Transmit MIMO Radar Beampattern Design via Optimization on the Complex Circle Manifold
Transmit MIMO Radar Beampattern Design via Optimization on the Complex Circle Manifold
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DOI：
10.1109/tsp.2019.2914884
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发表时间：
2019-04
影响因子：
5.4
通讯作者：
Khaled Alhujaili;V. Monga;M. Rangaswamy
中科院分区：
文献类型：
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作者：
Khaled Alhujaili;V. Monga;M. Rangaswamy
多输入多输出（MIMO）雷达系统适应天线波形的能力使得发射波束方向图设计更加灵活。在认知雷达中，一个流行的成本函数是最小化与理想波束模式的偏差（这是通过对环境的了解而达到的）。在发射波形存在实际约束的情况下，发射波束方向图的优化变得特别具有挑战性。这类约束中最难的一个是非凸恒模约束，这是最近许多工作的主题。与大多数现有方法不同，我们开发了一种解决方案，该解决方案涉及非凸复圆流形的直接优化。也就是说，我们推导了一种新的投影、下降和收缩（PDR）更新策略，该策略允许单调成本函数改进，同时保持复圆流形（常模集）上的可行性。对于二次代价函数（如波束方向偏离的情况），我们提供了单调代价函数改进的分析保证以及收敛到局部最小值的证明。我们将提出的PDR算法与其他候选MIMO波束图设计方法进行了比较，结果表明PDR算法可以优于竞争的宽带波束图设计方法，同时计算成本更低。最后，通过在波束方向图代价函数中添加惩罚项，将天线间的正交性纳入PDR框架。通过正交波形，还证明了对目标方向失配的鲁棒性。
The ability of multiple-input multiple-output (MIMO) radar systems to adapt waveforms across antennas allows flexibility in the transmit beampattern design. In cognitive radar, a popular cost function is to minimize the deviation against an idealized beampattern (which is arrived at with knowledge of the environment). The optimization of the transmit beampattern becomes particularly challenging in the presence of practical constraints on the transmit waveform. One of the hardest of such constraints is the non-convex constant modulus constraint, which has been the subject of much recent work. In a departure from most existing approaches, we develop a solution that involves direct optimization over the non-convex complex circle manifold. That is, we derive a new projection, descent, and retraction (PDR) update strategy that allows for monotonic cost function improvement while maintaining feasibility over the complex circle manifold (constant modulus set). For quadratic cost functions (as is the case with beampattern deviation), we provide analytical guarantees of monotonic cost function improvement along with proof of convergence to a local minima. We evaluate the proposed PDR algorithm against other candidate MIMO beampattern design methods and show that PDR can outperform competing wideband beampattern design methods while being computationally less expensive. Finally, orthogonality across antennas is incorporated in the PDR framework by adding a penalty term to the beampattern cost function. Enabled by orthogonal waveforms, robustness to target direction mismatch is also demonstrated.