Sum capacity of equal-power users in overloaded channels

We consider the sum capacity of code-division multiple-access (CDMA) signature-sequence sets in overloaded channels that contain an orthogonal subset of dimension N. We introduce a family of signature-sequence sets that consists of a hierarchy of orthogonal subsets (HOS), and show that various signature-sequence sets designed for channel overloading belong to this family. Assuming an equal average energy (EAE) constraint on the user signals, an expression for the sum capacity of the HOS family is derived. We point out that the maximum sum capacity over the HOS family is achieved by the multiple-orthogonal (m-O) CDMA sequence sets. The sum capacity of m-O is only slightly less than the upper bound imposed by the Gaussian multiple-access channel. Moreover, m-O is superior to a system with N orthogonal sequences and (K-N) pseudonoise (PN) sequences (PN/O), which, in turn, outperforms a system with K PN sequences. Both for PN/O and sequence sets over HOS, there is no additional loss in sum capacity if we require the sequences to consist of chips that are binary or quaternary valued.