This paper considers a frequency-division duplex (FDD) two-way channel with channel estimation error, where channel gains are independent of each other. It derives the exact closed-form outage probability expressions in the FDD system with analog network coding (ANC) by use of probability theory. To provide more insights, an approximated version for the exact outage probability is also developed in the medium-to-high signal-to-noise ratio (SNR) region. The simulation results show that the derived exact outage probabilities match the results of Monte Carlo simulations in all SNR regions, while the approximated outage probabilities also approach the simulation results when the channel condition is good. It is interesting that ANC in the FDD two-way channel is proved to outperform that of in the time-division duplex (TDD) channel by the computer simulation.
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