Signatures constructed from Welch bound equality sequences have been shown to be optimal in terms of sum capacity in synchronous CDMA systems. Unfortunately, these codebooks are a function of the number of active signatures and need to be reassigned as the number of active users changes to maintain optimality. We describe and analyze two subclasses of Welch bound equality sequences from a theoretical and practical viewpoint. We show that maximum Welch bound equality sequences are equiangular and thus each active interferer experiences the same amount of interference. We show that codebooks constructed by concatenating multiple orthonormal basis come closer to the Welch bound when not all signatures are active. Discussions and illustrations for both constructions are presented.
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