论文标题
关于平衡复杂正交设计的独特性
On the Uniqueness of Balanced Complex Orthogonal Design
论文作者
论文摘要
复杂的正交设计（COD）在构建时空块代码中起着至关重要的作用。它们的真实类似，真实的正交设计（或等效地，正方形组成公式的总和）具有悠久的历史。 Adams等。 （2011年）介绍了平衡复杂的正交设计（BCOD）的概念，以解决实际的注意事项。 BCOD的恒定代码速率为$ 1/2 $，最小解码延迟为$ 2^m $，其中$ 200M $是列数。了解BCOD的结构有助于设计时空块代码，并且它本身也令人着迷。 我们证明，当列的列数固定时，所有（不可分解的）平衡复杂的正交设计（BCOD）具有相同的参数$ [2^m，2m，2m，2^{M-1}] $，此外，它们都是相等的。
Complex orthogonal designs (CODs) play a crucial role in the construction of space-time block codes. Their real analog, real orthogonal designs (or equivalently, sum of squares composition formula) have a long history. Adams et al. (2011) introduced the concept of balanced complex orthogonal designs (BCODs) to address practical considerations. BCODs have a constant code rate of $1/2$ and a minimum decoding delay of $2^m$, where $2m$ is the number of columns. Understanding the structure of BCODs helps design space-time block codes, and it is also fascinating in its own right. We prove, when the number of columns is fixed, all (indecomposable) balanced complex orthogonal designs (BCODs) have the same parameters $[2^m, 2m, 2^{m-1}]$, and moreover, they are all equivalent.
