Near Optimum Power Control and Precoding under Fairness Constraints in Network MIMO Systems

Algorithm 2

Iterative SINR and precoding optimization.

Given 𝑡=0,𝜖⁽⁰⁾=1,𝑃_tot,𝜀_gap and 𝐓_𝑘⁽⁰⁾=𝐈_𝑁𝑡 for all 𝑘.

Initialize SINR targets Γ⁽⁰⁾=diag(𝛾^tgt_𝑘) and transmission

powers 𝐩⁽⁰⁾ solving either problem (22) or (23).

Repeat:

 (1) 𝑡=𝑡+1.

 (2) For 𝑘=1 to 𝐾

   (a) Given {𝐓^(𝑡−1),𝐏^(𝑡−1)}, compute the inter ference

    𝜁_𝑘,𝑠=𝑓(𝐓^(𝑡−1),𝐏^(𝑡−1)) as in (38).

   (b) Calculate the optimum loading matrix 𝐓_𝑘^(𝑡) as

     (𝐓_𝑘^(𝑡))^(𝑠,𝑠)=𝜁_𝑘,𝑠𝑁_𝑡∑^𝑁𝑡_𝑗=1𝜁_𝑘,𝑗∀𝑠∈[1,𝑁_𝑡].

   (c) Calculate the new SINR targets Γ^(𝑡) and

    update the optimum transmit power 𝑃_𝑘^(𝑡) as

     𝛾_𝑘^(𝑡)=𝛾^tgt_𝑘⋅𝜖^(𝑡−1)∀𝑘

     𝑃_𝑘^(𝑡)=𝜁_𝑘,𝑠|(𝐓_𝑘^(𝑡))^(𝑠𝑠)|²(𝛾_𝑘^(𝑡)+1)∀𝑘,𝑠

 (3) Update the control parameter 𝜖:

   (a) If objective is power minimization: 𝜖^(𝑡)=𝜖^(𝑡−1);

   (b) If objective is throughput maximization:

     𝜖^(𝑡)={𝜖^(𝑡−1)−𝜅(∑_𝑘𝑃_𝑘^(𝑡)−𝑃_t𝑜𝑡)}⁺.

Until |𝑃_𝑘^(𝑡)−𝑃_𝑘^(𝑡−1)|≤𝜀_gap,∀𝑘.