In array signal processing, a fundamental problem is to design a sensor array with low-redundancy and reduced mutual coupling, which are the main features to improve the performance of direction-of-arrival (DOA) estimation. For a $N$-sensor array with aperture $L$, it is called low-redundancy (LR) if the ratio $R=N(N-1)/(2L)$ is approaching the Leech's bound $1.217\leq R_{opt}\leq 1.674$ for $N\rightarrow\infty$; and the mutual coupling is often reduced by decreasing the numbers of sensor pairs with the first three smallest inter-spacings, denoted as $\omega(a)$ with $a\in\{1,2,3\}$. Many works have been done to construct large LRAs, whose spacing structures all coincide with a common pattern ${\mathbb D}=\{a_1,a_2,\ldots,a_{s_1},c^\ell,b_1,b_2,\ldots,b_{s_2}\}$ with the restriction $s_1+s_2=c-1$. Here $a_i,b_j,c$ denote the spacing between adjacent sensors, and $c$ is the largest one. The objective of this paper is to find some new arrays with lower redundancy ratio or lower mutual coupling compared with known arrays. In order to do this, we give a new restriction for ${\mathbb D}$ to be $s_1+s_2=c$ , and obtain 2 classes of $(4r+3)$-type arrays, 2 classes of $(4r+1)$-type arrays, and 1 class of $(4r)$-type arrays for any $N\geq18$. Here the $(4r+i)$-Type means that $c\equiv i\pmod4$. Notably, compared with known arrays with the same type, one of our new $(4r+1)$-type array and the new $(4r)$-type array all achieves the lowest mutual coupling, and their uDOFs are at most 4 less for any $N\geq18$; compared with SNA and MISC arrays, the new $(4r)$-type array has a significant reduction in both redundancy ratio and mutual coupling. We should emphasize that the new $(4r)$-type array in this paper is the first class of arrays achieving $R<1.5$ and $\omega(1)=1$ for any $N\geq18$.

翻译：在阵列信号处理中，设计具有低冗余和低互耦的传感器阵列是提升波达方向（DOA）估计性能的关键问题。对于孔径为$L$的$N$传感器阵列，若其冗余率$R=N(N-1)/(2L)$趋近于Leech界$1.217\leq R_{opt}\leq 1.674$（当$N\rightarrow\infty$时），则称其为低冗余（LR）阵列；互耦效应通常通过减少前三个最小间距的传感器对数量（记为$\omega(a)$，$a\in\{1,2,3\}$）来降低。现有研究已构建多种大型低冗余阵列（LRA），其间距结构均遵循统一模式${\mathbb D}=\{a_1,a_2,\ldots,a_{s_1},c^\ell,b_1,b_2,\ldots,b_{s_2}\}$，且满足约束$s_1+s_2=c-1$，其中$a_i,b_j,c$表示相邻传感器间距，$c$为最大间距。本文旨在寻找比已知阵列具有更低冗余率或更低互耦的新阵列。为此，我们提出新约束条件$s_1+s_2=c$，并针对任意$N\geq18$得到2类$(4r+3)$型阵列、2类$(4r+1)$型阵列和1类$(4r)$型阵列。这里$(4r+i)$型表示$c\equiv i\pmod4$。值得注意的是，与同类型已知阵列相比，我们新提出的$(4r+1)$型阵列和$(4r)$型阵列均实现最低互耦，且其uDOF值在任意$N\geq18$时最多仅减少4；与SNA和MISC阵列相比，新$(4r)$型阵列在冗余率和互耦两方面均有显著降低。需强调，本文提出的$(4r)$型阵列是首类可在任意$N\geq18$时同时实现$R<1.5$和$\omega(1)=1$的阵列。