In the direction estimation for the signals incident on a sensor array, maximum likelihood (ML) based methods can provide superior performance than subspace based ones such as the multiple signal classification (MUSIC). When the incoming signals are noncircular the exploitation of the property can allow us to improve estimation performance. Based on the deterministic ML criterion, a direction estimation method for strictly noncircular signals is proposed that can outperform the conventional alternating maximization (AM) with no use of noncircularity. Using a generalized Gaussian probability density function, we approach the ML estimation, which is formulated as a nonlinear multidimensional problem. The application of the alternating projection to the multidimensional problem leads to the maximization of an objective function of two variables associated with the direction and the initial phase of a noncircular signal. Theoretically optimizing the phase variable, we obtain the maximum through one-dimensional search with respect to the direction variable only. The complexity of the proposed noncircular AM (NC-AM) is far less than that of the existing ML based method, noncircular decoupled maximization (NC-DM). Moreover, simulation results demonstrate that NC-AM outperforms NC-DM as well as the noncircular MUSIC.

中文翻译：

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非圆形信号的基于最大似然的方向估计

在对入射到传感器阵列上的信号进行方向估计时，基于最大似然 (ML) 的方法可以提供比基于子空间的方法（例如多信号分类 (MUSIC)）更优越的性能。当输入信号是非圆形时，利用该特性可以使我们提高估计性能。基于确定性ML准则，提出了一种严格非圆信号的方向估计方法，该方法可以在不使用非圆性的情况下优于传统的交替最大化（AM）。我们使用广义高斯概率密度函数来进行 ML 估计，将其表述为非线性多维问题。将交替投影应用于多维问题导致与非圆形信号的方向和初始相位相关的两个变量的目标函数的最大化。理论上优化相位变量，我们仅针对方向变量通过一维搜索来获得最大值。所提出的非循环AM（NC-AM）的复杂度远低于现有的基于机器学习的方法——非循环解耦最大化（NC-DM）。此外，仿真结果表明 NC-AM 优于 NC-DM 以及非圆形 MUSIC。