In this paper, a multi-user full-duplex (FD) two-way relaying system with decode-and-forward protocol is considered where all the nodes are assumed to be mobile and to have FD abilities. The residual self-interference (RSI) at each node is modeled as a Rician distributed random variable and the effect of mobility is incorporated by adopting the first order auto-regressive (AR) model. Then, the signal-to-interference-plus-noise-ratio (SINR) based scheduling schemes namely random scheduling, absolute channel power-based (CPB) scheduling, hybrid scheduling, and normalized CPB scheduling, are modified and the user pair selection is carried out on the basis of instantaneous channel statistics. The performance of the considered framework is analyzed for the modified scheduling schemes in terms of error probability and average rate. Next, the closed-form expressions for the symbol error probability (SEP) and average rate are derived for independent and non-identically distributed Rayleigh fading channels. Also, the numerical analysis highlighting the impact of user mobility and imperfect channel estimation on the scheduling strategies, fairness is presented. Furthermore, the impacts of the degree of traffic asymmetry, scheduling fairness, user mobility, channel estimation errors and RSI on the system performance are investigated. Numerical results are validated through the Monte Carlo simulations.
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