Power allocation based on SEP minimisation in three-user two-way channel

A three-user two-way channel in which three users exchange their messages through a two-way communication is considered by applying the physical-layer network coding and the superposition coding. The equivalent squared minimum distance (ESMD) is derived as a criterion for power allocation by analysing the average symbol error probability (SEP). Optimal and suboptimal power allocations are proposed based on the ESMD maximisation under total power constraint. Inspired by the result, a proportional power allocation is proposed under per-node power constraint. This scheme improves SEP at high signal-to-noise ratio (SNR) and consumes significantly less power. The average power consumption for each node is mathematically derived as a closed form. Furthermore, a compensation algorithm is introduced, which saves power and simultaneously achieves remarkable SEP improvement over entire SNR range. The numerical simulations over Rayleigh fading channels confirm the superiority of the proposed algorithms.