Walsh Words
Definition: A group of 2N vectors or words which contain 2N binary elements which with themselves and their logical inverses form a mutually orthogonal set.
Note: Every Walsh word of a given length is orthogonal to all other Walsh words of that length and all inverses of the other Walsh words of that length.
Walsh Words
Application: IS-95 uses Walsh words having 64 chips to identify the logical channels on the forward link. The logical channels are separable from the aggregate of forward-link CDMA signals based on the orthogonality of the Walsh words and their inverses. The orthogonality of the Walsh words is also used on the reverse link in the 64-ary orthogonal modulation scheme. The critical property of the Walsh words used on both the forward and reverse links is their orthogonality. The Walsh words do not in general have uniformly distributed power spectra and do not generally have low cross-correlation at arbitrary time shifts. Therefore, the PN codes are used to provide this uniform power distribution over the physical channel and to provide low correlation between shifted versions of the transmitted signals.
Walsh Words
Example: Walsh words may be produced using the simple iterative scheme illustrated below. The rule is to produce the next matrix of Walsh words by repeating the entire present matrix to the right and to the bottom and to repeat with all signs or states reversed to the diagonal.
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