Performance Analysis of Relay Subset Selection for Amplify-and-Forward Cognitive Relay Networks

Algorithm 1

The pseudocode of the proposed algorithm.

INPUTS: 𝑃_𝑠,𝜁,Γ=[1,2,…,𝑁],𝑁₀,𝑔_𝑖,ℎ_𝑖,𝑓_𝑖∀𝑖∈Γ

for 𝑖=1,2,…,𝑁

   𝑃_𝑖=(𝐴_𝑖)²(𝑃_𝑠|𝑔_𝑖|²+𝑁₀)      // use minimum amplification

   𝐼_𝑖=𝑃_𝑖𝑓_𝑖²

end for

Ω⊂𝑃_1×𝑁      // non-trivial subsets of 𝑃

𝐿⊂Ω=𝐴𝑙𝑙𝑠𝑢𝑏𝑠𝑒𝑡𝑠𝑜𝑢𝑡𝑜𝑓Ω𝑠.𝑡.𝑓𝑜𝑟𝑗th𝑠𝑢𝑏𝑠𝑒𝑡𝐿_𝑗,𝐼^𝑗=∑_{𝑖∈𝐿𝑗}𝐼_𝑖=∑_{𝑖∈𝐿𝑗}𝑃_𝑖𝑓_𝑖²≤𝜁

for 𝑗=1∶𝐽    // number of selected subsets in 𝐿

 while 𝐼^𝑗≤𝜁

    𝑃_𝑖=𝑃_𝑖+Δ    for maxℎ_𝑖𝑓_𝑖 // 𝑖  denotes 𝑖th element of 𝑗th selected subset 𝐿_𝑗

 endwhile

    𝛾_𝑗=∑_{𝑖∈𝐿𝑗}𝛾_2𝑖=∑_{𝑖∈𝐿𝑗}𝑃_𝑖ℎ_𝑖²    𝑗=1,…,𝐽

end for

𝐿_𝑗′∈𝐿  s.t. 𝛾_𝑗′  corresponding to 𝐿_𝑗′  is maximum

OUTPUTS: 𝐿_𝑗′,𝛾_𝑗′