The Optimal Antenna Layout for Maximum Ergodic Capacity of MISO Beamforming System

Algorithm 1

Process of SA algorithms.

(1) Generate a random initial configuration of antennas 𝐏_𝟎, and 𝐏^opt=𝐏_𝟎, compute the cost function value 𝑓(𝐏₀);

(2) Set the initial temperature 𝑇(0)=𝑇₀ and the iterations 𝑖=1;

(3) Do while 𝑇(𝑖)>𝑇_end

 (1) for inner loop 𝑚=1∼𝐾

 (2) Do some small random perturbation to the 𝐏^opt that yields a nearby solution 𝐏_new. Compute 𝑓(𝐏_new)

 and Δ𝑓=𝑓(𝐏_new)−𝑓(𝐏^opt)

 (3) if Δ𝑓≤0, 𝐏^opt=𝐏_new;

 (4) if Δ𝑓>0, 𝑢=exp(−Δ𝑓/𝑇(𝑖)); generate a random variable 𝑐=random[0,1], if 𝑐<𝑢, 𝐏^opt=𝐏_new.

 (5) end for

(4) 𝑖=𝑖+1;

(5) 𝑇(𝑖+1)=𝑇(𝑖);

(6) End Do while

(7) Output 𝐏^opt