## 1 Introduction  
The volume of data being transferred over wireless communication channels is almost doubling each year, owing to the popularity of smartphones and wireless local area networks (WLANs). Thus, high-speed data communication at speeds of faster than 10 Gbps will be required for future wireless communication systems [1; 2; 3]. In this context, multiple-input multiple-output (MIMO) systems have attracted significant attention, because they can improve the transmission rate (TR) within a limited frequency band [4; 5]. Moreover, these systems have already been developed as commercial products in accordance with the Long Term Evolution (LTE) and IEEE802.11n standards [6; 7]. In multi-user MIMO (MU-MIMO) systems, the channel capacity \(C\) is improved by employing a TR between a base station (BS) and multiple user equipment (UE) units, where the UE has a small number of antennas [8; 9]. The MU-MIMO system has been incorporated into the LTE-Advanced and IEEE802.11 ac standards [10].  
With a view to further improving the frequency utilization of future wireless systems using MU-MIMO transmission, the concept of _massive MIMO_ has recently been proposed [11; 12]. In massive MIMO systems, the number of antennas at the BS is significantly larger than that of the UE and is also significantly larger than the number of UE units. Massive MIMO enables low-complexity signal processing, because the inter-user interference is easily mitigated by the high beamforming resolution [13]. Generally speaking, estimation of the channel state information (CSI) in MIMO/MU-MIMO systems [8] is essential [14; 15]. However, when CSI feedback from the user terminals (UTs) to the BS is employed, a very large overhead occurs compared with the communication data, especially when there are a large number of antennas at the BS [16].  
Thus, the countermeasure of _implicit_ beamforming (IBF) has been proposed [17]. IBF exploits channel reciprocity in the time-division duplex (TDD) mode, that is, when the transmit frequency is identical to the receive frequency. Further, IBF can be used in WLAN systems. Because massive MIMO will be employed in small cell systems, the TDD mode should be used from the perspective of frequency utilization. However, it is necessary to calibrate the amplitude and phase errors between the branches of the array, because of individual differences in the radio frequency (RF) devices of the receivers and transmitters [18; 19]. Thus, various automatic calibration methods for adaptive BS antennas that are well suited to TDD communication systems have been proposed in previous studies [20; 21].We note that some of these methods allow the transmitter and receiver calibration values to be obtained automatically [20; 21; 22; 23; 24]. In recent research, the calibration method for massive antennas utilizing the channel reciprocity in a TDD system is proposed [25; 26; 27].  
In this paper, we extend the calibration system described in [20; 21] for applicability to MU-MIMO systems with a large number of antennas at the BS. Our testbed assumes a 16-element MIMO system. The amplitude and phase errors are evaluated on this testbed, and the efficacy of the calibration method is determined by examining the radiation pattern and \(C\). Finally, the throughput performance obtained for MU-MIMO transmission under IBF with the developed calibration circuit is evaluated in terms of the medium access control (MAC) efficiency for IEEE802.11 ac signals [28].  
The remainder of this paper is organized as follows. The problems encountered with CSI feedback and the concept of IBF are introduced in Section 2. The calibration method, testbed, and its performance are described in Section 3. The radiation pattern and \(C\) given by the proposed calibration method are investigated in Section 4. In Section 5, the efficacy of the calibrated IBF is verified by examining the throughput performance while considering the MAC efficiency. Section 6 concludes the paper.