Multi-Hop Bi-Directional Relay Transmission Schemes Using Amplify-and-Forward and Analog Network Coding

In this paper, we investigate two different multi-hop bi-directional relay transmission schemes based on amplify-and-forward (AF) protocol and analogue network coding (ANC). In the first scheme, referred to as the AF-ANC-Central scheme, AF is employed at each of the intermediate nodes, while ANC is only utilized at the central relay. In the second scheme, referred to as the AF-ANC-Even scheme, the even relays perform ANC and the odd relays only perform subtraction and AF. For reference purpose, the AF-No-ANC scheme is also considered, where the intermediate relays only perform AF and no ANC is employed. Bit error rate (BER) lower bounds of these three schemes are obtained, and are verified by Monte Carlo simulations to be asymptotically tight ones at high signal-to-noise ratios (SNRs). It is shown that the combination of AF and ANC is able to significantly improve system throughput when compared with the AF-No-ANC scheme. The BER performance of the AF-ANC- Central and AF-No-ANC schemes are of the same at high SNR region under the same transmission powers and system configuration, but the AF-ANC-Central scheme is able to double the system throughput. The AF-ANC-Even is able to further increase the system throughput with an SNR loss upper bounded by 1.76 dB when compared to the AF-ANC-Central and AF-No-ANC schemes.