## 4 Simulations and Discussions  
To demonstrate the effectiveness of our proposed method, simulation experiments are used to illustrate the ISR performance of blind separation by the charrelation matrix and the Bit Error Rate (BER) performance of this method executed in DS-CDMA systems. The results are shown in Figures 2-6. The ISR and BER performance index are utilized to show the advantage of performance of the proposed approach. Figure 3: BER performance comparison between JADE and the proposed method for user separation in DS-CDMA systems. Figure 2: ISR performance comparison of JADE and the proposed method. Figure 4: BER performance comparison among the proposed blind separation scheme and conventional scheme. Figure 5: Performance of estimate the chip code for four users in a DS-CDMA system. Figure 6: Estimation accuracy of the chip code for different users in a DS-CDMA system with the JADE method and the proposed method. To begin with, we demonstrate the performance of the ISR, which can be computed in numerical analysis as follows [19]:  
\[\mathit{ISR}_{{}_{num}}=\frac{1}{2K}\left[\sum_{i=1}^{K}\left[\sum_{j=1}^{K} \frac{\left|v_{{}_{ij}}\right|^{2}}{\max_{{}_{j}}\left|v_{{}_{ij}}\right|^{2}}-1 \right]+\sum_{j=1}^{K}\left[\sum_{i=1}^{K}\frac{\left|v_{{}_{ij}}\right|^{2}}{ \max_{{}_{i}}\left|v_{{}_{ij}}\right|^{2}}-1\right]\right] \tag{36}\]  
where \(\mathbf{V=}\left(v_{{}_{ij}}\right)=\mathbf{W}\tilde{\mathbf{G}}\) is the unmixing-mixing global matrix, and \(\mathbf{W=}\tilde{\mathbf{G}}^{-1}\) is the estimated unmixing matrix. The simulation parameters are that the number of sources is 4, the mixing matrix is randomly generated, and 10 simulations are implemented, and the channel fading gains of 4 users are set as 1, 0.8, 0.2 and 0.05, which are same as in the following simulation conditions. The other parameters are marked in Figure 2. It is readily seen that the proposed method outperforms JADE from the Figure 2 as previously exposed. Next the Bit Error Rate (BER) of user separation performance in DS-CDMA systems by this method is given. The simulation parameters in DS-CDMA systems are that the number of users is four, the length of spreading code is 31, and Gold Sequence is considered as spreading code, the length of samples is set as short with 1000 bits, 10 simulations are executed, and the modulation mode is BPSK. For comparison, the performance of another BSS algorithm, JADE (using the same data) is indicated as well. From the simulation results shown in Figures 2 and 3, we can conclude that the new approach has better performance than the JADE algorithms applied in DS-CDMA systems when the number of samples is short and the SNR of receiver signal is low. We also know from Figure 3 that the performance becomes worse with the increasing number of users. Next, we compared the new method with the conventional scheme and blind scheme used in multiuser detection. The conventional schemes include Decorrelation (DEC), Matched Filter (MF) Minimum Mean-Square-Error (MMSE), Parallel Interference Cancellation (PIC) and Successive Interference Cancellation (SIC). The blind schemes are JADE and the new method. All schemes were tested using Gold code of length \(C=31\). The number of users is \(K=4\). The number of samples is 10,000 bits, the modulation mode is BPSK, and 10 simulations are carried out. The different parameters are marked in Figure 4. According to Figure 4, we can know that blind scheme is superior to the conventional scheme and proposed method is better than the JADE at lower SNR. In the end, the blind chip sequence estimation is investigated for DS-CDMA systems. The simulation parameters are that the Walsh code of length 64 is tested, and 10 simulations are implemented. The different parameters are marked in Figure 5 (SNR = \(-\)8 dB) and Figure 6, respectively. Figures 5 and 6 show the chip sequence can be estimated completely at low SNR. From Figure 6, we can know that the proposed method has better performance compared to JADE.