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The sequence adaptation problem for code division multiple access (CDMA) systems with antenna arrays is considered. The problem can be formulated as a sequence adaptation game. Each user would like to choose a signature sequence that minimises his/her interference based on an interference measure. It is well known that, with arbitrary interference measures, sequence adaptation in antenna array systems may not have an equilibrium point (Nash equilibrium). The authors prove that additivity, continuity and symmetry of the interference measures are three sufficient conditions for this existence. Adaptive algorithms are also developed for sequence adaptation in antenna array systems. Simulations show that sequence adaptation with antenna arrays can significantly improve the system throughput over the existing system with antenna arrays.