## 1 Introduction  
Massive multiple-input multiple-output (MIMO) system is a powerful technology that can increase both spectral efficiency (SE) and energy efficiency (EE), and it has been actively discussed to be included in the 3 rd generation partnership project (3 GPP) standard as core technology for 5G systems [1; 2; 3]. The massive MIMO system uses a large amount of transmitter (TX) antennas and serves limited number of user equipments (UEs) and/or Internet of things (IoT) devices/sensors, so it is a combination scheme of multi-user (MU) MIMO and beamforming, and its drastic performance gain has already been proven in various literature [4; 5; 6; 7; 8]. Recently, it has also been proven that massive MIMO is quite effective in supporting many Internet of things (IoT) and/or Industrial Internet of things (IIoT) devices, and thus can be used for a core technology to configure wireless sensor networks [9; 10; 11; 12; 13; 14; 15]. The calibration of transceiver impairment is very important problem to support distributed IoT devices using massive MIMO [9; 10], because without getting accurate channel information, it is impossible to support the distributed IoT devices. In [9], authors proposed very effective channel calibration method to reduce the channel mismatch due to the radio frequency (RF) impairment. In their method,they used power headroom which is reported periodically and/or aperiodically from distributed IoT devices to base station (BS), to deliver the RF impairment information of IoT devices. Based on the RF impairment information which is embedded in power headroom, BS performs precoding with the compensation of channel mismatch. This is very important scheme to support distributed IoT devices using massive MIMO equipped data center. A more general work for transceiver impairment calibration was also proposed in [10]. In [10], authors investigated massive MIMO-based distributed detection with general transceiver impairments at both a massive-antenna data center and multiple single-antenna sensors. They first derived closed-form expressions to show the dependence of both the probability of detection and the probability of false alarm on the transceiver impairments, then they showed that hardware impairments create finite ceilings on the detection performance. In addition, they formulated an optimization problem to maximize the probability of detection, while maintaining a constant false alarm probability and a sum sensor reporting power budget. By exploiting the inherent structures in the problem formulation, they developed an iterative algorithm to solve the problem via invoking the alternating direction method of multipliers. In addition with the results, there has been a high interest to equip the sensor fusion center with massive MIMO framework [11; 12; 13; 14; 15]. In [11], authors considered a decentralized multi-sensor estimation problem where sensor nodes observe noisy versions of a correlated random source vector. The sensors amplify and forward their observations over a fading coherent multiple access channel to a fusion center. The fusion center is equipped with a massive MIMO and adopts a minimum mean-square error (MMSE) approach for estimating the source. They optimized the transmission power at each sensor node to increase energy efficiency in various scenarios. In [12; 13], authors studied channel-aware decision fusion over MIMO channels, in the presence of a massive MIMO at the fusion center. They tried to develop linear fusion rules, and presented a wide choice of low-complexity sub-optimal rules which efficiently exploit massive MIMO benefits and are able to achieve near-optimal performance. In [14], authors considered the uplink detection and estimation of a zero mean Gaussian signal in a wireless sensor network when the fusion center is configured with a massive MIMO. For the detection problem, they studied the Neyman-Pearson (NP) detector and energy detector (ED), and found optimal values for the sensor transmission gains.