Energy-Efficient Dual-Iteration Power Allocation for Two-Phase Relay System with Massive Antennas

Algorithm 1

Energy-efficient dual-iteration power allocation.

Step 1.  (Initialization): 𝑝_𝑆𝑘=𝑃_𝑆𝑘,max(𝑘=1,2,…,𝐾), 𝐸^𝑈_𝑏=∞, 𝐸^𝐿_𝑏=𝐸^𝐿_𝑏𝐩_𝑆 in (28), and 𝜀>0.

Step 2.  (Update for relay node): 𝑋=𝑆 and 𝑌=𝑅.

Sub-step 1: Executing the Sub-Algorithm.

Sub-step 2: 𝑝^𝑜_𝑅𝑘=𝑝_𝑅𝑘(𝑝_𝑆𝑘,𝑐^𝑜_𝑘), 𝐸^𝑈_𝑏=𝐸^𝑜_𝑏𝐩_𝑆 and 𝐸^𝐿_𝑏=𝐸^𝐿_𝑏(𝐩^𝑜_𝑅).

Step 3. (Update for  source nodes): 𝑋=𝑅 and 𝑌=𝑆.

Sub-step 1: Executing the Sub-Algorithm.

Sub-step 2: 𝑝^𝑜_𝑆𝑘=𝑝_𝑆𝑘(𝑝_𝑅𝑘,𝑐^𝑜_𝑘), 𝐸^𝑈_𝑏=𝐸^𝑜_𝑏𝐩_𝑅 and 𝐸^𝐿_𝑏=𝐸_𝑏(𝐩^𝑜_𝑆).

Step 4. (Judgment): if 𝐸^𝑜_𝑏𝐩_𝑆−𝐸^𝑜_𝑏𝐩_𝑅≤𝜀, stop; else go back to Step 2.

Sub-Algorithm: Bi-section algorithm

Step 1. Let 𝑢=1/𝐸^𝑈_𝑏 and 𝑣=1/𝐸^𝐿_𝑏.

Step 2. Compute 𝜅=(𝑢+𝑣)/2, 𝑒_𝑏=1/𝜅 and 𝑐^𝑜_𝑘𝑒_𝑏,𝐩_𝑋.

Step 3. Compute 𝑓=𝐹𝑒_𝑏,𝐜^𝑜(𝑒_𝑏,𝐩_𝑋). If 𝑓>0 and the constraint 𝑇_𝑌 is valid, then 𝑢=𝜅; Else 𝑣=𝜅.

Step 4. If 𝑣−𝑢<𝜀, 𝐸^𝑜_𝑏𝐩_𝑋=𝑒^𝑜_𝑏; Else go back to Step 2.