Network coding noise reduction via relay power allocation in a two-unicast wireless system

Network coding (NC) is known as a promising approach to improve the cooperative communication network throughput. However, in certain situations, it can introduce additional noise terms which is recently referred to as NC noise. We consider such a problem in a two-unicast wireless system and seek to answer the following question: "Can we reduce or remove network coding noise by proper power allocation at the relay?" To this end, we provide a mathematical framework for the output signal-to-noise (SNR) ratio and instantaneous sum-rate of the network-coded cooperative communication (NC-CC) system with the notion of power assignment at the relay. Based on this framework, we provide two novel closed-form power allocation techniques that are suitable for slow and fast fading conditions. Numerical analysis is used to confirm the accuracy of the derived theory and to show the effectiveness of proposed solutions in terms of average sum-rate and outage probability. It is shown that such techniques offer a significant advantage in overcoming the adverse effects of NC noise, especially in slow fading, without introducing significant extra costs or system complexity