In this paper, we analyze the impact of channel estimation errors in an amplify-and-forward (AF)-based two-way relaying network (TWRN) where adaptive modulation (AM) is employed in individual relaying path. In particular, the performance degradation caused by channel estimation error is investigated over Nakagami-m fading channels. We first derive an end-to-end signal-to-noise ratio (SNR), a cumulative distribution function, and a probability density function in the presence of channel estimation error for the AF-based TWRN with adaptive modulation (TWRN-AM). By utilizing the derived SNR statistics, we present accurate expressions of the average spectral efficiency and bit error rates with an outage-constraint in which transmission does not take place during outage events of bidirectional communications. Based on our derived analytical results, an optimal power allocation scheme for TWRN-AM is proposed to improve the average spectral efficiency by minimizing system outages.

In this paper, we study the impact of imperfect channel information on an amplify-and-forward (AF)-based two-way relaying network (TWRN) with adaptive modulation which consists of two end-terminals and multiple relays. Specifically, we consider a single-relay selection scheme of the TWRN in the presence of outdated channel state information (CSI) and channel estimation errors. First, we choose the best relay based on outdated CSI, and perform adaptive modulation on both relaying paths with channel estimation errors. Then, we discuss the impact of the outdated CSI on the statistics of the signal-to-noise ratio (SNR) per hop. In addition, we formulate the end-to-end SNRs with channel estimation errors and offer statistic analyses in the presence of both the outdated CSI and channel estimation errors. Finally, we provide the performance analyses of the proposed TWRN with adaptive modulation in terms of average spectral efficiency, average bit error rate, and outage probability. Numerical examples are given to verify our obtained analytical results for various system conditions.