Joint Tx/Rx FDE and spectrum combining for SC-ANC bi-directional relay in presence of timing offset

Recently, we proposed a joint transmit/receive frequency-domain equalization (FDE) for single-carrier (SC) analog network coded (ANC) bi-directional relay and showed that the proposed joint transmit/receive FDE achieves better BER performance than the use of either transmit FDE or receive FDE only. However, our previous study for SC-ANC bi-directional relay assumed no arrival timing offset. However, the signals transmitted from base station (BS) and mobile terminal (MT) may not necessarily arrive at the relay station (RS) at the same time. The arrival timing offset causes the inter-symbol interference and accordingly, BER performance degradation. In this paper, we propose a joint transmit/receive FDE and spectrum combining for SC-ANC bi-directional relay in the presence of timing offset. RS performs oversampling and transmit FDE while both MT and BS receivers perform oversampling, receive FDE and spectrum combining. Transmit and receive FDE weights when using the spectrum combining are jointly optimized based on minimum mean square error (MMSE) criterion. Computer simulation confirms that the proposed joint transmit/receive FDE and spectrum combining obtains both spatial and frequency diversity gain and achieves a good BER performance even in the presence of timing offset.