**ABSTRACT**
### On Quasi-Orthogonal Signatures for CDMA Systems

#### Robert W. Heath Jr., Thomas Strohmer, and Arogyaswami J. Paulraj

Codebooks constructed from Welch bound equality sequences are optimal in
terms of sum capacity in synchronous CDMA systems. These optimal codebooks
depend on both the sequence length as well as the number of active
sequences. Thus to maintain optimality a typically different codebook is
needed for every possible number of active users to maintain optimality.
Further, all the sequences need to be reassigned as the number of active
users changes. This paper describes and analyzes two promising subclasses
of Welch bound equality sequences that have good properties when only a
subset of sequences is active. One subclass, based on maximum Welch bound
equality sequence sets, has equiangular sequences thus each user
experiences the same amount of interference. The interference power depends
only on the total number of active users. Another subclass, constructed by
concatenating multiple orthonormal basis, comes closer to the Welch bound
when not all signatures are active. Optimal unions of orthonormal basis are
derived. The loss in sum capacity when subsets of sequences are active is
characterized. Discussions, code constructions, and illustrations are for
both subclasses are presented.

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