A Low-Complexity Resource Allocation Algorithm for MIMO-OFDMA Multicast Systems with Spectrum-Guarantee Provisioning

Algorithm 1

Inputs:

𝒩={1,2,…,𝑁}

𝒢={1,2,…,𝐺}

𝒞={𝐶₁,𝐶₂,…,𝐶_𝐺} such that (10) is fulfilled.

𝑅_𝐺×𝑁=[𝑅_𝑗,𝑛]  % computed by(5)

Outputs:

𝑋_𝐺×𝑁=[𝑥_𝑗,𝑛]

Initialization:

𝑥_𝑗,𝑛=0, for 𝑗=1⋯𝐺 and 𝑛=1⋯𝑁

While 𝒞≠{}:

 Find 𝑗̃∈𝒢 an 𝑛∈𝒩 with 𝑅_̃𝑗,𝑛≥𝑅_𝑗,𝑛 ∀𝑗,𝑛

If ∑^𝑁_𝑛=1𝑥_̃𝑗,𝑛≥𝐶_̃𝑗  % examines(9)

𝒞←𝒞⧵{𝐶_̃𝑗}

𝒢←𝒢⧵{𝑗}̃

Else

 Set 𝑥_̃𝑗,𝑛=1

𝒩←𝒩⧵{𝑛}  % satisfies(8)

While 𝒩≠{}:

 Find 𝑗^∗,𝑛^∗ such that 𝑅_{𝑗∗,𝑛∗}≥𝑅_𝑗,𝑛 ∀𝑗,𝑛

 Set 𝑥_{𝑗∗,𝑛∗}=1

𝒩←𝒩⧵{𝑛^∗}  % satisfies(8)

 Update (6).