This lecture note briefly describes two examples in mathematics on how and why cross terms are disliked: orthogonal space-time block code (OSTBC) from orthogonal designs and free probability theory. The first example shows that the elimination of cross terms can significantly simplify the optimization that has many practical applications in, for instance, multiple antenna systems in wireless communications. The second example gives an intuitive and/or fundamental understanding of free probability theory, which has important applications in random matrix theory.

中文翻译：

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不需要的交叉术语 [讲义]

本讲义简要介绍了数学中关于如何以及为什么不喜欢交叉项的两个示例：来自正交设计和自由概率论的正交空时分组码 (OSTBC)。第一个例子表明，交叉项的消除可以显着简化优化，在许多实际应用中，例如无线通信中的多天线系统。第二个例子给出了对自由概率论的直观和/或基本理解，它在随机矩阵理论中有重要的应用。