# Deep Learning-Based Secure MIMO Communications with Imperfect CSI for Heterogeneous Networks
## 1 Introduction  
In recent years, the heterogeneous wireless network, which can support high-density and high-rate traffic, has attracted much research interest from both academic and industry sectors [1; 2; 3]. The cooperation between the macro base stations (BSs) and the femto BSs can greatly improve the quality of service (QoS) of the user equipment, as well as the spectrum efficiency and the energy efficiency [4]. Therefore, ultra-dense heterogeneous technology has been adopted as one of the potential solutions to the next-generation wireless sensor network [5]. On the other hand, the architecture of heterogeneous wireless networks brings up many challenges to the physical-layer security [6; 7; 8]. Several signal-level algorithms, such as beamforming [9; 10], artificial noise [11; 12] or stochastic geometry approach [13; 14], have been proposed as the classicalsolutions to the secure multiple-input multiple-output (MIMO) communication scheme. Consequently, as an improvement, deep learning-based secure communication has been proposed to protect the message transmission to the legitimate users [15]. However, due to the noise and the signal distortion or delay of channel estimation, it is difficult to obtain the ideal channel state information (CSI) from both the legitimate users and the eavesdroppers in most of practical scenes [16; 17; 18; 19; 20; 21]. For example, authors in [22; 23; 24] derived a new outage probability expression and optimize the transmission capacity under different assumptions. Deep learning technology has already shown astonishing capabilities in dealing with complex network in mobile communications, such as channel estimation, signal detection, modulation recognition and channel equalization. For example, Ref. [25] used a 2D image to present the time-frequency channel fading matrix. By using a super-resolution network and a denoising network, the proposed scheme produces more accurate channel estimation. Under the constraint of one-bit quantization, authors in [26] proposed deep neural network-based auto-encoder for OFDM receiver. Modulation recognition algorithm was considered in [27], where a convolutional neural network followed by a long short-term memory as the classifier was adopted to improve the robustness for modulation recognition. A CNN-based channel prediction scheme was designed in [28] in massive MIMO systems under channel aging effects, where an autoregressive network was used to model the temporal channel correlation of the wireless channel. Considering perfect free space optical communications, a pilot independent deep learning-based channel estimator was proposed in [29; 30]. Simulation results indicated that the proposed scheme provided close enough performance to the perfect channel estimation scheme. Although there are some works on learning-based channel estimation algorithms, with imperfect CSI, the impacts of CNN-based MIMO detector on physical-layer security performance is still an open question. Motivated by that, in this paper, we will discuss the deep learning-based secure MIMO communication algorithm for heterogeneous networks with imperfect CSI. In the heterogeneous networks, there exist both macro BSs and femto BSs, which can serve a group of users within different areas. In general, the macro BS provides the massive connections and the large-scale cell coverage in the hot spots. The femto BS can help enlarge the wireless coverage and the data rates of the user in network edge. In some practical scenarios, secure messages transmitted from the macro BS to the users may be intercepted by the femto BS. In this case, with the help of zero-forcing algorithm [31], the macro BS chooses null-space eigenvectors to prevent information leakage to the femto BS. Classically, the receiver obtains the CSI through pilots signal transmitted from the base station, and there exists a time difference between the channel estimation and the data packet transmission.