Relay Selection and Subcarrier-Pair Based Energy-Efficient Resource Allocation for Multirelay Cooperative OFDMA Networks

Algorithm 1

Bisection-based energy-efficient resource allocation algorithm.

(1) Initialize  𝑞_min = 0, 𝑞_max >> 0 with 𝐹(𝑞_min) > 0 and 𝐹(𝑞_max) < 0, 𝜀.

(2) (i)Update  𝑞_middle←(𝑞_min+𝑞_max)/2;

   (ii) Initialization: 𝜆_𝑘, 𝜇_𝑛, and 𝜈_𝑘;

     (a) Obtain the optimal power via (27) and (28);

     (b) Obtain (𝑚,𝑚^′) via (35);

     (c) Obtain (𝑛,𝑘) for given (𝑚,𝑚^′) via (32);

     (d) Update the dual variables 𝜆_𝑘, 𝜇_𝑛, and 𝜈_𝑘 via (23);

     (e) Repeat (a) → (d) until convergence;

(3) If 𝐹(𝑞_middle)>0,𝑞_min←𝑞_middle; otherwise, 𝑞_max←𝑞_middle;

(4) Repeat  Steps 2 and 3 until 𝐹(𝑞_middle)<𝜀.