论文标题
多相golay互补阵列的结构
Constructions of Polyphase Golay Complementary Arrays
论文作者
论文摘要
Golay互补矩阵（GCM）由于其在全向预编码中的潜在应用，最近引起了相当大的关注。在本文中，我们将GCM推广到多维Golay互补阵列（GCA），并提出了GCA对和GCA四边形的新结构。通过在交换环上引入一组身份来促进这些结构。我们证明，如果在所有维度上的阵列大小的乘积是第四纪的golay数字，则对产品的分解有其他限制，则可以证明第四纪GCA对是可行的。对于二进制GCM四边形，我们猜想可行的尺寸是任意的，并在78 $ \ tims $ 78和其他较少密度分布的尺寸内验证尺寸。对于第四纪GCM四边形，可以覆盖1000范围内的所有正整数，以在一个维度中的尺寸覆盖。
Golay complementary matrices (GCM) have recently drawn considerable attentions owing to its potential applications in omnidirectional precoding. In this paper we generalize the GCM to multi-dimensional Golay complementary arrays (GCA) and propose new constructions of GCA pairs and GCA quads. These constructions are facilitated by introducing a set of identities over a commutative ring. We prove that a quaternary GCA pair is feasible if the product of the array sizes in all dimensions is a quaternary Golay number with an additional constraint on the factorization of the product. For the binary GCM quads, we conjecture that the feasible sizes are arbitrary, and verify for sizes within 78 $\times$ 78 and other less densely distributed sizes. For the quaternary GCM quads, all the positive integers within 1000 can be covered for the size in one dimension.
