## 1 Introduction  
The ever increasing demand for high quality wireless services results in a high power consumption of wireless systems, and multiple input multiple output (MIMO) systems are a key technology for today's wireless communications and have already been adopted in several standards, i.e., 3 GPP-LTE-A/Pro, IEEE 802.11n/ac/ax, etc. A traditional point-to-point MIMO system normally uses almost the same number of transmitter (TX)/receiver (RX) antennas to maximize the channel capacity. The 3 GPP LTE-Advanced standard (Release 11) incorporates up to eight TX antennas for a real implementation. Increasing the number of TX antennas to hundreds or more is well-known to result in enormous capacity gains. Keeping this in mind, [PERSON] suggested a MIMO system with hundreds of TX antennas [1; 2; 3], which is referred to as a massive MIMO or large-scale (LS) MIMO system. The LS-MIMO system transmits dozens of different signal streams to dozens of different userswith same time-frequency resources. Thus, it is a kind of multi-user (MU) MIMO system that performs point-to-multi-point communications [4]. The LS-MIMO system can also be used to achieve a high energy efficiency (EE) because if we increase the number of TX antennas with a limited number of RX antennas, we can generate an excessive amount of beamforming gain, which consequently gives us an opportunity to reduce the radiation power [5; 6; 7; 8]. There are many research challenges to realize an LS-MIMO system. A lot of antennas must be packed in a limited space; thus, using fractal antennas can be a great help [9; 10; 11; 12; 13; 14; 15; 16]. Another important thing to consider is that it requires a lot of power amplifiers (PAs), which must be connected to each antenna. The PA is the most expensive and power hungry device in a modern base station (BS). Current PA suffers nonlinear distortion and/or low EE since the high peak-to-average power ratio (PAPR) of the orthogonal frequency division multiplexing (OFDM) signal hinders the efficient use of the PA. For the amplification, we could employ a PA with high levels of input back-off (IBO) to achieve a large linear dynamic range, but this approach results in power inefficiency. Therefore, a low complexity signal processing technique with little distortion is essential to improve the EE of the LS-MU-MIMO-OFDM. A current BS uses a digital pre-distorter (DPD) to reduce the nonlinear distortion and/or improve the EE of the BS [17]. For the LS-MU-MIMO-OFDM system, however, it requires many DPDs, which must be connected to many PAs/antennas. Thus, these can not be used due to their high price and complexity. Some related techniques to improve the EE of PA, such as envelope elimination and restoration (EER) [18] and envelop tracking (ET) [19] are also very popular. In particular, the ET technique could be used in conjunction with the power allocation techniques in MIMO systems to optimize the overall system performance and power efficiency. EER and ET must also be applied to each PA, and thus these are very difficult to be applied to the LS-MU-MIMO-OFDM due to many PAs. As previously mentioned, simply increasing the IBO is not very helpful because it reduces the EE. Due to the practical importance of this problem, various OFDM PAPR reduction techniques have been introduced in the literature [20] such as clipping and filtering (CAF) [21; 22; 23], selected mapping (SLM) [24; 25; 26], partial transmission sequence (PTS) [27; 28], tone reservation/active constellation extension [29; 30; 31], block coding [32], and companding [33], etc. In addition, single-carrier frequency division multiple access (SC-FDMA) or DFT-S-OFDMA has already been adopted in 3 GPP-LTE-(A) for an uplink signal to improve the EE of the terminals [34; 35]. Most of the techniques that have been introduced consider a single input single output (SISO) system, since the PAPR reduction is usually applied separately for each TX antenna.