LAUSR

This paper considers a massive MIMO full-duplex relaying (FDR) system, in which multiple single-antenna sources simultaneously communicate with multiple single-antenna destinations using a single relay that is equipped with $N_{\mathrm {tx}}$ transmit antennas and $N_{\mathrm {rx}}$ receive antennas. Under the practical scenario of imperfect channel-state information, the relay processes the received signals by means of maximum-ratio combining/maximum-ratio transmission (MRC/MRT) or zero-forcing (ZF) processing, and employs either the decode-and-forward (DF) or amplify-and-forward (AF) scheme. Considering hardware impairments, closed-form expressions of the lower bounds on the sum spectral efficiencies for DF and AF schemes are derived for both the MRC/MRT and ZF processing methods. Based on the obtained expressions, various power scaling laws are established to show the relationships among the transmit powers of the sources, relay, and pilots in order to maintain a desirable quality of service when $N_{\mathrm {tx}}$ and $N_{\mathrm {rx}}$ go to infinity but with a fixed ratio. In particular, it is found that the massive MIMO FDR systems under consideration are not affected by the loop interference, can save power, and improve the rate performance when the three transmit powers are scaled down to ${1/ {N_{\mathrm {rx}}^{a}}}$ , ${1 / {N_{\mathrm {tx}}^{b}}}$ , and ${1 / {N_{\mathrm {rx}}^{c}}}$ , respectively, where $a + c = 1$ , $b + c < 1$ , and $b > 0$ . Numerical results corroborate the accuracy of the closed-form expressions and show that, when the loop interference level is small, using low-quality hardware at the relay and high-quality hardware at the sources and the destinations is a good design choice in the practical design of low-cost massive MIMO FDR systems.