Does power allocation affect NOMA?

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Till now, we simulated various performance parameters like bit error rate (BER), capacity and outage probability of NOMA by using fixed power allocation method. By fixed power allocation, we mean that regardless of the channel condition, we always set $\alpha_1 = 0.75$ (for far user) and $\alpha_2 = 0.25$ (for near user). This is one way to allocate power. And the advantages of this fixed power allocation method are:

• No computation required
• No knowledge of channel state information (CSI) is required

But this is not the optimum way to allocate power. If we write a simple MATLAB code to plot the BER as a function of power allocation coefficients, we get a plot like this: (Download the code here)

Some notes about this plot

• In this plot, we consider user 1 to be the far user and user 2 to be the near user.
• Also, we have used fixed power allocation method. That is, we did not alter the coefficients based on channel conditions. We have just plotted the BERs when we fix different values of power allocation coefficients.
• The solid lines are for a transmit power of 40 dBm and the dotted lines are for 20 dBm.
• The above plot can be interpreted in terms of $\alpha_2$ by doing the transformation $\alpha_2 = 1 - \alpha_1$. (since, we know that, $\alpha_1 \gt \alpha_2$ and, $\alpha_1 + \alpha_2 =1$)

What can we infer from this plot?

• Firstly, we see that some values of power allocation coefficients are better than others. That is the BER is low for some values of $\alpha_1$ and high for other values.
• The near user (user 2) experiences low BER ($\lt10^{-4}$) at two regions of this plot. i.e., around $\alpha_1 < 0.1$ (in other words, $\alpha_2 \gt 0.9$) and around $\alpha_1 \approx 0.8$ (in other words, $\alpha_2 \approx 0.2$).



• The BER for near user (user 2) is lower when $\alpha_1 < 0.1$ ($\alpha_2 \gt 0.9$) than when $\alpha_1 \approx 0.8$ ($\alpha_2 \approx 0.2$). So, can we choose $\alpha_1 < 0.1$ and $\alpha_2 \gt 0.9$)? No. Because the far user (user 1) has very high BER in this regime



• If we want both users to fairly benefit from NOMA, the ideal regime to operate is $\alpha_1\in[0.5,1]$, $\alpha_2\in[0,0.5]$.



• Towards the left end of the plot, $\alpha_1 \approx 0$ and $\alpha_2 \approx 1$. This means a very large power is allocated to the near user (user 2). Therefore, he has a very low BER.



• As $\alpha_1 \approx 0$ and $\alpha_2 \approx 1$, the near user's (user 2) data is dominating and hence, the far user (user 1) will not be able to directly decode his signal. This explains his high BER.



• Towards the right end of the plot, $\alpha_1 \approx 1$ and $\alpha_2 \approx 0$. This means a very large power is allocated to the far user (user 1). Therefore, he has a decreasing BER trend.



• As $\alpha_1 \approx 1$, the interference from the high power far user (user 1) data is so large that the near user (user 2) suffers high BER.

In our next post, we will see some ways to optimize the power allocation coefficients based on the knowledge of instantaneous channel state information (CSI). Thank you!

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How to do power allocation in NOMA?