The growing demand for high-speed data, quality of service (QoS) assurance and energy efficiency has triggered the evolution of 4G LTE-A networks to 5G and beyond. Interference is still a major performance bottleneck. This paper studies the application of physical-layer network coding (PNC), a technique that exploits interference, in heterogeneous cellular networks. In particular, we propose a rate-maximising relay selection algorithm for a single cell with multiple relays based on the decode-and-forward strategy. With nodes transmitting at different powers, the proposed algorithm adapts the resource allocation according to the differing link rates and we prove theoretically that the optimisation problem is log-concave. The proposed technique is shown to perform significantly better than the widely studied selection-cooperation technique. We then undertake an experimental study on a software radio platform of the decoding performance of PNC with unbalanced SNRs in the multiple-access transmissions. This problem is inherent in cellular networks and it is shown that with channel coding and decoders based on multiuser detection and successive interference cancellation, the performance is better with power imbalance. This paper paves the way for further research in multi-cell PNC, resource allocation, and the implementation of PNC with higher-order modulations and advanced coding techniques.