Analysis and Implementation of Asynchronous Physical Layer Network Coding

Physical layer network coding has attracted extensive theoretical interest, although relatively little research has been done in support of deployment to wireless networks where internode synchronization is difficult to achieve. In particular, wireless networks constructed with inexpensive and commercially available software defined radio technology, or more generally, radio front-end samplers connected to internet-based remote processors (i.e., the Internet of Things network) may exhibit large time, frequency, and phase offsets that are difficult to control. In this paper, we define an asynchronous discrete-time model that accounts for these impairments as part of the information transfer between network users and a relay. Derived from this model are maximum likelihood algorithms for relay parameter estimation and a symbol decoder inspired from asynchronous multi-user detection. Additionally, null space-based frequency offset estimation that reduces computational complexity is proposed. Simulation results and the design and performance of a two-user system implemented with the Universal Software Radio Peripheral (USRP) platform and GNU radio are included to demonstrate the proof of concept. Our results indicate that the physical layer network coding technique can be successfully deployed and yields significant benefits even in the presence of impairments found in practical settings.