Coordinated Beamforming with Altruistic Precoding and User Selection for MU-MIMO System

Algorithm 1

Decentralized user selection with interference assignment.

(1) Stage 𝑛=0: Set all users inactive. For 𝑡th TTI, let the selected user set Ω_𝑖(𝑡)=∅, unselected user set Ψ_𝑖(𝑡)={1,2,…,𝐾_𝑖(𝑡)}.

  The number of selected users served by other BS is assumed as an integer 𝐾_𝑗, and 0≤𝐾_𝑗≤𝑁.

(2) Stage 𝑛=1: For each BS 𝑖, find the best user 𝑘 with largest lower bound on the capacity

          𝐶_𝑘,𝑖(𝑡)=max_{𝑘=1,2,…,𝐾𝑖(𝑡)}log₂𝐻_𝑘,𝑖²_𝐹𝜎²_𝑛+∑^𝐽_𝑗≠1𝐾_𝑗𝜆₁(𝐻_𝑘,𝑗𝐻^𝐻_𝑘,𝑗)

Let Ω_𝑖(𝑡)=Ω_𝑖(𝑡)+{𝑘}, Ψ_𝑖(𝑡)=Ψ_𝑖(𝑡)−{𝑘}.

(3) Stage 𝑛=𝑛+1:

  (a) Temporarily activate the user 𝑘 in candidate user set Ψ_𝑖(𝑡), and calculate the lower bound on the capacity 𝐶_𝑘,𝑖(𝑡)

   shown in (24).

  (b) For each BS 𝑖, find the user 𝑘 with the maximum sum capacity,

                (𝑘,𝑖)=argmax_{𝑘∈Ψ𝑖(𝑡)}𝐶_𝑘,𝑖

  (c) For each BS 𝑖, let Ω_𝑖(𝑡)=Ω_𝑖(𝑡)+{𝑘}, Ψ_𝑖(𝑡)=Ψ_𝑖(𝑡)−{𝑘}. If 𝑛≤𝑁−𝜉, return to (3). Else, quit the algorithm.