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How to do power allocation in NOMA? (with fairness to far/weak user)

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Next post: NOMA with more than two users Power allocation is very important in non orthogonal multiple access (NOMA). In the previous post " Does power allocation affect NOMA? ", we saw how the bit error rate (BER) of NOMA has a strong relationship with the values of power allocation coefficients. We used fixed power allocation till now. That is, we fixed the values of $\alpha_1$ and $\alpha_2$ irrespective of the channel conditions. But there are better ways to optimize $\alpha_1$ and $\alpha_2$ dynamically based on the values of channel state information (CSI).  There are a few different dynamic power allocation schemes each trying to accomplish a specific goal. The goal could be maximizing the sum rate, maximizing the energy efficiency, etc., The power allocation scheme we are going to see in this post is a simple one whose goal is to provide user fairness. Let's call this fair power allocation ...