A sequence set with ambiguity function (AF) specifications is frequently required in multi-transmit active sensing systems which exploit waveform diversity. This paper formulates a new model to jointly design sequence set and mismatched filter bank with AF requirements, which is a generalization of the auto-AF and cross-AF adopted in the matched filter scheme to attain lower AF sidelobe levels with an increased degree-of-freedom. The aforementioned designs result in nonconvex and nonlinear high-order polynomial (HOP) optimization problems with HOP constraints. Although the maximum block improvement (MBI) method has exhibited the powerful HOP optimization ability to design a short sequence with slow-time AF, it cannot tackle HOP constraints and involves high-complexity tensor operations. To address these issues, we develop a generalized MBI method for the HOP constrained optimization formulations. In addition, the proposed algorithm significantly reduces the computational complexity via designing an equivalent polynomial function for the original multi-linear tensor function. Numerical results demonstrate the excellent performance of our design solutions.

中文翻译：

---

具有模糊函数约束的序列集和失配滤波器组设计的广义MBI算法

在利用波形分集的多发射主动传感系统中，经常需要具有模糊函数 (AF) 规范的序列集。本文提出了一种新的模型来联合设计序列集和失配滤波器组来满足 AF 要求，这是对匹配滤波器方案中采用的自动 AF 和交叉 AF 的推广，以实现更低的 AF 旁瓣水平和增加的度数。 -自由。上述设计导致具有 HOP 约束的非凸和非线性高阶多项式 (HOP) 优化问题。尽管最大块改进 (MBI) 方法展示了强大的 HOP 优化能力来设计具有慢时间 AF 的短序列，但它不能解决 HOP 约束并且涉及高复杂度的张量操作。为了解决这些问题，我们为 HOP 约束优化公式开发了一种广义 MBI 方法。此外，该算法通过为原始多线性张量函数设计等效多项式函数，显着降低了计算复杂度。数值结果证明了我们设计解决方案的卓越性能。