Efficient Wireless Broadcasting through Joint Network Coding and Beamforming

Algorithm 2

Codebook-based allocation algorithm.

step 1: Initialization

   𝑉={𝑧₁,𝑧₂,…,𝑧_𝐾}

   𝑉₁=𝑉₂=⋯=𝑉_𝑄×𝑀=∅(emptyset)

step 2: For each MS 𝑧_𝑗 in 𝑉, compute SINR_𝑖𝑗 over all possible 𝑄×𝑀 beams. Then, assign MS 𝑧_𝑗

to beam 𝑖^∗ that maximizes SINR_𝑖𝑗 such that

    𝑖^∗=argmax_𝑖{SINR_𝑖𝑗}

{Note that if MS 𝑧_𝑗 is assigned to beam 𝑖^∗ in set 𝑙_𝑞 of a codebook, the interference will come from

all other beams in set 𝑙_𝑞, except beam 𝑖^∗}

step 3: Update

    𝑉=𝑉−{𝑧_𝑗}

   𝑉_𝑖∗=𝑉_𝑖∗∪{𝑧_𝑗}

step 4: If 𝑉≠∅ then go to step 2. Otherwise, the algorithm terminates and returns a set of MSs in

𝑉₁,𝑉₂,…,𝑉_𝑄×𝑀.