On sequence design for a synchronous CDMA channel

The sum capacity on a symbol-synchronous CDMA system having processing gain N and supporting K power constrained users can be achieved by employing at most 2N-1 sequences. Analogously, the minimum received power (energy-per-chip) on the symbol-synchronous CDMA system supporting K users that demand specified data rates can be attained by employing at most 2N-1 sequences. If there are L oversized users in the system, we need at most 2N-L-1 sequences. We show the above results by proving a converse to a well-known result of Weyl on the interlacing eigenvalues of the sum of two Hermitian matrices, one of which is of rank 1. The converse is analogous to a known converse to the interlacing eigenvalues theorem for bordering matrices.