# A Survey on Massive MIMO Systems in Presence of Channel and Hardware Impairments
## 5 Hardware Impairments
### Phase Noise  
Phase noise is the most important parameter in many oscillators. In an ideal oscillator, the spectrum is line at the carrier frequency, but in practical systems the spectrum is non zero at the vicinity of the carrier frequency [68]. Therefore, in the ideal case the spectrum of the desired signal is convolved with Dirac function, and it is downconverted or upconverted without any change. But, in practical systems the spectrum of the signal at the output of the oscillator changes and, since the spectrum is expanded, an interference between the desired signal and the signal in adjacent channel will occur [68]. Therefore, analyzing the effect of phase noise and compensating it in massive MIMO systems is vital. Several models for phase noise have been proposed in the literature such as [PERSON]'s model, linear time invariant model, and linear time variant model [69; 70; 71].  
In [72], the effect of phase noise in uplink of single-carrier massive MIMO system with imperfect channel knowledge has been investigated. The results show that this noise causes channel aging effects and, therefore, the time duration for data transmission and the number of supported users has to be reduced. However, this noise does not effect the array gain. In [73], the effect of phase noise on downlink sum-rate of OFDM massive MIMO system with MF and ZF precoder was investigated. It is shown that, although MF precoder has lower sum-rate per user, it is more robust to phase noise than ZF precoder. This is also true for the case where we have channel estimation errors. In [74], the authors investigated the effect of phase noise in single input multiple output (SIMO) and multiple input single output (MISO) systems. Two configurations were considered for these systems. In the first configuration all the RF chains use a common local oscillator and in the second configuration each RF chain has a separate local oscillator. The second-order term in the high-SNR capacity expansion, which the authors refer to as phase noise number, is defined as  
\[\chi=\lim_{\rho\rightarrow\infty}(C(\rho)-0.5\ln(\rho)), \tag{10}\]  
where the first term in the right hand side of (10) is the capacity of phase noise channel and \(\rho\) is the SNR. It is concluded that in the uplink the phase noise number is larger when separate oscillators are used. However, the phase noise number of the downlink channel is larger when a common oscillator is used for all the antennas. In [75], the authors have investigated the effects of phase noise on the performance of massive MIMO systems when the number of BS antennas (\(M\)) and number of users (\(K\)) are large but their ratio \(\beta=\frac{M}{K}\) is fixed. It is assumed that the number of active oscillators is \(M_{osc}\) and \(\frac{M}{M_{osc}}\) antennas are attached to each oscillator. The analysis show that when \(\beta\) is small, the performance of the system when all the BS antennas are connected to a single oscillator is better than the case where each BS antenna has its own oscillator. However, when \(\beta\) is large and at low SNR, we have the opposite behavior. Table 2 summarizes the effect of the mentioned hardware impairments and their possible solutions.