# Utilizing Multi-Dimensional MmWave MIMO Channel Features for Location Verification
## 1 Introduction
The authors in [10] further study the physical characteristics of 5G IoT in various application scenarios and describe the possible security threats resulting from the 5G IoT physical layer. Based on virtual angles of arrival in mmWave systems and machine learning methods, the authors in [11] propose a physical layer authentication scheme to detection spoofing attacks. Two effective pilot contamination attack detection approaches are proposed for power non-orthogonal multiple access in massive MIMO 5G communications, based on the sparseness and statistics of mmWave virtual channels [12]. Following this line, the authors in [13] present a new physical layer countermeasure using channel virtual representation to defend against pilot contamination attack. In [14], unique beam pattern features are utilized to achieve physical layer spoofing attack detection and the detection problem is cast as a machine learning classification through the sector level sweep (SLS) process. The authors in [15] develop a physical layer authentication scheme by using signal-to-noise ratio (SNR) trace features to detect spoofing attacks in mmWave systems. Frequency-selective Rayleigh channel time variations are used to detect spoofing attacks in wireless networks, considering the channel estimation errors [16]. To improve the spoofing detection accuracy, a logistic regression-based authentication approach is developed without the requirements of the known channel model [17]. The authors jointly use multipath delay and channel gain characteristics of the channel impulse response to achieve performance improvement of physical layer authentication [18]. The above existing approaches demonstrate the uniqueness and usability of physical layer features for spoofing attack detection and authentication. It is noted that the above existing approaches are developed for spoofing detection by conventional channel state information. These approaches cannot be extended directly to mmWave MIMO communication systems because it is difficult for them to sufficiently excavate fine-grained physical layer characteristics from mmWave MIMO channels. Hardware-impairment-based authentication generally needs to employ high-precision hardware equipment for hardware feature extraction and bears high computational complexity [14; 15]. Moreover, machine-learning-based authentication framework requires an expensive training stage with a large amount of training data, which might be unrealistic in practice. In addition, the analytic establishment of statistical performances still remains an open problem in machine-learning-based authentication frameworks. To this end, we explore the exploitation of multi-dimensional mmWave MIMO channel features to design a new location verification scheme for mmWave MIMO communication systems. These channel features include azimuth angle of arrival (AAoA),elevation angle of arrival (EAoA) and path gain, which are jointly used to validate the legitimacy of transmitters and to improve the authentication performance. The main difference between the schemes proposed in this paper and those in previous works [16; 17; 18] is that the previous approaches mainly focus on channel statistics in the time domain while this paper extracts channel features in the time domain as well as the angle domain. In addition, the scheme proposed in this paper attempts to explore the exploitation of multi-dimensional mmWave MIMO channel features to achieve location verification. The main contributions of this paper are summarized as follows:  
* By exploiting multi-dimensional mmWave MIMO channel features in both the time domain and angle domain, we develop a new location verification scheme to achieve validation of a transmitter location for mmWave MIMO communication systems. * To determine estimation error variances of channel features in terms of AAoA, EAoA, and path gain, we estimate the mmWave MIMO channels based on maximum-likelihood estimation theory.