# Deep Learning-Based Secure MIMO Communications with Imperfect CSI for Heterogeneous Networks
## 5 Simulation Results  
In this section, simulation results are provided to verify the proposed DCNN models. The impacts of system parameters, such as the correlation factor of imperfect CSI \(\xi\), the normalized doppler frequency \(f_{d}\), the number of antennas is evaluated in different setup scenarios. Since the equivalent channel fading matrix of femto BS is zero-forced, BER of users with different detectors is used to evaluate the system performance. Specifically, QPSK modulation is employed in all simulation setups. Since the constellations of QPSK modulation is 2-D complex signal, we can generalize the setup to an arbitrary modulation order. We set the data packet length as 600 bits, and each batch consists 10 data packets. During the training phase, a training data set with 10000 batches as well as a validation data set with 1000 batches are fed to the DCNN, and a test data set with 1000 batches is used to evaluate the BER performance of the proposed schemes. The popular TensorFlow framework [44] is adopted in our simulations, while the adaptive moment estimation (Adam) optimizer is used to minimize the loss value during training phase. In particular, the optimization parameters are listed as follows: learning rate is 0.001, \(\beta_{1}=0.9\), \(\beta_{2}=0.999\), \(\epsilon=10^{-8}\). Since the testbed of our paper is under construction at this moment, we will present experiment results on real datasets in future works. Figure 4: DCNN type-II: Training model of CNN without accurate CSI. Figure 5 depicts the BER performance versus the SNR of the system with MIMO setup as \(N_{M}=4\), \(N_{U}=4\), \(N_{F}=2\), the normalized doppler frequency \(f_{d}=0.1\), and the correlation factor of imperfect CSI \(\xi=0.90\). The BER of three types of detectors, such as standard MLD, DCNN type-I and DCNN type-II are compared. As a benchmark, the BER curves obtained by MLD with the perfect CSI is also presented. We can see from this figure that the outdated CSI has obvious adverse effects on BER performance. As shown in this figure, in the high SNR region, DCNN-based detectors show a performance gain of about 4 dB in comparison to the standard MLD. The reason is that the former can refine the imperfect channel matrix and produce more accurate CSI, then the BER of the system can be improved. Moreover, two types of DCNN-based detectors show almost the same performance with slight gap. Similar results can be obtained from Figures 6 and 7, where the correlation factors of imperfect CSI are \(\xi=0.8\) and \(\xi=0.7\), respectively. However, accurate CSI is necessary for DCNN type-I, which is used to calculate the model loss function. Thus, the application of DCNN type-I is limited, because in some practical scenarios, it is difficult to obtain the accurate CSI especially in the wireless MIMO communications. Compared with the loss function, only the received signal \(y\), the beamforming matrix \(\mathbf{B}\) and the original message \(x\) are needed, which enlarge the application scenarios of the DCNN type-II. On the other hand, without the help of the accurate CSI, DCNN type-II leads to deteriorated performance compared with type-I. Figure 8 depicts the BER performance versus the correlation factor of imperfect CSI \(\xi\), where the average SNR of the system is SNR = 20 dB. The BER of three types of detectors, such as standard MLD, DCNN type-I and DCNN type-II are compared. As shown in this figure, DCNN-based detectors indicate considerable performance gains relative to the standard MLD. This is because DCNN-based detectors can refine the imperfect channel matrix and produce more accurate CSI, hence the BER of the system can be improved. Moreover, two types of DCNN-based detectors show almost the same performance. Figure 6: BER performance of deep learning-based MLD with \(\xi=0.8\). Figure 7: BER performance of deep learning-based MLD with \(\xi=0.7\). The effect of the normalized frequency \(f_{d}\) is present in Figure 9, where the MIMO configuration remains the same with previous setup.