### Ergodic Capacity Analysis of Full-duplex Mimo Relay Channel using Tracy-Widom Distribution with Processing Delay

*Ajib Setyo Arifin, Tomoaki Ohtsuki*

**Abstract**: We

explore full-duplex technique in wireless communication particularly for relay

networks. We consider the relay to operate in full-duplex, which transmission

and reception are conducted in the same channel. We investigate potential

benefits of full-duplex technique in relay networks, which uses multiple

antennas for transmission and reception combined with Amplify-Forward (AF)

scenario. We study the effects of multiple antennas in terms of relay capacity.

We derive an ergodic capacity expression using Tracy-Widom distribution. Using

Singular Value Decomposition (SVD) and perfect Channel State Information (CSI),

we investigate three scenarios: First, we consider the relay to have antenna

larger than that of both source and destination. Second, we consider both relay

and destination to have antenna larger than that of source. Third, we consider

both relay and source to have antenna larger than that of destination. We show

the results that the capacity of relay with full-duplex technique is almost

twice the capacity of half-duplex. We show that increasing the number of destination

antennas is not help much when one of source antennas is small. Moreover, the

capacity decreases due to channel hardening effect, when the number of

destination antennas is larger than that of source.

**Keywords**: Ergodic capacity; Multiple antennas; Full-duplex relay; Self-interference.

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