嵌套线性阵列（NLA）的L型单基地MIMO雷达的二维（2-D）到达方向（DOA）估计问题。为了获得比传统的嵌套L形（NLs）MIMO雷达更多的自由度（DOF），我们提出了扩展NLs（ENLs）MIMO雷达，方法是与NLs MIMO雷达相比以相同的放大倍数扩展发射机阵列中的所有传感器位置。ENLs MIMO雷达可以提供$Ø（{\mathrm{中号}}_{\mathrm{1个}}{\mathrm{中号}}_2{ñ}_{\mathrm{1个}}{ñ}_2）$ 自由度仅 $Ø（{\mathrm{中号}}_{\mathrm{1个}}+{\mathrm{中号}}_2+{ñ}_{\mathrm{1个}}+{ñ}_2）$ 传感器，在哪里 ${\mathrm{中号}}_{\mathrm{1个}}（{ñ}_{\mathrm{1个}}）$ 和 ${\mathrm{中号}}_2（{ñ}_2）$分别表示发射机（接收机）阵列中NLA的第一级和第二级传感器的数量。此外，为避免空间平滑多信号分类（SS-MUSIC）和SS-ROOT-MUSIC中的特征值分解，空间谱搜索和多项式根查找技术，同时提高估计精度，我们提出了一种免搜索的迭代泰勒算法扩展（SF-ITE）算法进行DOA估计，该算法采用离散傅里叶变换（DFT）方法获得粗略估计，然后利用迭代泰勒展开技术获得精细估计。与SS-MUSIC和SS-ROOT-MUSIC相比，SF-ITE通过仅执行一次迭代即可获得更精确的估计。此外，我们推导了一个角度配对程序，以帮助最终解决比传感器总数更多的目标。最后，提供了仿真结果以验证ENLs MIMO雷达和SF-ITE算法的优越性。