This paper investigates a signal detection method with a RAKE combiner for the case wherein the receiving signals use the same spreading code. In the case where multiple user interference with the same spreading code (MUI-SC) occurs, blind channel estimation is difficult and as far as we know has not been investigated. To tackle the issue of MUI-SC, we propose two blind channel estimation methods based on the multimodulus algorithm (MMA), i.e., MMA-IQ and MMA-I methods. When a one dimensional modulation scheme, such as differential binary phase-shift keying (DBPSK), is used, the output of the MMA-IQ channel estimation method can, under MUI-SC, have two states. The first state is that the channel estimate corresponds to a channel response for one of the received signals, and the second state is that the channel estimate corresponds to combined channel responses for two of the received signals. This is because the MMA-IQ uses two degrees of freedom (both axes in the IQ-plane), however one DBPSK signal uses only one degree of freedom. In the case of the second state, it is possible to detect two signals/packets at once. However, in the MMA-IQ, the receiver has to recognize the state of the channel estimate before the signal detection, thus we also propose a state recognition method. In the MMA-I channel estimation method, only the I-axis is used thus the channel estimate always corresponds the case with one signal. Numerical results show that the average number of detected packets of the MMA-IQ is more than that of the MMA-I in high signal-to-noise power ratio case. In addition, several aspects of the MMA-I and MMA-IQ based RAKE signal detection methods are shown.