Walsh Functions

Hadamard-Walsh functions are binary orthogonal sequences, with power-of-two lengths. They can be generated by the recursion

where


and M is a power of two. The rows of any instance form a mutually orthogonal set over the inner product.

The sequences of order 8, for example, are:
.

The Walsh functions of order 64 are used as orthogonal cover on the forward link channels. They are also used as orthogonal modulation symbols in the reverse link. Although the functions are the same, they are used for entirely different purposes in the forward and reverse links.

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