In this paper, joint transmit/receive frequency-domain equalization (FDE) is proposed for analog network coded (ANC) single-carrier (SC) bi-directional multi-antenna relay. In the proposed scheme, diversity transmission using transmit FDE is performed at relay station (RS) equipped with multiple antennas while receive FDE is carried out at base station (BS) and mobile terminal (MT) both equipped with single antenna. The transmit and receive FDE weights are jointly optimized so as to minimize the end-to-end mean square error (MSE). We evaluate, by computer simulation, the throughput performance and show that the joint transmit/receive FDE obtains the spatial and frequency diversity gains and accordingly achieve better throughput performance compared to either the transmit FDE only or the receive FDE only. It is also shown that ANC SC bi-directional multi-antenna relay can extend the communication coverage area for the given required throughput compared to conventional direct transmission.

In this paper, we propose an efficient channel estimation scheme in bi-directional wireless orthogonal frequency division multiplexing (OFDM) relay systems applying analog network coding (ANC). In the relay systems applying ANC, channel separation is needed to estimate each of the bi-directional channels simultaneously from the combined received signal. In the conventional channel estimation schemes, relatively higher-ratio pilots are needed to obtain accurate channels. In contrast, we propose a channel estimation scheme with sparse pilots, while maintaining high accuracy for channel estimation. In the proposed scheme, Walsh codes are inserted as the pilot symbols at both end nodes, and the individual channels are obtained by correlation processing from the combined signals. The improved bit error rate (BER) and throughput performances of the proposed scheme are shown through computer simulations.

Timing asynchronism strongly degrades the performance of analog network coded (ANC) bi-directional transmission. This letter investigates receiver design for asynchronous broadband bi-directional transmission over frequency selective fading channels. Based on time domain oversampling, we propose fractionally spaced frequency domain minimum mean square error (MMSE) equalizers for bi-directional ANC based on orthogonal frequency division multiplexing (OFDM) and cyclic prefixed single carrier (CP-SC) radio access. Simulation results show that the proposed fractionally spaced equalizer (FSE) can eliminate the negative effect of timing misalignment in bi-directional transmissions.