Estimating the covariance matrix of a random vector is essential and challenging in large dimension and small sample size scenarios. The purpose of this paper is to produce an outperformed large-dimensional covariance matrix estimator in the complex domain via the linear shrinkage regularization. Firstly, we develop a necessary moment property of the complex Wishart distribution. Secondly, by minimizing the mean squared error between the real covariance matrix and its shrinkage estimator, we obtain the optimal shrinkage intensity in a closed form for the spherical target matrix under the complex Gaussian distribution. Thirdly, we propose a newly available shrinkage estimator by unbiasedly estimating the unknown scalars involved in the optimal shrinkage intensity. Both the numerical simulations and an example application to array signal processing reveal that the proposed covariance matrix estimator performs well in large dimension and small sample size scenarios.

中文翻译：

---

复杂高斯分布下大协方差矩阵的改进收缩估计

在大尺寸和小样本情况下，估计随机向量的协方差矩阵至关重要且具有挑战性。本文的目的是通过线性收缩正则化在复杂域中生成一个性能优于大型协方差矩阵的估计器。首先，我们开发了复杂的Wishart分布的必要矩性质。其次，通过最小化实际协方差矩阵与其收缩估计量之间的均方误差，我们获得了复杂高斯分布下球形目标矩阵封闭形式的最佳收缩强度。第三，通过无偏估计最佳收缩强度所涉及的未知标量，我们提出了一种新的收缩估计器。