通过二次优化设计单模码并非总是困难的
Designing Unimodular Codes via Quadratic Optimization is not Always Hard
AI总结：
针对单模二次规划（UQP）的NP难问题，提出一种专用局部优化方案和单调误差界改进技术（MERIT），在雷达码设计等场景中实现高效求解并给出优于半定松弛的次优性保证。
摘要：
在雷达码设计场景以及其他主动感知和通信应用中，存在一个NP难问题：在单模向量集上优化二次型。为了解决这个问题（我们称之为单模二次规划（UQP）），人们设计并研究了几种计算方法。引入了一种专门针对UQP的局部优化方案，并证明其相比一般局部优化方法能产生更优结果。此外，提出了一种 extbf{单调误差界改进技术}（MERIT），以获得UQP的全局最优解或具有良好次优性保证的局部最优解。所提供的次优性保证是依赖于具体情况的，并且通常优于半定松弛的$π/4$近似保证。给出了几个数值示例来说明所提方法的性能。示例表明，对于包括雷达码设计中使用的几种矩阵结构的情况，MERIT能够在次优性保证和计算时间方面高效求解UQP。
英文摘要：
The NP-hard problem of optimizing a quadratic form over the unimodular vector set arises in radar code design scenarios as well as other active sensing and communication applications. To tackle this problem (which we call unimodular quadratic programming (UQP)), several computational approaches are devised and studied. A specialized local optimization scheme for UQP is introduced and shown to yield superior results compared to general local optimization methods. Furthermore, a \textbf{m}onotonically \textbf{er}ror-bound \textbf{i}mproving \textbf{t}echnique (MERIT) is proposed to obtain the global optimum or a local optimum of UQP with good sub-optimality guarantees. The provided sub-optimality guarantees are case-dependent and generally outperform the $π/4$ approximation guarantee of semi-definite relaxation. Several numerical examples are presented to illustrate the performance of the proposed method. The examples show that for cases including several matrix structures used in radar code design, MERIT can solve UQP efficiently in the sense of sub-optimality guarantee and computational time.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
