# A Survey on Massive MIMO Systems in Presence of Channel and Hardware Impairments
## 6 Time Varying Channels
### Time Varying Flat Fading Channels  
In this subsection, the channel is modeled as quasi-static block fading where due to Doppler effect the channel coefficients change symbol-by-symbol based on the Jake's model (the generalization to other Doppler models is more-or-less straightforward). In high speed environments, it is very probable that the channel coefficients change between the time they are estimated and the time they are used by the precoder or equalizer. This phenomenon is called channel aging and degrades the performance of massive MIMO systems. In [79], the sum-rate of a multi-cell massive MIMO system in the presence of channel aging has been analyzed. The analysis were done both in the uplink and the downlink and for both MF and ZF detectors and precoders, respectively. The results indicate that channel aging degrades the performance of the system, as expected. However, with some channel prediction techniques the effect of channel aging can be mitigated. The authors in [80] have considered a multi-cell massive MIMO system with RZF precoder and investigated the effect of channel aging on the performance of the system. In [81], the effects of channel aging on the sum-rate and spectral efficiency of massive MIMO systems with ZF and MF precoders were studied. The results showed that channel aging causes loss in both the sum-rate and the spectral efficiency of the system. Moreover, the impact of channel aging on ZF precoder is much larger than the MF precoder. In [82], the effect of channel aging on the achievable sum-rate of an FDD massive MIMO system was studied, as the dimension of the system increased. MF and MMSE detectors were considered in the uplink and MF and RZF precoders were considered in the downlink analysis. The results indicate that, if the frame duration is properly  
\begin{table}
\begin{tabular}{l l l} \hline \hline
**Impairment** & **Effect** & **Possible Solution** \\ \hline CFO & - Performance degradation & - Using low complexity CFO estimation techniques \\  & - Sum-rate limitation in the OFDM case & - Using less sensitive waveforms such as SC-FDP \\ PAD & - Performance degradation & - Using Precoders that produce constant envelop signals \\  & - Sum-rate limitation & - Using less sensitive waveforms such as SC-FDP \\  & - Out of band radiation & - Using clipping and system degree of freedom to compensate clipping distortion \\ I/Q Imbalance & - Performance degradation & - Using Precoders that analyze real and imaginary parts separately \\  & - Sum-rate limitation & \\  & - Inaccurate channel estimation & \\ Phase noise & - Performance degradation & - Using more robust precoders \\  & - Channel aging & - Using phase noise tracking techniques \\ Channel Aging & - Performance degradation & - Using channel prediction techniques \\  & - Sum-rate limitation in the OFDM case & - Using less sensitive waveforms such as SC-FDP \\ \hline \hline \end{tabular}
\end{table}
Table 2: Effect of channel and hardware impairments and their possible solutions.  
selected, the effect of channel aging can be substantially mitigated. It was also showed that in high speed environments, using all BS antennas can result in very small achievable rates.