Analysis of DF relay selection in massive MIMO systems with hardware ımpairments

We consider a massive multiple-input multiple-output (m-MIMO) system in which a source communicates with a destination with the help of multiple single-antenna decode-and-forward (DF) relays. Employing optimal relay selection, we analyze the system performance in presence of hardware impairments (HWI) for two m-MIMO scenarios: massive-antenna source and single-antenna destination (m-MIMO I), and massive-antenna source and destination (m-MIMO II). We obtain lower bounds on the average signal-to-noise plus distortion ratio (SNDR) of the system and show that in the m-MIMO II regime, the HWI levels at the relays become the only limiting factors. Employing extreme value theory, we demonstrate that as the number of relays increases the end-to-end SNDR of the system tends to Gumbel and Weibull distributions for the m-MIMO I and m-MIMO II systems, respectively. In addition, for both arbitrary numbers of source and destination antennas and m-MIMO scenarios, we provide closed form expressions for optimal power allocation between the source and the selected relay, and the effects of HWI level distributions between the receiving and the transmitting parts of the relay (which can be exploited for optimal system design under cost constraints).