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Blind signal detection in multiuser code division multiple access (CDMA) system is particularly attractive when only the desired user signature is known to a given receiver. A problem common to several existing blind multiuser CDMA detectors is that the detection performance is very sensitive to the signature waveform mismatch (SWM) which may be caused by channel distortion. In this paper, we consider the design of a blind multiuser CDMA detector that is robust to the SWM. We present a convex formulation for this problem by using the second-order cone (SOC) programming. The resulting SOC problem can be solved efficiently using the recently developed interior point methods. Computer simulations indicate that the performance of our new robust blind multiuser detector is superior to those of many existing methods.