Efficient Wireless Broadcasting through Joint Network Coding and Beamforming

Algorithm 3

Optimized codebook algorithm.

step 1: Initialization

    𝐿={𝑙₁,𝑙₂,…,𝑙_𝑄}

   Given 𝑉₁,𝑉₂,…,𝑉_𝑄×𝑀

   compute 𝑇_𝑄

step 2: For each set 𝑙_𝑞 of a codebook where 𝑞∈{1,2,…,𝑄}, compute the maximum value of PERs

over all MSs assigned to a set 𝑙_𝑞 such that

    𝑋_𝑙𝑞=max_𝑖{max_𝑗{PER_𝑖𝑗}}_𝑙𝑞

step 3: Eliminate a set 𝑙^∗_𝑞 over all existing sets such that

   𝑙^∗_𝑞=argmin_𝑙𝑞{𝑋_𝑙𝑞}

step 4: For each MS 𝑧_𝑗 in a set 𝑙^∗_𝑞, compute SINR_𝑖𝑗 over all existing beams 𝑖 except all beams in

a set 𝑙^∗_𝑞. Then, assign MS 𝑧_𝑗 to beam 𝑖^∗ that maximizes SINR_𝑖𝑗 such that

   𝑖^∗=argmax_𝑖{SINR_𝑖𝑗}

step 5: Compute 𝑇_𝑄−1

step 6: If 𝑇_𝑄−1≤𝑇_𝑄,

   update 𝑉₁,𝑉₂,…,𝑉_{(𝑄−1)×𝑀}

   𝐿=𝐿−{𝑙^∗_𝑞}

    𝑄=𝑄−1

    then go to step 2

step 7: The algorithm terminates, then returns a set of MSs in 𝑉₁,𝑉₂,…,𝑉_𝑄×𝑀, an optimized codebook

𝐿, and the expected number of transmissions 𝑇_𝑄.