Suboptimal Greedy Power Allocation Schemes for Discrete Bit Loading

Algorithm 1

Full GPA algorithm applied to the initialisation step of the UPA algorithm.

Initialisation:

(1)   Set power available for GPA to 𝑃^gpa_𝑎=𝑃^ex in (12b)

    For each subchannel 𝑖 do the following:

(2)    Set 𝑏^gpa_𝑖=𝑏^𝑢_𝑖 in (10) and index 𝑘_𝑖=𝑘 in (9)

(3)    Cal. the min required upgrade power 𝑃^up_𝑖=𝛾^QAM_𝑘𝑖+1−𝛾^QAM_𝑘𝑖CNR_𝑖

Recursion:

  while   𝑃^gpa_𝑎≥min(𝑃^up_𝑖)   and   min(𝑘_𝑖)<𝐾, 1≤𝑖≤𝑁

(4)    𝑗=argmin_{1≤𝑖≤𝑁}(𝑃^up_𝑖)

(5)    𝑘_𝑗=𝑘_𝑗+1, 𝑃^gpa_𝑎=𝑃^gpa_𝑎−𝑃^up_𝑗

    if   𝑘_𝑗=1

(6)     𝑏^gpa_𝑗=log₂𝑀₁, 𝑃^up_𝑗=𝛾^QAM₂−𝛾^QAM₁CNR_𝑗

    elseif   𝑘_𝑗<𝐾

(7)     𝑏^gpa_𝑗=𝑏^gpa_𝑗+log₂𝑀_𝑘𝑗𝑀_𝑘𝑗−1, 𝑃^up_𝑗=𝛾^QAM_𝑘𝑗+1−𝛾^QAM_𝑘𝑗CNR_𝑗

    else

(8)     𝑏^gpa_𝑗=𝑏^gpa_𝑗+log₂𝑀_𝑘𝑗𝑀_𝑘𝑗−1, 𝑃^up_𝑗=+∞

    end

    end