Construction of Equiangular Signatures for Synchronous CDMA Systems

Robert Heath Jr., Joel Tropp, Inderjit Dhillon, Thomas Strohmer

Abstract:   Welch bound equality (WBE) signature sequences maximize the uplink sum capacity in direct-spread synchronous code division multiple access (CDMA) systems. WBE sequences have a nice interference invariance property that typically holds only when the system is fully loaded and the signature set must be redesigned and reassigned as the number of active users changes to maintain this property. An additional equiangular constraint on the signature set, however, maintains interference invariance. Finding such signatures requires imposing equiangular side constraints on an inverse eigenvalue problem. This paper presents an alternating projection algorithm that can design WBE sequences that satisfy equiangular side constraints. The proposed algorithm can be used to find Grassmannian frames as well as equiangular tight frames. Though one projection is onto a closed but non convex set, it is shown that this algorithm converges to a fixed point, and these fixed points are partially characterized.