Asynchronous Compute-and-Forward

The impact of time asynchronism on the performance of compute-and-forward strategy in relay networks is considered. While the key idea in compute-and-forward is to decode a linear synchronous combination of the transmitted codewords, the relays receive random asynchronous versions of the combinations due to the distributed nature of the network. Over a symbol-asynchronous network, we show that by using a simple equalizer as a part of the signaling scheme, one can transform the asynchronous system into a synchronous one albeit with a smaller channel gain. With frame-asynchronism, we propose to use extra antennas at the relays to efficiently remove the asynchronous delays. By applying a linear filter with a delay-dependent structure before the decoder of compute-and-forward, the achievable rate is maximized at all signal-to-noise-ratios (SNRs).