CDMA codeword optimization: Interference avoidance and convergence via class warfare

Interference avoidance has been shown to reduce total square correlation (T SC) for given ensembles of user signature waveforms (codewords) in a synchr onous code-division multiple-access (CDMA) system. In all experiments we ha ve 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 e nsembles for greedy interference avoidance algorithms augmented by a techni que called "class warfare" whereby users which reside in more heavily loade d 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 "atta cks" and subsequent codeword adjustment by attacked users are shown to stri ctly decrease TSC. Along,the way we also show, using linear algebra and a v ariant of stochastic ordering, equivalence between minimization of TSC and maximization of sum capacity.