Energy Efficient Design for Two-Way AF Relay Networks

Algorithm 1

Optimal power allocation (OPA) algorithm.

Step  1. Initialization, 𝜙_𝑚=0, 𝜙_𝑙=0, 𝜙_ℎ=0.

Step  2. Calculate 𝜙̌ and 𝜙 according to (12a)–(12c) and (14). Set 𝜙_𝑙=𝜙̌ and 𝜙_ℎ=𝜙.

Step  3. Set 𝜙_𝑚=(𝜙_𝑙+𝜙_ℎ)/2.

Step  4. If its first derivative with respect to 𝜙 satisfies (𝑑𝑈(𝜙)/𝑑𝜙)|_{𝜙=𝜙𝑚}>0, then 𝜙_𝑙=𝜙_𝑚, else 𝜙_ℎ=𝜙_𝑚.

Step  5. Repeat Step  3 until 𝜙_ℎ−𝜙_𝑙≤𝜀 where 𝜀 is a small positive constant to control the convergence accuracy.

Step  6. Calculate the optimal solution 𝑃^∗_𝑖=𝑓_𝑖(𝜙_𝑚), 𝑖={𝑎,𝑏,𝑟} according to (12a)–(12c).