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85 http://journals.cihanuniversity.edu.iq/index.php/cuesj CUESJ 2024, 8 (1): 85-90

 Review ARticle

Dynamic Power Allocation for Downlink NOMA
Yazen S. Almashhadani, Ghassan A. Qasmarrogy

Department of Communication and Computer Engineering, Cihan University-Erbil, Kurdistan Region, Iraq

ABSTRACT

Dynamic power distribution for connected non-orthogonal multiple access (NOMA) is an important research area in wireless 
communication systems. This study focuses on the implementation and evaluation of dynamic power distribution strategies in the 
context of NOMA downlink. We compare the performance of dynamic power distribution and power distribution schemes to evaluate 
their impact on system output, interference control, and overall efficiency. Through extensive simulation and analysis using MATLAB, 
this article presents the comparison between dynamic power distribution and fixed power distribution, and the advantages of dynamic 
power distribution in adaptive to change the channel conditions and the user’s need to improve the system performance. Our results 
show that data rates and non-loss can provide an important insight into the benefits of dynamic power distribution in NOMA downlink 
systems and emphasize the importance of adaptive power management techniques in improve wireless communication networks.

Keywords: Non-orthogonal multiple access, Rayleigh channel, user pairing, power allocation, outage probability

INTRODUCTION

The emergence of dynamic power allocation (DPA) for 
downlink non-orthogonal multiple access (NOMA) as a 
key area in the field of wireless communication systems 

is aimed at increasing both spectral efficiency and system 
performance.[1]

In addition, NOMA is capable of allowing several users to 
share time-frequency resources by employing power domain 
multiplexing resulting in increased spectral efficiency and 
better user experience. In this scenario, downlink where a base 
station (BS) communicates with several users simultaneously, 
optimization of system performance through DPA becomes 
important as it allocates levels of power depending on 
channel conditions, user demands, and interference 
management methods. This introduction lays the foundation 
for investigating the significance of DPA in downlink NOMA 
systems and how they enhance throughput, system capacity, 
and overall network performance.[2] The NOMA with multiple 
users as shown in Figure 1.

The aim of this study focuses on examining the efficiency 
of DPA strategies in the framework of downlink NOMA using 
the software MATLAB. The notion behind DPA is that it alters 
the assigned powers to users as per channel conditions and QoS 
requirements for a purpose of enhancing system throughput 
and minimizing interference.

On the other hand, some schemes allocate a fixed amount 
of power to each user in spite of channel variations. Our 
objective is to assess how adaptive power regimes enhance 
system’s efficiency and general performance by comparing it 

with the performances of DPA approaches when compared 
against fixed power allocations (FPA). Through simulation-
based analysis and performance evaluation, we seek to provide 
insights into the benefits of DPA in downlink NOMA systems 
and highlight the advantages of adaptive power management 
techniques in improving wireless communication networks. 
This study contributes to the ongoing research efforts in 
optimizing power allocation strategies for enhancing the 
performance of NOMA systems in practical scenarios. Through 
simulation-based analysis and performance evaluation, we 
seek to provide insights into the benefits of DPA in downlink 
NOMA systems and highlight the advantages of adaptive power 
management techniques in improving wireless communication 
networks. This study contributes to the ongoing research 
efforts in optimizing power allocation strategies for enhancing 
the performance of NOMA systems in practical scenarios.

While (OFDM) introduce a larger number of narrow 
band sub-channels which gives more transmit data rate, 

Corresponding Author: 
Yazen S. Almashhadani, Department of Communication and 
Computer Engineering, Cihan University-Erbil, Kurdistan Region, 
Iraq. E-mail: yazen.mahmood@cihanuniversity.edu.iq

Received: May 19, 2024

Accepted: June 14, 2024

Published: June 30, 2024

DOI:10.24086/cuesj.v8n1y2024.pp85-90

Copyright © 2024 Yazen S. Almashhadani, Ghassan A. QasMarrogy. This is an 
open-access article distributed under the Creative Commons Attribution License.

Cihan University-Erbil Scientific Journal (CUESJ)



Almashhadani and Qasmarrogy: Dynamic Power Allocation for NOMA

86 http://journals.cihanuniversity.edu.iq/index.php/cuesj CUESJ 2024, 8 (1): 85-90

each sub-channel is orthogonal. They are narrow bands and 
closely spaced. Due to its capability to lever with multipath 
interference at the receiver OFDM is being used also, it splits 
the stream of high-rate data into a lower-rate stream that is 
transmitted simultaneously over a number of subcarriers.[3]

The rest of the paper will be organized as follows, in 
chapter two, related work will be showed and discussed, 
chapter three will investigate the system model, chapter four 
will show the analysis and result, and finally, in chapter, five a 
conclusion will be demonstrated.

RELATED WORK

Several studies have explored the application of DPA for 
downlink NOMA using MATLAB software. In a study by,[4] 
the authors proposed a DPA algorithm for downlink NOMA 
systems to maximize the sum rate of users while considering 
the quality-of-service requirements. The algorithm was 
implemented and evaluated using MATLAB simulations, 
demonstrating improved system performance compared to 
FPA schemes.

Similarly Liu et al.[5] investigated the impact of DPA 
in downlink NOMA systems using MATLAB. The authors 
developed a novel power allocation strategy that dynamically 
adjusts power levels based on channel conditions and user 
priorities. Through extensive simulations, they showed that 
DPA outperformed FPA in terms of system throughput and 
interference management.

Furthermore, Saeed and Sileh[6] conducted a comparative 
study between dynamic and FPA techniques in downlink 
NOMA systems using MATLAB. Their results indicated that 
DPA led to higher spectral efficiency and improved user 
fairness compared to FPA strategies.

Overall, these related works highlight the significance 
of DPA in optimizing the performance of downlink NOMA 
systems and emphasize the utility of MATLAB software for 
implementing and evaluating such algorithms.

SYSTEM MODEL

This paper focus on the downlink communication in NOMA. 
The scenario comprising a BS and M users each with 
corresponding channel condition denoted hi where the channel 
coefficient linked from the BS to the ith user, consider that U1 

is the first user, with channel h1 being closest to the BS which 
deliberates the stronger user, the subsequent user U2 is the 
second stronger user, and this pattern continuous accordingly. 
User UM being the farthest/weaker follows this sequence.[7]

Figure 2 illustrates the system model of the downlink 
communication; we assume four users, that is, (M = 4) are 
distributed with different distances from the BS. Wireless 
paths assumed to undergo Rayleigh fading channel coefficients 
ordered as.[7]

∣h1∣2>∣h2∣2>∣h3∣2….∣hM∣2 (1)

Denote the messages to be transmitted to the users as 
X1, X2... XM. The BS utilizes superposition coding with these 
messages and sends the resultant NOMA signal into the 
channel, we can represent XNOMA concisely as follows:

X P XNOMA i i
i

M
�

�� ±�
1

 (2)

Here, P represents the total transmitted power, αi signifies 
the power allocation coefficient for the ith user.

The power allocation coefficients must be ordered as 
α1 < α2 <….αM, since the strong channel condition is assigned 
less power than the user with weak channel condition.

The received signal at user i is given by

y X hi NOMA NOMA i i_ �� ��  (3)

Where ωi is the additive white Gaussian Noise with zero 
mean and variance σ2.

Given that UM is allocated the highest power allocation; its 
intended message dominates the received signal. Consequently 
UM engages in direct decoding, interpreting the signals intended 
for all other users as interference. UM–1 should directly decode 
UM message, then perform successive interference cancelation 
(SIC) to remove it. After SIC, UM–1 becomes the dominating 
message signal. Thus, UM–1 can directly decode its message by 
regarding the message signals of all other remaining users as 
interference. We can apply a similar thought process to attain 
the decoding rule for the remaining users. In general, for any 
given user i, the signal to interference ratio (SINR) to decode 
his own signal is given by

α

α σ
= +

γ =
+∑

2 

_  
2  2

1

 

   

i i
i NOMA M

j j
j i

P h

P h

| |

| |
 (4)

The resultant rate for any intended user i based on 
Shannon’s capacity formula[8] can be written as

= + γ_   2 _log (1 )i NOMA i NOMAR B  (5)

Where B is the overall bandwidth. Therefore, the total 
capacity of downlink NOMA system with M users is given by 
the summation of the data rates of all users in the system as 
follows

R RNOMA i NOMA
i

M
�

��� _
1

 (6)

On the other hand, orthogonal resource blocks use the 
orthogonal multiplexing approach. In orthogonal multiple 

Figure 1: Non-orthogonal multiple access[2]



Almashhadani and Qasmarrogy: Dynamic Power Allocation for NOMA

87 http://journals.cihanuniversity.edu.iq/index.php/cuesj CUESJ 2024, 8 (1): 85-90

Figure 2: Downlink NOMA for M users

access (OMA) system, when the total bandwidth and power 
are shared among the users equally, therefore, the achieved 
data rates of users given as:

σ
 

= + 
 

2 

_   2 2

 
log 1

 
i i

i OMA

P hB
R

N
| |

 (7)

In OMA system, equally assigned user power is formulated as

Pi = 1/MP (8)

The total capacity of downlink OMA is calculated as

R ROMA i OMA
i

M
�

��� _
1

 (9)

NOMA User Pairing

NOMA concurrently serves multiple users within the same 
frequency band. Although SIC technique is applied, the 
severe interference is noticed when the number of users is 
increases beyond the limit and yield a throughput drop of the 
overall system. The hybrid NOMA with OMA is utilized for 
interference degradation and diminished the complexity, of 
course this is tradeoff with the utilized spectrum.[9] Four users 
are considered in this work, so there are four possible user 
pairing can be chosen. The maximum channel gain difference 
between users is promises for better improvement of the 
date rate rather than other pairing distribution; hence, after 
rearrange, the four channel gains of the four users as ∣h1∣2 > 
∣h2∣2 > ∣h3∣2 > ∣h3∣2, the stronger with the weaker (U1 with 
U4) is paired then the second stronger with the second weaker 
(U2 with U3) is paired. The SIC for every pair is applied as 
independent to the other pair.

The users in the first pair have to choose α1 < α4, the rates 
of the first and fourth user as follows:

α
σ

 
= + 

 

2 
1 1

1 2 2

 1
log 1

2
P h

R
| |

 (10)

After SIC

α
α σ

 
= + 

+ 

2 
4 4

4 2 2  2
1 4

 1
log 1

2
P h

R
P h

| |
| |

 (11)

The users in the second pair have to choose α2 < α3, the 
rates of the first and fourth user as follows:

α
σ

 
= + 

 

2 
2 2

2 2 2

 1
log 1

2
P h

R
| |

 (12)

After SIC

α
α σ

 
= + 

+ 

2 
3 3

3 2 2  2
2 3

 1
log 1

2
P h

R
P h

| |
| |

 (13)

Thus, the summation of the two pairs is calculated as 
follows:

R = R1 + R2 + R3 + R4 (14)

Power Allocation

Power and resource allocation are performed in every pair 
of users sharing the same subcarrier.[10] For intended pair, 
the more power is allocated for far user, whereas the rest is 
allocated for the near user due to the channel coefficient of 
the far user is less than the channel coefficient of near user. 
The far user should meet its required target data rate. The 
different rates of far and near users will be summed for the 
corresponding transmit power. The power allocation strategies 
are aimed to maximize the overall system capacity measured 
in bits per second. There are two types of power allocation, 
the FPA and DPA based on channel condition. The former 
is constant (not change with the channel gain, the latter is 
providing the fair power allocation between users when the 
amount of power is adjusted according to the variation of 
channel gain by taking the feedback from the channel state 
information (CSI).[11]

Deriving the power allocation coefficients starts by denote 
R* as the target rate for far user choosing αf and αn such that 
Rf ≥ R* is our goal.

We will set Rf = R*.

α
α σ

+ =
+

2 
*

2 2  2
log (1  )f f

f n

h P
R

h P

| |
| |  (15)



Almashhadani and Qasmarrogy: Dynamic Power Allocation for NOMA

88 http://journals.cihanuniversity.edu.iq/index.php/cuesj CUESJ 2024, 8 (1): 85-90

Now remove the for both sides

α
α σ

+ =
+

2 
*

2  2
1 2f f R

f n

h P

h P

| |
| |  (16)

α
α σ

= −
+

2 
*

2  2
2 1f f R

f n

h P

h P

| |
| |

 (17)

Assume ξ = 2 1R* − , ξ is the target SINR for the far user 
who has target rate R*

α
α σ

= ξ
+

2 

2  2

f f

f n

h P

h P

| |
| |

 (18)

∣hf∣2 Pαf = ξ ∣hf∣2 Pαn + ξσ2 (19)

αf + αn = 1, so αn = 1–αf (20)

∣hf∣2 Pαf = ξ ∣hf∣2 P(1–αf) + ξσ2 (21)

∣hf∣2 Pαf = ξ ∣hf∣2 P–ξ∣hf∣2 Pαf + ξσ2 (22)

Collecting all the αf from to the LHS

∣hf∣2 Pαf + ξ ∣hf∣2 Pαf = ξ ∣hf∣2 P + ξσ2 (23)

αf ∣hf∣2 P(1 + ξ) = ξ (∣hf∣2 P + σ2) (24)

( )
σ

α
ξ +

=
+ ξ

2  2

  2 

( )
 

1
f

f
f

h P

h P

| |
| |

 (25)

Now will put a limit to αf ensuring will not exceed 1

( )
( )

σ
α

ξ +
=

+ ξ

2  2

2 
min(1,  )

1
f

f
f

h P

h P

| |
| |

 (26)

After utilizing the aforementioned formula to obtain αf, 
we can effortlessly determine αf.

αn = 1–αf (27)

Outage Probability

The outage probability is defined as the probability that the 
signal-to-noise ratio (SNR) of a channel fall below a certain 
target rate of data for evaluating any communication channel 
performance. NOMA allows all users to share the bandwidth 
equally, and hence, the data rate of each user necessity to 
be within the definite limits of channel capacity. The outage 
occurs when the data rate of a user or the sum rates of all users 
exceeds Shannon’s corresponding data rate, which implies a 
data loss. [12] The general expression of the probability of 
outage is given as:

POutage = P (R < R*) (28)

Where; R is the calculated channel capacity and R* is the 
target data rate of the user.

SIMULATION RESULTS

In this scenario, we assume four users with different distanced 
from the BS in the downlink NOMA mobile system, the channel 
is Rayleigh fading with 10,000 random generated paths and 
path exponent n = 4. These users are divided into two groups 
and two users per group since the user grouping scheme is 

used to maximize the system throughput and every group has 
its own subcarrier. Therefore, NOMA is applied on every two 
users considering a perfect SIC. The analysis of the system 
will mainly base on the assumption of two types of power 
allocation (FPA and DPA). The data rate per frequency and 
outage probability are simulated using MATLAB in this study.

Figure 3 shows the sum rate of two different pairing 
users’ types of hybrid NOMA, the maximum channel difference 
pairing {(U1, U4), (U2, U3)} gives a higher data rate compared 
with adjacent channel pairing users {(U1, U2), (U3, U4)} in high 
SNR levels also the hybrid NOMA is better than OMA but the 
improvement is not significant, the performance of Single 
Carrier SC-NOMA is poor due to the big interference added as 
created from the signals to the users, especially when users are 
close together in terms of power levels.

In Figure 4. The comparison in sum rates is shown 
between the FPA and DPA for the four users. The users pairing 
of maximum channel gain difference is considered in each 
group; hence, every two users can be classified into far user 
and near user. The fixed power coefficient values of far and 
near users as αf = 0.7, αn = 0.3, respectively, nevertheless DPA 
adapt its coefficient values based on the channel gain value 
to optimize the allocation of transmit power between the 
near and far users to meet the specification, due to that DPA 
outperform FPA pointedly.

Figures 5 and 6 simulate the outage probability versus 
data rate. The simulation parameters of the system set constant 
transmit power as 30 dBm, noise power σ2 of −114 dBm/
Hz and the two users in each pair have the power allocation 
coefficient of αf = 0.7, αn = 0.3.

Figure 5 shows a comparison of the outage probability 
performances of FPA and DPA versus the target rate of the far 
user R*. Far user and near user are located at the distances 
d1 = 1000 m, d2 = 500 m respectively, and compared their 
outage failure. We can notice that FPA exhibits significant 
underperformance with its outage probability reaching a 
saturation point of 1 beyond target rate of 2 bps/Hz, FPA 
not take in consideration the instantaneous CSI, in addition, 
disregards the target rate requirements. Therefore, FPA 

Figure 3: System sum rate under different multiplexing techniques



Almashhadani and Qasmarrogy: Dynamic Power Allocation for NOMA

89 http://journals.cihanuniversity.edu.iq/index.php/cuesj CUESJ 2024, 8 (1): 85-90

although less complicated to implement, has low performance 
in general. The outage probability of near user behaves a 
sudden change from 4 to 7 bps/Hz values of R*, then turn into 
always record outage at 7 bps/Hz and later.

The supposed system of four users (paired users) is 
evaluated and tested the outage probability for the distances 
of the users away from the BS by 400 m, 500 m, 800 m, and 
100 m, respectively, as shown in Figure 6. FPA results in an 
outage after 16 bps/Hz, whereas DPA is better performed until 
fall in outage beyond 21 bps/Hz. Therefore, DPA has results in 
lower outage probability compared to FPA due to its ability to 
adapt to changing channel conditions and interference levels. 
DPA optimally allocates power resources to users based on their 
channel conditions, leading to improved system reliability and 
performance.

CONCLUSION

In this study, the analysis of NOMA was conducted using 
MATLAB software to evaluate data rate and outage probability 
in a multipath Rayleigh fading channel. By doing so, we were 
able to measure NOMA’s performance in maximizing data 
rates and minimizing outage probabilities among multiple 
users that share the same resources. Our findings show that 
NOMA can greatly enhance spectral efficiency and system 
capacity over traditional OMA systems.

Furthermore, we accurately simulated and modeled 
outage probability and data rate through interactions amongst 
users, channels, and power allocations into a NOMA system 
using MATLAB hence giving us an insight on how different 
parameters affect data rates as well as outage probabilities 
thus enabling optimization of system performance.

In general, the users were classified into group of two 
according to the maximum channel gain difference then the 
power was distributed among the pair of users and it was 
obvious from the simulation results that the hybrid NOMA 
with DPA was better than fixed hybrid-NOMA for both 
outage probability and data rate. Furthermore, this system 
can be extended to more than four users which get the 
same achievements; it is also promising for future wireless 
communication systems of which some cases may involve 
critical considerations regarding spectral efficiency as well as 
resource utilization.

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Figure 6: Outage probability of the system

Figure 5: Outage probability of far and near user



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