## 1 Introduction  
Fifth-generation (5G) mobile communication systems, which will enable high speed, low latency, and large capacity, are becoming commercially available globally. Thus far, several new services that exploit these features, such as sports viewing [1] and autonomous driving [2], have been considered. To transmit high-capacity data, such as video data from a mobile terminal to a base station (BS), ultra-high-speed communication is required for the uplink channel. In the 3 rd Generation Partnership Project (3 GPP), 5G supports downlink and uplink peak rates of 20 and 10 Gbps, respectively [3]. Multiple-input multiple-output (MIMO) systems are essential for achieving ultra-high-speed communication [4, 5]. Hence, evaluating the performance of MIMO terminals is necessary, not only for the downlink channels, but also for the uplink channels. A straightforward method for evaluating a MIMO terminal is field testing in an actual scenario [6]. However, with field testing the repeatability and controllability of the measured data cannot be observed, and, moreover, is a very time-consuming and labor-intensive process. Hence, over-the-air (OTA) testing, which evaluates the performance of MIMO mobile terminals by creating a realistic propagation environment in the laboratory, is very important. OTA measurement methods have been standardized by 3 GPP and the Cellular Telecommunication and Internet Association (CTIA) [7, 8]. In 3 GPP, OTA test methodologies are classified into three categories:  
1. [label=(0)]
2. Reverberation chamber based methods,
3. Two-stage methods,
4. Multiple probe antenna based methods. Many papers in which OTA measurements have been done using these three methods have been published. The evaluation target and issues focused on are highlighted in Table 1. The characteristics of the three OTA measurement methods are summarized as follows. In a _reverberation chamber based method_, the chamber refers to a metallic cavity or cavities that can emulate an isotropic multipath environment that represents a reference environment for systems designed to work during fading [9; 10]. The Rayleigh propagation environment in a chamber is well known as a good reference for mobile terminal systems in urban environments. The advantages of this method are its simple structure, small size, and low cost. However, it is difficult to control the multipath propagation characteristics, such as the cross-polarization power ratio (XPR), spatial correlation, and cluster, owing to the simplicity of the device. In the _two-stage method_, the measurement is divided into two stages: first, measurements of the MIMO antenna patterns that contain all the necessary information to evaluate the antenna's performance, such as radiation power, efficiency, and correlation, are made; then, the measured antenna patterns are incorporated with the chosen MIMO OTA channel models for real-time emulation [11; 12]. The advantage of this method is the reduced number of instruments required, compared with the _multiple probe antenna based method_ introduced next. However, this method requires nonintrusive complex radiation pattern measurements for accurate evaluation of the MIMO terminals. In the _multiple probe antenna based method_, such as one with a fading emulator, a number of test antenna probes located in the chamber reproduce the channel characteristics in a controlled and repeatable manner to test MIMO performance [13; 14; 15; 16; 17]. The disadvantage of this method is that it requires many instruments, such as a probe antenna, a power divider, and a phase shifter. However, a fading emulator is capable of emulating realistic and accurate multipath environments [20; 21; 22; 23; 24]. In OTA testing, investigations primarily focus on evaluating the performance of mobile terminals in downlink channels [9; 10; 11; 12; 13; 14; 15; 16; 17]. For the uplink channel, OTA testing of a massive MIMO BS has been conducted; however, MIMO terminal OTA testing has not yet been reported [18; 19].