In this paper, we consider a multiple-input multiple-output (MIMO) radar system for localizing a target based on its reflected echo signals. Specifically, we aim to estimate the random and unknown angle information of the target, by exploiting its prior distribution information. First, we characterize the estimation performance by deriving the posterior Cram\'er-Rao bound (PCRB), which quantifies a lower bound of the estimation mean-squared error (MSE). Since the PCRB is in a complicated form, we derive a tight upper bound of it to approximate the estimation performance. Based on this, we analytically show that by exploiting the prior distribution information, the PCRB is always no larger than the Cram\'er-Rao bound (CRB) averaged over random angle realizations without prior information exploitation. Next, we formulate the transmit signal optimization problem to minimize the PCRB upper bound. We show that the optimal sample covariance matrix has a rank-one structure, and derive the optimal signal solution in closed form. Numerical results show that our proposed design achieves significantly improved PCRB performance compared to various benchmark schemes.

翻译：本文研究基于目标反射回波信号进行定位的多输入多输出（MIMO）雷达系统。具体而言，我们通过利用目标的先验分布信息，旨在估计随机且未知的目标角度信息。首先，我们推导了后验克拉美-罗界（PCRB）来表征估计性能，该界量化了估计均方误差（MSE）的下界。由于PCRB形式复杂，我们推导了其紧上界以近似估计性能。基于此，我们通过分析证明：利用先验分布信息后，PCRB始终不大于未利用先验信息时随机角度实现的平均克拉美-罗界（CRB）。其次，我们将发射信号优化问题建模为最小化PCRB上界。研究表明最优样本协方差矩阵具有秩一结构，并推导了闭式最优信号解。数值结果表明，与多种基准方案相比，所提设计实现了显著改善的PCRB性能。