Performance Enchantment of Power Allocation for MIMO Non-Orthogonal Multiple Access Network

In the evolving landscape of wireless communications, achieving high spectral efficiency and massive connectivity is paramount, especially with the burgeoning growth of Internet of Things (IoT) devices. The number of IoT devices alone is predicted to reach over 27 billion by 2025 [1], necessitating uninterrupted connectivity and increasing traffic demands.

NOMA has emerged as a promising technology to meet these demands by allowing multiple users to share the same frequency resources through power domain multiplexing [2].

By superimposing signals and employing Successive Interference Cancellation (SIC) at the receiver, NOMA significantly enhances capacity and user connectivity compared to traditional Orthogonal Multiple Access (OMA) schemes.

NOMA systems offer higher bandwidth performance, improved user engagement, higher connectivity, and greater flexibility compared to standard OMA solutions [3]. By enabling more users and supporting more Machine Type Communications (MTC) or IoT devices, NOMA boosts total capacity [4]. Multiple-Input Multiple-Output (MIMO) technology, which leverages multiple antennas at the transmitter and receiver, further boosts the performance of wireless networks by enhancing data rates, improving link reliability, and increasing spectral efficiency [5]. Integrating MIMO with NOMA (MIMO-NOMA) creates a synergistic framework capable of handling the high data rate requirements and massive device connectivity in modern wireless networks [6]. However, one of the critical challenges in MIMO-NOMA systems is the efficient allocation of power among users. Power allocation directly impacts the performance of NOMA systems, affecting both the achievable data rates and the effectiveness of SIC. Optimizing power allocation in a MIMO-NOMA network is essential to maximize system performance, ensure fair resource distribution, and maintain quality of service (QoS) for all users. This study focuses on enhancing the performance of power allocation strategies in MIMO-NOMA networks. By exploring advanced power allocation algorithms and techniques, we aim to improve system throughput, reduce interference, and achieve better user fairness. The proposed solutions are evaluated through rigorous simulations, demonstrating their effectiveness in various network scenarios and highlighting their potential in real-world applications.

Additionally, users with better status can use SIC technology to eliminate interference caused by other users with lower status, thus enhancing user fidelity in the NOMA system [7]. The NOMA concept allows users to plan their transmissions more easily. Power domain NOMA (PD-NOMA) has been studied as a potential flexible tool in several design processes and research projects because of its efficacy [8]. The complexities of power distribution in the NOMA framework are multifaceted, especially when synergized with device-to-device (D2D) communications. NOMA solidifies its position as a principle of 5G and its successors, allowing many users to use the same time-frequency services, thereby increasing spectral efficiency.

Multi-input multiple-output (MIMO) and multiple-input single-output (MISO) multi-antenna technologies employ the spatial domain to enhance the accuracy of SE and energy efficiency (EE) of communications in a hybrid multi-antenna NOMA system. Therefore, multi-antenna technology combined with NOMA can enhance communication performance, particularly in CR-based networks [9, 10]. Individual beamforming vectors supplied by numerous CR BS antennas can be assigned to work for group SUs (i.e., groups) in group-based MISO-NOMA-CR-based systems. More specifically, NOMA is used to service the SUs in each cluster. In addition to offering more variety than conventional OMA-NOMA systems, MIMO-NOMA systems may also provide more degrees of freedom, boost competitiveness, and improve diversity when paired with Sparse Code Multiple Access (SCMA).

Furthermore, these systems can circumvent the difficulty of identifying a single MIMO-NOMA operation. It is important to remember that not all B5G-capable devices can be affected by even several antennas because of capacity limitations. This issue may be solved using iterative linear receivers [11]. Power allocation has been carried out in a different study following user grouping [12, 13]. Additionally, relay-based NOMA for power and resource distribution has been covered in recent works [14-16].

In this work, we develop a downlink technique to allocate power coefficients amongst 2×2 MIMO-PD-NOMA users, assuming that the weakest user is not experiencing an outage, and provides an appealing algorithm that is more equitable than the current solution when the weakest user is experiencing an outage [17]. As well, we introduce a 2×2 MIMO-NOMA model with fixed power allocation to enhance spectral efficiency and reliability in wireless communications. NUFP Allocation ensures high network fairness and reduces outage probability for near users. MNUFP allocation further optimizes power allocation, improving fairness and reducing outage probabilities even more effectively. Additionally, this work compares the sum rate and outage performance of 2×2 MIMO-NOMA with MIMO-OMA and demonstrates that the NUFP and MNUFP algorithms reduce the outage probability for near users from 0.94 to 0.16 at 5.5 bps/Hz. These proposed power allocation strategies significantly reduce the outage probability for near users, thereby enhancing overall network performance and meeting the low latency requirements of 5G networks.

This is how the remainder of the paper is structured. The definition of NOMA and its underlying principles are covered in Section 2. The system model is presented in Section 3. Comparing the outage probability, attainable rate, and sum rate between MIMO-NOMA and MIMO-OMA, as well as describing and discussing the simulation findings, are achieved in Section 4.

3.1 MIMO-NOMA

To describe the attributes of the suggested system, Figure 2 illustrates a 2×1 downlink MIMO system that is part of the downlink transmission system paradigm. Here, $d_1>d_2 \mathrm{~s}$ assumed. $U_2$ is the strong user, and $U_1$ is the weak one. The power level of each user can be determined by the base station based on the total power limit. However, in NOMA the bandwidth is shared between two $U E \mathrm{~s}$ and the entire network can be shared between $U E s$. The near-end user $\left(U_1\right)$ uses the SIC process to decode its signals. The remote user $\left(U_2\right)$ considers the $U E_1$ signal to be relevant and directly determines the corresponding signal. MIMO may be applied to diversity gain (to lower BER) or spatial multiplexing (to boost speed). Two antenna BS and two users, each with a separate assigned power $(P)$ from the total transmission power constitute the model of the system. The strong user is the one with the lowest allotted power $\left(a_1\right)$, while the weak user has power $\left(a_2\right)$. Every user has a distance of di from the BS, with user1 being the furthest away at d1 and user2 being the closest at d2 . The transmitted signals from antennal and/or antenna2 in the propose system shown in Figure 2 are first modulated using the BPSK modulation technique to create $x_1$ and $x_2$ correspondingly. In this case, diversity is achieved using MIMO. Therefore, transmission antennas 1 and 2 transmit the same message. Assume that the transferred data for $U_1$ and $U_2$ is represented by $x_1$ and $x_2$. By MIMO guidelines, let $h_{t h}$ stand for the Rayleigh fading channel between the $t_{t h}$ transmitter and the $r_{t h}$ receiver.

2.png

Figure 2. System model of the MIMO-NOMA

The downlink NOMA system's physical layer responsible of modulating, encoding, and superimposing the multiplexed users' messages on the selected channel. Moreover, it assigns different power levels based on power domain multiplexing. The BS employs a power allocation algorithm that gives users with poor channel conditions more power and users with excellent channel conditions less power to ensure significant signal acknowledgement. The BS employs a multiplexing technique that ranks users in accordance with decreasing channel gain to enhance SIC performance at the receiver. Figure 3 illustrates the architecture of the NOMA system, in which the BS acts as the transmitter and the mobile equipment (ME) as the receiver.

Alternatively, to correctly decode the overlaid message received at each user, the SIC is carried out iteratively at the receiver side. The correlation of the SC, SIC, power allocation, and user pairing based on channel gain order can be applied using this NOMA system architecture. To decode the desired signal after cancelling the combined signal, users with good channel conditions execute SIC in accordance with the BS acknowledgement. The user with the weak channel situation, on the other hand, decodes the necessary signal after treating the undesirable signal as noise. For every user, to distinguish it from other transmitted signals, the modulated signal is acquired using the assigned power coefficient, and hence $x_1$ and $x_2$ are generated respectively by,

3.png

Figure 3. Diagram of SC and SIC in NOMA communication system

The signal that both antennas have broadcast is provided by,

$X=\sqrt{P}\left(\sqrt{a_1} x_1+\sqrt{a_2} x_2\right)$              (2)

where $a_1$ and $a_2$ are the allocation coefficients of the NOMA power. Since $U_1$ is chosen to be the weak user. Two antennas simultaneously broadcast $x$. Thus, the signal that $U_1$ received is as follows:

$y_1=x h_{11}+x h_{12}+n_1=x\left(h_{11}+h_{12}\right)+n_1$           (3)

In the same way, the $U_2$ receives a signal that is given by,

$y_2=x h_{21}+x h_{22}+n_2=x\left(h_{21}+h_{22}\right)+n_2$              (4)

where $n 1$ and $n 2$ are AWGN noise samples with variance $\sigma^2$, and a mean of zero. $U_1$ must now calculate $x_1$ from $y 1$. The $x_1$ signal will be delivered more powerfully since $U_1$ is a weak user. Thus, by treating the information that was sent as interference $\left(x_2\right)$, it may infer $x_1$ straight from $y_2$,

$y_1=\sqrt{P}\left(\sqrt{a_1} x_1+\sqrt{a_2} x_2\right)\left(h_{11}+h_{12}\right)+n_1$                   (5)

$\begin{aligned} & y_1=\sqrt{P} \sqrt{a_1} x_1\left(h_{11}+h_{12}\right) +\sqrt{P} \sqrt{a_2} x_2\left(h_{11}+h_{12}\right)+n_1\end{aligned}$               (6)

For $U_1$, received coupled signals $\left(x_1, x_2\right)$, decode the data from the near user first with the low power, along with the noise channel ratio and the power to interference power from many other users for the user. Now, the SINR equation is written for $U_1$ in decoding $x_1$ as follows,

$\gamma_1=\frac{P a_1\left|h_{11}+h_{12}\right|^2}{P a_2\left|h_{11}+h_{12}\right|^2+\sigma^2}$              (7)

Thus, the rate that may be achieved at $U_1$ is provided by

$R_1=log _2\left(1+\gamma_1\right)$             (8)

For $U_2$, the received signals $y_2$ is directly demodulated,

$\begin{gathered}y_2=\sqrt{P} \sqrt{a_1 x_1\left(h_{21}+h_{22}\right)} \sqrt{P} \sqrt{a_2} x_2\left(h_{21}+h_{22}\right)+n_2\end{gathered}$              (9)

The equation of SINR of $x_1$ at $U_1$ for direct decoding is,

$\gamma_{12}=\frac{P a_1\left|h_{21}+h_{22}\right|^2}{P a_2\left|h_{21}+h_{22}\right|^2+\sigma^2}$           (10)

$y_2^{\prime}=\sqrt{P} \sqrt{a_2} x_2\left(h_{21}+h_{22}\right)+n_2$                (11)

Currently, the SNR allows $U_2$ to decode its signal, which is provided by.

$\gamma_2=\frac{P \alpha_2\left|h_{21}+h_{22}\right|^2}{a^2}$                  (12)

To eliminate user 2's interference at the receiver side of user1, SIC is carried out. As a result, the obtained data rate at user1 is determined by

$R_{12}=log _2\left(1+\gamma_{12}\right)$                 (13)

$R_2=log _2\left(1+\gamma_2\right)$             (14)

In MIMO-OMA, the broadcast split into two equal intervals. Two antennas deliver signals to $U_1$ for the first time and to $U_2$ for the second time.

$y_1, o m a=\sqrt{P} x_1\left(h_{11}+h_{12}\right)+n_1$             (15)

Similarly, $P x_2$ is the signal transmitted from the antennas to $U_2$ at time slot 2. Hence $U_2$ will receive the following signal:

$y_{2}, oma=\sqrt{P} x_2\left(h_{22}+h_{21}\right)+n_1$            (16)

The SNRs at $U_1$ and $U_2$ are,

$\gamma_1, o m a=\frac{P\left|h_{12}+h_{11}\right|^2}{\sigma^2}$        (17)

$\gamma_{2, o m a}=\frac{P\left|h_{21}+h_{22}\right|^2}{\sigma^2}$             (18)

Consequently, for $U_1$ and $U_2$, the MIMO-OMA attainable rates are,

$R_{1, o m a}=\frac{1}{2} log _2\left(1+\gamma_{1, o m a}\right)$             (19)

$R_{2, o m a}=\frac{1}{2} log _2\left(1+\gamma_{2, o \mathrm{ma}}\right)$            (20)

Only half of the time slots are used to interact with each user, which accounts for factor 1/2 in Eqs. (18) and (19). (The entire duration is valid for transmission to two users while in MIMO-NOMA).

3.2 Power allocation in MIMO-NOMA with fairness to far user

The target rate for the far user is determined based on the desired QoS, which ensures that the user meets a predefined throughput requirement under varying channel conditions. This target rate influences the power allocation strategy, as the power assigned to the far user must be sufficient to achieve the desired rate. Higher target rates require increased power allocation, particularly when the channel conditions are less favorable. Conversely, lower target rates allow for reduced power allocation, optimizing overall system efficiency. This power control mechanism ensures that the far user’s QoS is met while maintaining fairness and minimizing interference in the system.

As of the present, power has been allocated regardless of channel conditions when the values of $a_1$ and $a_2$ are specified. However, there are more effective methods for dynamically optimizing $a_1$ and $a_2$ depending on values of the CSI.

There are several different dynamic power allocation strategies that aim to accomplish different goals. To maximize EE, the overall rate, etc., could be the goal. We'll talk about a simple power allocation technique in this part that attempts to ensure user fairness. This power allocation plan will be referred to as fair PA. The weaker/far user is given priority by proposed fair PA. In other words, the power allocation coefficients are determined in a way that meets the goal rate for the distant user. All the available power is only assigned to the near user once the distant user's target rate has been met. Now let's extract the power allocation coefficients required to satisfy this requirement. Therefore, using Eq. (7), to avoid the user going through an outage, find the weak user power allocation factor $a_1$.

In mathematical terms,

$R_1=log _2\left(1+\frac{P a_1\left|h_{11}+h_{12}\right|^2}{P a_2\left|h_{11}+h_{12}\right|^2+1}\right)=R^*$            (21)

where, $R^*$ is the target rate of $U_1$. Hence, the target SINR of $U_1$ is obtained as

$\mu=\frac{P a_1\left|h_{11}+h_{12}\right|^2}{P a_2\left|h_{11}+h_{12}\right|^2+1}$               (22)

where, $\mu=2^{R *}-1$. Further simplifying Eq. (21) gives the relation

$a_1=\frac{\mu\left(1+P\left|h_{11}+h_{12}\right|^2\right)}{P\left|h_{11}+h_{12}\right|^2(\mu+1)}$              (23)

The power allocation coefficients $a_1$ and $a_2$ in the proposed algorithms are determined as follows:

Near User Fair Power:

1: Select a specific target SINR for the weak user to ensure a given quality of service.

2: Compute $a_1$ from Eq. (23) using given channel gain, transmit SNR, and the required target SINR.

3: If computed $a_1>1$, then limit it to 1, otherwise do not modify it.

4: If limiting is performed in step 3, then set $a_2=0$, otherwise set

$a_2=1-\frac{\mu\left(1+P\left|h_{11}+h_{12}\right|^2\right)}{P\left|h_{11}+h_{12}\right|^2(\mu+1)}$

Modified Near User Fair Power:

1: Select a specific target SINR for the weak user to ensure a given quality of service.

2: Compute $a_1$ from Eq. (23) using given channel gain, transmit SNR, and the required target SINR.

3: If computed $a_1>1$, then limit it to 0; otherwise, do not modify it.

4: If limiting is performed in step 3, then set $a_2=0$; otherwise set

$a_2=1-\frac{\mu\left(1+P\left|h_{11}+h_{12}\right|^2\right)}{P\left|h_{11}+h_{12}\right|^2(\mu+1)}$

This approach ensures efficient and adaptive power allocation while maintaining fairness and meeting the quality-of-service requirements.

3.3 Proposed 2×2 MIMO-NOMA near user fair power algorithm

$a_1$ is a function of target $\operatorname{SINR} \mu$ based on Eq. (22). The goal is to give the strongest user the highest target SINR without suffering an outage. Because of the channel's randomness, it is difficult to guarantee the intended goal SINR while using a fixed power allocation. By using the fact $a_1 \leq$ 1 , and restricting $a_1$ to be a nonlinear function of $\mu$, also modify $a_1$ to $a_1^*$, given by

$a_1^*=min \left(1, \frac{\mu\left(1+P\left|h_{11}+h_{12}\right|^2\right)}{P\left|h_{11}+h_{12}\right|^2(\mu+1)}\right)$            (24)

where, the minimum of x and y is given by $\min (x, y)$. As a result, for $a_1^*=a_1$, and for $a_1>1$, this work has $a_1^*=1$.

A weak user with a high goal SINR (provided by Eq. (17)) effectively obtains a power allocation factor larger than unity, so integrating the user into the outage. The system's outage performance would therefore markedly worsen. It would be feasible to minimize the weak user's target rate demand in this situation and set the power allocation coefficient to unity. Lowering the target rate would improve the outage performance of the weaker user, which would also help the stronger user. The stronger user would have been impacted by the outage if the target rate had been higher since the weaker user would have received all the power.

3.4 Proposed 2×2 MIMO-NOMA modified near user fair power algorithm

The choice of the 2×2 MIMO configuration balances system complexity and performance, making it practical for NOMA. It provides spatial diversity to improve reliability and allows efficient implementation of power allocation schemes, such as NUFP and MNUFP, enhancing fairness and outage performance. Additionally, it serves as a clear framework to analyze SIC and a foundational model for scaling to larger systems. This configuration ensures meaningful insights while maintaining computational feasibility. However, giving the weakest user zero power would help the stronger user by concentrating on their outage and freeing up more power for the stronger user to use. This is because increasing the power assigned to the stronger user causes the stronger user to have a higher SINR even in the case of a weak user outage. This may raise the achievable data rates for the network because neither user will be negatively impacted by a lower nominal value of the target rate. It is therefore beneficial to raise the close user's SINR at the cost of providing the far user with more electricity during the outage. Consequently, the suggested MNUFP allocation mechanism is shown.