Controlling the radar beam-pattern by optimizing the transmit covariance matrix is a well-established approach for performance enhancement in multiple-input-multiple-output (MIMO) radars. In this paper, we investigate the joint optimization of the waveform covariance matrix and the antenna position vector for a MIMO radar system to approximate a given transmit beam-pattern, as well as to minimize the cross-correlation between the probing signals at a number of given target locations. We formulate this design task as a non-convex optimization problem and then propose a cyclic optimization approach to efficiently approximate its solution. We further propose a local binary search algorithm in order to efficiently design the corresponding antenna positions. We show that the proposed method can be extended to the more general case of approximating the given beam-pattern using a minimal number of antennas as well as optimizing their positions. Our numerical investigations demonstrate a great performance both in terms of accuracy and computational complexity, making the proposed framework a good candidate for usage in real-time radar waveform processing applications such as MIMO radar transmit beamforming for aerial drones that are in motion.

通过优化发射协方差矩阵来控制雷达波束方向图是一种行之有效的方法，用于增强多输入多输出（MIMO）雷达的性能。在本文中，我们研究了MIMO雷达系统的波形协方差矩阵和天线位置矢量的联合优化，以逼近给定的发射波束方向图，并最大程度地减小了多个雷达信号之间的互相关性。给定目标位置。我们将此设计任务表述为非凸优化问题，然后提出一种循环优化方法来有效地逼近其解决方案。我们还提出了一种本地二进制搜索算法，以有效地设计相应的天线位置。我们表明，所提出的方法可以扩展到使用最少数量的天线以及优化其位置来逼近给定波束模式的更一般情况。我们的数值研究表明，在准确性和计算复杂性方面均具有出色的性能，使所提出的框架成为用于实时雷达波形处理应用（例如MIMO雷达发射波束成形在运动中的空中无人机）的良好候选者。