## 4 Simulation and Numerical Results
### Communication Performance  
#### 4.2.1 BER Performance  
In this subsection, the bit error rate (BER) performance of the proposed signal detection method for the integrated MIMO-OFDM-IM system is evaluated via Monte Carlo  
Figure 8: Complexity comparison. (**a**) The variation in number of complex multiplications with the number of activated subcarriers. (**b**) The variation in number of complex multiplications with the number of transmitting antennas.  
Figure 7: The variation in MSEs of range and velocity estimation with SNR under different methods (\(N_{r}=N_{t}=4\), \(N_{c,sub}=8\), \(K=4\), \(H=4\)). (**a**) Range estimation. (**b**) Velocity estimation.  
simulations with \(10^{4}\) trials. In this simulation, the communication symbol is modulated by BPSK modulation. Similar to the previous section, the spectral efficiency is uniformly set to 4 bps/Hz. Five detection methods are used for comparative analysis, including the maximum likelihood (ML) detection method, minimum mean square error (MMSE) detection method, improved MMSE detection method [50], subblock-wise detection method [51], and the proposed method. In Figure 9, the BER of different methods for different SNR levels is depicted with \(N_{r}=N_{t}=4\). According to the result of Figure 9a, it can be observed that the performance loss of the MMSE detection method is substantial, whilst the performance of the improved MMSE detection method has improved, albeit not significantly. In contrast, the performance of the subblock-wise detection method has greatly improved. Finally, the proposed detection method achieves a better BER performance and has only a small performance loss compared with the ML detection method. A further comparison shows that, with an increasing \(K\) (Figure 9b), the BER performance of all detection methods decreases slightly, mainly because the modulation symbols to be detected will increase with the increase in \(K\). In this case, the performance of the proposed method is still slightly better than the subblock-wise detection method, and both methods are still very close to the ML detection method.  
Figure 10 shows the BER performances of different detection methods for different SNR levels with \(N_{r}=N_{t}=8\). As seen from Figure 10, the BER performance of the ML detection method, subblock-wise detection method, and the proposed detection method are obviously superior to other detection methods. Comparing Figure 10 with Figure 9, it can be observed that the BER performances of all information detection methods have obviously improved with the increase in the number of transmitting and receiving antennas. In particular, the performance of the subblock-wise detection method is closer to that of the proposed information detection method. However, the algorithm complexity of the subblock-wise detection method is significantly higher than that of the proposed method, which will be shown in the statistical results of the algorithm complexity later. It is worth mentioning that the ML detection method has a better BER performance than other methods, but its algorithm complexity is very high. Comparing Figure 10a and Figure 10b, it can be observed that all information detection methods are sensitive to \(K\).  
Figure 9: The BER performance of different information detection methods under the proposed integrated MIMO-OFDM-IM system (\(N_{r}=N_{t}=4\)). (**a**) \(N_{c\_sub}=8\), \(K=3\); (**b**) \(N_{c\_sub}=8\), \(K=6\).