Undesired Cross Terms [Lecture Notes]

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.