In this article, we propose a new algorithm that designs a transmit beampattern for multiple-input multiple-output (MIMO) radar considering coexistence with other wireless systems. This design process is conducted by minimizing the deviation of the generated beampattern (which in turn is a function of the transmit waveform) against an idealized one while enforcing the waveform elements to be constant modulus and in the presence of spectral restrictions. This leads to a hard nonconvex optimization problem primarily due to the presence of the constant modulus constraint (CMC). In this article, we exploit the geometrical structure of CMC, i.e., we redefine this constraint as an intersection of two sets (one convex and other nonconvex). This new perspective allows us to solve the nonconvex design problem via a tractable method called iterative beampattern with spectral design (IBS). In particular, the proposed IBS algorithm develops and solves a sequence of convex problems such that constant modulus is achieved at convergence. Crucially, we show that at convergence the obtained solution satisfies the Karush–Kuhn–Tucker conditions of the aforementioned nonconvex problem. Finally, we evaluate the proposed algorithm over challenging simulated scenarios, and show that it outperforms the state-of-the-art competing methods.

中文翻译：

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恒定模量约束下光谱兼容的 MIMO 雷达波束图设计

在本文中，我们提出了一种新算法，该算法考虑与其他无线系统的共存，为多输入多输出 (MIMO) 雷达设计发射波束图。这个设计过程是通过最小化生成的波束图（它是发射波形的函数）与理想化波束图的偏差来进行的，同时强制波形元素为恒模并在存在频谱限制的情况下。这主要是由于恒模量约束 (CMC) 的存在导致了一个困难的非凸优化问题。在这篇文章中，我们利用了 CMC 的几何结构，即将这个约束重新定义为两个集合的交集（一个是凸的，另一个是非凸的）。这种新视角使我们能够通过一种称为具有光谱设计的迭代波束图案 (IBS) 的易处理方法来解决非凸设计问题。特别是，所提出的 IBS 算法开发并解决了一系列凸问题，以便在收敛时实现恒模。至关重要的是，我们表明在收敛时获得的解决方案满足上述非凸问题的 Karush-Kuhn-Tucker 条件。最后，我们在具有挑战性的模拟场景中评估了所提出的算法，并表明它优于最先进的竞争方法。我们表明在收敛时获得的解满足上述非凸问题的 Karush-Kuhn-Tucker 条件。最后，我们在具有挑战性的模拟场景中评估了所提出的算法，并表明它优于最先进的竞争方法。我们表明在收敛时获得的解满足上述非凸问题的 Karush-Kuhn-Tucker 条件。最后，我们在具有挑战性的模拟场景中评估了所提出的算法，并表明它优于最先进的竞争方法。