Ambrish Kumar Hello Sir,

Reason for allocating more power to the poor channel gain user is that we want to improve the quality of the signal received to the user. As near channel gain is more, he can successfully decode it own signal easily but in case of user with poor channel condition, it is not able to decode its own signal properly.

For relay purpose also, far user is consider as relay and if it is unable to decode it own signal then the error will also propagate to the next connected device.

In case of OMA, we allocate same power but in NOMA we take care of individual requirement of the device as one device may be near or other will be far.

Hello Sandeep, thanks for your answer.

According to you, in NOMA, more power should be allocated to the user with poor channel conditions, and based on the same concept, several research articles are available in the literature. However, this statement is declared as a myth about NOMA in the following paper.

Non-Orthogonal Multiple Access: Common Myths and Critical Questions | IEEE Journals & Magazine | IEEE Xplore

Their clarification is stated as follows:

The power allocation depends on what point (rate pair) in the capacity region is being targeted, and depending on that specific point the amount of power allocated to the user with the weaker channel can be higher than, equal to, or less than that of the other user. That is, |h1| > |h2| alone does not imply a < 1/2; that is, we should not necessarily allocate less power to the user with the stronger channel.

Example 1: Assume |h1| = 10|h2| (equivalently g1 = 100g2). As shown in Fig. 2, points B, C, and D on the capacity region are obtained for a = 0.025, a = 0.5, and a = 0.8, respectively. Consequently, the power allocated to the strong user (aP) would be less than, equal to, and more than that of the weak user (aP) if we are targeting to achieve points B, C, and D, respectively. Each point corresponds to a different rate pair (R1, R2). From Table 1, it is seen that the achievable sum rates (R1 + R2) for these points are 2.05, 3.62, and 3.77 bps/Hz, respectively. This clearly shows that the sum-rate increases by allocating more power to the stronger user. Indeed, if the achievable sum rate is the only system performance metric, the stronger user must receive all power; that is, a = 1 is optimal. Then, what is the reason for the common myth that power allocation in NOMA should be in reverse order of the users’ channel gains? The first answer to this question is that it is intuitive to assign more power to a user with a weaker channel to compensate for the higher channel loss. Such a mechanism, known as power control [4], has been adopted in 2G-4G cellular networks, particularly in the uplink. Power control is important for the efficient and fair operation of cellular systems. This intuition leads to a more concrete answer to the above question. Allocating a higher power to users with weaker channels is motivated by supporting a certain quality of service (QoS) or improving user fairness. QoS is usually quantified by Ri≥ ri where ri is the minimum required rate for user i. For weaker users, this “usually” implies allocating more power to compensate for the worse channel condition, but in general, it depends on the value of ri , the minimum required rate. As an example, for r1 = 1 and r2 = 0.1, and a ∈ [0.015 0.9] is acceptable in Fig. 2. Clearly then, it is not necessary to allocate a higher power to the weaker user, as any a ∈ (0.5 0.9] satisfies the QoS requirements while giving less power to the weaker user. In contrast, user fairness “commonly” improves if more power is allocated to the weaker user. An example of this is moving from D to B in Fig. 2, which is equivalent to increasing the weaker user’s power from 0.2 P to 0.975 P. This, however, does not imply that allocating more power to the weak user is better in terms of fairness. A vivid example of this is a = 0, which is an extremely unfair power allocation in view of user fairness.

In short, NOMA per se does not imply allocating a higher power to the user with the worse channel. Power allocation depends on the targeted point on the capacity region of the users scheduled in one cluster.

Hello Sir,

I agree it is not required to allocate more power to weak user.

Further, I appreciate your reference regarding myth about NOMA

Then, what about the published work?

Totally agree with Prof. Mojtaba Vaezi that the sum rate and user fairness cannot be increased simultaneously and hence power should be allocated depending on the requirement.

Thank you very much Prof. Majtaba Varzi and Mr. Anad Jee, for your answers to my question. Now it is clear to me that the NOMA can be used for two different purposes i.e. to increase the sum rate and user fairness. However, there is again a doubt/question that how sum-rate can be a direct addition of two rates, which are obtained under two different channel conditions?

Dear Dr. Vaezi,

Let us consider a scenario where two users exist i.e. a near-end and far-end users. Therefore, the transmitter will transmit the information into two identical phases. Suppose, in the first transmission phase, it transmits the information to a near-end user, and then in the second phase, it transmits the information to the far-end user. In particular, channel conditions are different in each transmission phase. Therefore, I just want to know, how we can directly add two rates, which are obtained under different channel conditions, in order to find the sum rate for end-to-end transmission. As per my understanding, the suggested paper is not concerned with the different channel conditions.

Dear Colleagues,

I agree with you that the allocation of power depends on the requirement.

Hi, Ambrish,

In terms of the answer on Feb. 4, here are some of my considerations.

Adding two rates in your case means a sum rate.

The achievable rate pair of the NOMA or Broadcast channel is

r1 ≤ log(1 + αP|h1|^2/N0),

r2 ≤ log(1 + (1 − α)P|h2|^2/( αP|h2| ^2 + N0),

where h1 and h2 are the channels.

See (5) in [1] for more details, and [2, Chapter 6.2.2, pp. 279].

When you mentioned the different channel conditions, do you mean the channels could have different relations and values? It may be the topic of symmetric and asymmetric channels. For example, in the suggested paper, Figure 2, the channel |h1| = 10 |h2|, the asymmetric channel is considered.

[1] Qi, Yue, Xinliang Zhang, and Mojtaba Vaezi. "Over-the-Air Implementation of NOMA: New Experiments and Future Directions." IEEE Access 9 (2021): 135828-135844. https://ieeexplore.ieee.org/stamp/stamp.jsp?arnumber=9552864

[2] D. Tse and P. Viswanath, Fundamentals of Wireless Communication. Cambridge, U.K.: Cambridge Univ. Press, 2005.

I hope the discussion can make the topic clearer.

Best,

Yue

Dear Yue Qi,

Thanks for your answer!

My question is not about symmetric & asymmetric channels, which is related to imperfect channel conditions. I just want to understand how the sum rate is obtained. It is defined as the direct addition of two different channel capacities (OR rates) which are obtained for two different users under different channel conditions.

Dear all,

Let's say the far user has a weak channel and less power is allocated,

according to the Shannon capacity formula, the achievable maximum data rate becomes

B*log_2(1+h_{weak}^2*P_{weak})>? R_{req} (1)

The problem is whether (1) satisfies your data rate requirement or not.

If the data rate requirement is low, then the UE may send the same data repeatedly to make sure a reliable communication.

Also for further reading, you may have a look at this article [1].

[1] Z. Ding, R. Schober, and H. V. Poor “Unveiling the Importance of SIC in NOMA Systems - Part I - State of the Art and Recent Findings ”, IEEE Communication Letters

Best regards,

Thanks Mr. Dusun for your answer! I agree with you that reliability of the network at low rate can be enhanced by increasing the diversity order!

It is true, a lower transmit power is assigned to a strong user, and a weak user is assigned more power.

Note that a strong user experiences a better channel condition, but that does not mean the signal strength is stronger.