CDMA codeword optimization: interference avoidance and convergence via class warfare

Interference avoidance has been shown to reduce total square correlation (TSC) for given ensembles of user signature waveforms (codewords) in a synchronous code-division multiple-access (CDMA) system. In all experiments we have conducted, sequential application of interference avoidance produces an optimal codeword set when starting from randomly chosen initial codewords. Here we provide the first formal proof of convergence to optimal codeword ensembles for greedy interference avoidance algorithms augmented by a technique called "class warfare" whereby users which reside in more heavily loaded areas of the signal space purposely interfere with (attack) the reception of users in less crowded areas. Coordination of deliberate interference by a complete class of aggrieved user is also sometimes necessary. Such "attacks" and subsequent codeword adjustment by attacked users are shown to strictly decrease TSC. Along the way we also show using linear algebra and a variant of stochastic ordering, equivalence between minimization of TSC and maximization of sum capacity.