Is Analog Network Coding more energy efficient than TDMA?

In this paper, we investigate the possibility, from an energy efficiency point of view, of employing Analog Network Coding in the Multiple Access Relay Channel (MARC) instead of the conventional Time-Division Multiple Access (TDMA) protocol when time and not bandwidth is the available resource in the network. Towards this end, we derive a closed-form upper bound of the Bit Error Rate (BER) per source of Analog Network Coding when the optimal maximum-likelihood (ML) detector is employed. Based on this framework, we mathematically prove that as either the number of sources or the number of relays or the modulation order increases, the possibility of Analog Network Coding being more energy efficient than TDMA increases as well. These findings are substantiated by means of Monte Carlo simulations.