# MIMO Signal Detection Based on IM-LSTMNet Model
## 3 Experiments and Results of Signal Detection
### The Result of the Signal Detection
#### 3.2.1 The Influence of a Different Order of FrFT  
The introduction of FrFT in the MIMO-OFDM system can extend the Fourier transform to different orders, increase the flexibility of the system, and reduce the BER. In the simulation of this section, MIMO-OFDM signal detection based on FrFT is carried out in different orders. Figure 11 shows the comparison between the IM-LSTMNet signal detection method proposed by us and the traditional algorithm and two other neural network methods when the FrFT order is 1, that is, the traditional Fourier transform.  
As can be seen from Figure 11, when the FrFT order is 1, the IM-LSTMNet neural network detection is superior to the traditional algorithm, and it is also superior to the LSTM and CNN-LSTM detection algorithms. In particular, when SNR \(>\) 10 dB, the detection  
Figure 10: SNR = 10 dB; IM-LSTMNet model loss diagram.  
Figure 9: SNR = 10 dB; IM-LSTMNet model training diagram.  
performance of ZF and MMSE can no longer be improved with an increase in SNR. The detection performance of the three neural network methods can also decrease with an increase in SNR.  
Figures 12 and 13 describe the performance comparison between our proposed IM-LSTMNet method, the traditional ZF algorithm, and the MMSE algorithm, as well as the performance comparison between the IM-LSTMNet method and the simple LSTM and CNN-LSTM methods under FrFT order p of 1.4, 1.6, and 1.8.  
Figure 11: The MIMO-OFDM system’s BER with FrFT order of 1.  
Figure 12: The BER of IM-LSTMNet and traditional algorithms under different orders.  
As shown in Figure 12, when the order p is 1.4 and 1.8, the detection performance of ZF and MMSE (i.e., traditional methods) can no longer be improved with an increase in SNR when SNR > 10 dB. When the order p is 1.6, the performance of the traditional method can still improve with an increase in SNR. The detection performance of the IM-LSTMNet method can be improved with an increase in SNR with the three orders, and the performance is obviously better than that of ZF and MMSE, i.e., the two traditional algorithms. Therefore, the MIMO-OFDM system performance with order 1.6 is significantly better than that of the MIMO-OFDM system with order 1.4 and 1.8.  
As shown in Figure 13, with an order of 1.6, the signal detection performance of the three neural network methods for the MIMO-OFDM system is significantly better than that of the two cases with the orders of 1.4 and 1.8. At the same time, the detection performance of IM-LSTMNet is obviously better than that of LSTM and CNN-LSTM.  
In summary, replacing DFT with FrFT in the MIMO-OFDM system not only increases system flexibility, but also brings better performance to the system. In particular, when the FrFT order p is 1.6, the MIMO-OFDM system's BER is the lowest and the system performance is the best. Meanwhile, the IM-LSTMNet detection algorithm proposed by us has better performance than the traditional MIMO signal detection algorithm and other neural network signal detection algorithms such as LSTM under different order conditions.