# A Survey on Massive MIMO Systems in Presence of Channel and Hardware Impairments
## 5 Hardware Impairments
### Carrier Frequency Offset (CFO)
Therefore proposing low complexity and accurate techniques for CFO estimation in these systems, specially with OFDM waveform is crucial. In [47], a low complexity method for CFO estimation in SC-FDP massive MIMO systems was proposed. In this technique, each user sends first a pilot block to estimate its CFO at the BS and after CFO compensation another pilot block is sent for channel estimation. This technique has good performance and low complexity, which increases only linearly with the number of BS antennas. However, since a separate pilot block is used for the CFO estimation, the spectral efficiency decreases. To increase the spectral efficiency a blind CFO estimation technique was proposed [48]. In this technique null subcarriers are assigned to each user and it is shown that at large number of BS antennas the CFOs can be estimated blindly. However, the complexity of this technique is high being a cubic function of the number of BS antennas. A joint CFO and channel estimation technique for OFDM massive MIMO system was proposed in [49] to keep the spectral efficiency high. Here, the pilots sent for channel estimation are used for both CFO and channel estimation. Since the CFO estimation in this technique is done with linear grid search for each user, the complexity is high. In [50], a data aided technique for CFO estimation in OFDM massive MIMO system was proposed. In this paper it was assumed that the incident signal at BS from each user can be restricted within a narrow angular spread. In other words, when the number of BS antennas is large the users can be separated by their direction of arrival (DOA) and therefore the CFO of each user can be estimated. An iterative algorithm for estimating the CFO and DOA of each user was proposed in [50]. To have low complexity and keep the spectral efficiency high, an iterative channel and CFO estimation algorithm for SC-FDP and OFDM massive MIMO systems was proposed in [51]. In this technique, the same pilots are used for CFO and channel estimation to keep the spectral efficiency high. In this method, a least square channel estimation is done first, using the pilots. Next, the users are separated roughly using the estimated channel and then the CFO of each user is estimated individually as in a SISO system. Then, using the pilots and the estimated CFOs another channel estimation is done. With the new estimated channel, the users are separated again and another CFO estimation is done. This procedure is repeated until the MSE of channel and CF  
power amplifiers such as the Rapp model, [PERSON] model, Ghorbani model, and some models with memory [53; 54; 55; 56; 57]. Power amplifiers with large linear range are expensive and therefore using inexpensive RF chains increases the PAD issue in massive MIMO systems. In [45], the authors have derived the sum-rate of SC-FDP and OFDM massive MIMO systems in presence of PAD when the number of users is large. The PAPR and out-of-band radiation levels of these two systems have also been studied. The results show that when the number of users is small, PAPR and out-of-band radiation of SC-FDP is lower than OFDM. However, as the number of users increase the PAPR and out-of-bound radiation of SC-FDP increases and converges to that of OFDM. Also, the theoretical results show that the sum-rate of both systems for large number of users are identical and degrade significantly in compare to the case where we have no PAD. In fact, in the presence of PAD, the sum-rate of both systems saturate as the number of BS antennas increases. Therefore, handling the PAPR and PAD problem in massive MIMO systems is crucial. Since working with constant envelope signals in these power amplifiers is easier, References [58; 59] proposed precoders which produce signals with constant envelope in flat fading and frequency selective channels, respectively. In other words the precoder is designed in a way that the envelope of the precoded signal is constant, with the phase being used to reduce the interference levels.