Abstract

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. 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. Performance when subsets of sequences are active is characterized in terms of sum-squared correlation, average interference, and condition number of the Gram matrix.

Citations