Content-Centric Clustering and Power-Diverse Allocation in Downlink Network-Coded Multiple Access System

Abstract

Aiming to boost the throughput performance in mobile networks, network-coded multiple access (NCMA) has been proposed as a new framework in non-orthogonal multiple access (NOMA). Normally, user-centric design is adopted in NCMA to allocate the same power to different users. However, devices and the corresponding messages may have different quality-of-service (QoS) requirements (such as delay or throughput) due to the potential content diversity in Internet of Things (IoT) networks. In this paper, we present a power-diverse NCMA (PD-NCMA) system. In particular, a two-stage framework in NCMA downlink is adopted. Based on the throughput requirement of content, messages are given different levels, and content-centric clustering is solved dynamically in the first stage. Then, power allocation in each cluster is realized in the second stage. Numerical results demonstrate the feasibility of the proposed PD-NCMA, and the throughput of PD-NCMA significantly outperforms the traditional NCMA system.

1. Introduction

With the increasing number of mobile devices and data traffic connections, spectrum resources are becoming increasingly scarce [1]. To cope with the ever-growing demands for wireless capacity, non-orthogonal multiple access (NOMA) [2,3] is proposed and regarded as one of the promising spectrally efficient methods in sixth-generation (6G) wireless networks [4]. The typical NOMA technologies allow multiple users to share the same resource block with varied power, increasing the spectrum efficiency of the communication system [5]. As a representative of code-domain NOMA, sparse code multiple access (SCMA) [6] also exhibits excellent performance in the uplink with sporadic traffic. In addition, NOMA has also achieved performance improvement in low-latency [7] and -security [8] areas. Aiming to further enhance throughput performance, a new NOMA architecture named network-coded multiple access (NCMA) [9] is proposed. Unlike the conventional NOMA, which utilizes successive interference cancellation (SIC), NCMA combines physical layer network coding (PNC) [10] with multiuser decoding (MUD) to perform parallel decoding [11].

The original power-balanced NCMA (PB-NCMA) scheme [9] only considered low-order modulation and could only be utilized in uplink scenarios, which limited the deployment of NCMA. In [12], an enhanced symbol-level decoder, which retains the inter-correlation information among bits, was proposed to generalize PB-NCMA to high-order modulation. In addition, ref. [12] also pointed out that the phase rotation caused by channels has a severe impact on the PB-NCMA system. By adopting rate-diverse design, ref. [13] significantly improved throughput performance in uplink PB-NCMA. Furthermore, ref. [13] extended PB-NCMA to a three-user system to demonstrate multiuser performance. Nevertheless, this method increases the state of the PNC decoder and requires devices to adjust continually to accommodate more users [14], which is not conducive to multiuser NCMA. In [15], PB-NCMA was first extended to downlink communication, and artificially added phase rotation, referred to as phase rotation NCMA (PR-NCMA), was used to further boost throughput. Experimental results demonstrated the robustness of PB-NCMA and PR-NCMA designs in downlink systems. In order to improve the communication performance of remote users, ref. [16] put forth a NCMA-based coordinated direct and relay transmission (CDRT) method.

Despite the extensive research conducted on NCMA systems, downlink scenarios remain relatively underexplored in the existing literature. Furthermore, most prior studies adopt a user-centric, power-balanced design approach that assumes uniform user requirements. However, such an approach overlooks the inherent diversity in content and service demands [17,18,19], such as the practical downlink sensor networks, where some devices require extensive control data while others operate with minimal information [17]. Moreover, video users demand significantly higher throughput than voice users in cellular networks [19]. Traditional user-centric methods may not achieve maximum throughput performance.

In this paper, we propose a power-diverse design in NCMA multiuser downlink, referred to as PD-NCMA. More precisely, we consider a content-centric dynamic multiuser framework with two stages. In the first stage, users are grouped dynamically according to the content levels. Different from conventional PB-NCMA [12] and PR-NCMA [15], power-diverse design is adopted in the second stage since it improves MUD performance dramatically, which is critical to boost throughput. We compare several NCMA algorithms in

Table 1. Comparison of several NCMA algorithms.

Algorithm	PB-NCMA [12]	PR-NCMA [15]	PD-NCMA
Clustering	User-centric	User-centric	Content-centirc
Power allocation	Equal	Equal	Priority-based
Key enhancement	None	Phase rotation	Power-diverse
Performance	Baseline	20% improvement	30–50% improvement

.

The main contributions of this paper are summarized as follows:

• We propose a power-diverse downlink NCMA framework that exploits content heterogeneity to improve throughput without requiring channel-state information.
• Content-centric clustering followed by priority-driven power allocation is introduced in this paper, which enhances the MUD and throughput performance. The proposed scheme achieves higher throughput than existing PB-NCMA and PR-NCMA schemes in low-to-medium Signal-to-Noise Ratio (SNR) regions.

The rest of this paper is structured as follows. The multiuser NCMA downlink structure is presented in Section 2. In Section 3, dynamic clustering and power allocation design in PD-NCMA are introduced. Comprehensive simulation results will be assessed in Section 4, followed by the conclusion in Section 5.

2. Multiuser NCMA Downlink System

2.1. System Model

Consider the downlink system consisting of M users and 1 base station (BS) in Figure 1. M user devices are divided into N clusters. Notice that users and the BS can be considered sensor devices and control nodes or other equipment, respectively. Here we adopt a general description (user, BS, etc.) to introduce the system structure. It is worth noting that since the energy and efficiency performance of user equipment in downlink is much weaker than that of the BS, the number of users in one cluster needs to be further limited [20]. In addition, users are usually grouped pairwise to ensure decoding complexity in the NCMA system [21]. Thus, we adopt the same configuration. Each cluster contains two or one user (in general, two users per group is the recommended configuration, but when the number of users is odd, one user will be grouped separately), while each device only can be in one cluster. Thus, $N=\lceil {\displaystyle \frac{M}{2}}\rceil$, where $\lceil \rceil$ is the ceil operator. We assume that the total power budget of the BS is $P_T$, and the power among clusters is equal. Consequently, the power of cluster i satisfies ${\sum }_{i=1}^N{P}_i=P_T$. Additionally, frequency blocks are orthogonally occupied by clusters. Therefore, the impact among clusters is negligible and conventional NCMA (or the proposed PD-NCMA) method can be adopted in any cluster.

2.2. Information Processing of PD-NCMA

Without the loss of generality, a random cluster i ($i=1,2,\dots ,N$) is selected to describe the PD-NCMA scheme. Different user devices are represented by A and B, respectively. As depicted in Figure 2, complete PD-NCMA downlink propagation includes both PHY layer and MAC layer processing. The MAC layer large message for user s ($s\in \{A,B\}$) in cluster i is denoted by $M_i^s$. The Reed–Solomon (RS) code (other advanced erasure channel codes (such as fountain codes) are also possible at the NCMA MAC layer) is used at the MAC layer to encode message $M_i^s$ into multiple packets $C_{ij}^s$ where $j=1,2,\dots$:

$$C_i^s=G{M}_i^s={[C_{i1}^s,C_{i2}^s,\dots ,C_{ij}^s]}^T.$$

(1)

Notice that G represents the invertible generator matrix [22] for the RS code, and $C_i^s$ is the set of multiple packets $C_{ij}^s$. $C_{ij}^s$ further channel-coded into $V_{ij}^s$ and modulated into $X_{ij}^s$ at the PHY layer. Both user devices utilize the same modulation order, and the same convolutional code is adopted as for the PHY layer channel codes. Unlike PB-NCMA and PR-NCMA, the proposed PD-NCMA allocates varying power to the underlying signals $X_{ij}^s$ of two users without channel information (Dynamic clustering and power allocation will be further discussed in Section 3). The power assigned to user s in cluster i is denoted by $P_i^s$, and the superposed signal of $\{X_{ij}^A,X_{ij}^B\}$ can be expressed as

$$X_{ij}^{AB}=\sqrt{P_i^A}{X}_{ij}^A+\sqrt{P_i^B}{X}_{ij}^B.$$

(2)

NCMA superposed signals $X_{ij}^{AB}$ are then broadcast to users A and B continuously. At the receiver of user s in cluster i, the received signal is

$$Y_{ij}^s=H_{ij}^s{X}_{ij}^{AB}+W_{ij}^s,$$

(3)

where $H_{ij}^s$ is the downlink channel gain from the BS to user s, and $W_{ij}^s$ is complex Gaussian noise. Both MUD and PNC detectors are equipped at the PHY layer to decode $C_{ij}^A$, $C_{ij}^B$, and $C_{ij}^A\oplus C_{ij}^B$. Notice that $C_{ij}^A\oplus C_{ij}^B$ is the bit-wise exclusive OR (XOR) of $C_{ij}^A$ and $C_{ij}^B$. A detailed derivation of the PNC and MUD detectors was introduced in [15]. After the bridging operation and MAC layer RS decoding of $\{C_{ij}^A\oplus C_{ij}^B,C_{ij}^A,C_{ij}^B\}$, each user can recover the original large message $M_i^s$ after receiving enough $C_{ij}^s$. We focus on an example to explain the bridging operation. Figure 3 demonstrates the decoding outcomes in 5 continuous parts. In the third section, $C_{i3}^A$ and $C_{i3}^A\oplus C_{i3}^B$ are decoded by the MUD detector and PNC detector, respectively. Hence, PHY layer bridging [9], which utilizes the complementary XOR packet $C_{i3}^A\oplus C_{i3}^B$ and $C_{i3}^A$, can be applied to recover $C_{i3}^B$. Since an $L=3$ RS code is considered in the MAC layer to encode the original message into multiple packets, users need only $L=3$ packets to recover the message. As a result, user B can recover $M_i^B$ completely. This operation also means that the native packets $C_{i4}^B$ and $C_{i5}^B$ can be decoded synchronously based on re-encoding the recovered MAC layer message $M_i^B$, whereupon the original lone PNC packet $C_{i4}^A\oplus C_{i4}^B$ can be utilized to recover $C_{i4}^A$ with $C_{i4}^B$. This operation is known as MAC layer bridging [9]. As a result, user A now possesses enough native packets $C_{ij}^A,j=3,4,5,$ to recover $M_i^A$.

The proposed system employs complex-field superposition, where modulated signals are added in the wireless channel. Then, the Galois Field (GF) in Figure 3 enables efficient packet-level recovery without retransmission. This two-layer approach is standard in NCMA architecture [13,15] and not an inconsistency.

3. Dynamic Clustering and Power Allocation Design in PD-NCMA

In the traditional NOMA system, devices with better channel conditions will be allocated less power. The main purpose of this user-centric design is to maximize the sum rate. Therefore, it requires that the channel conditions of user devices in one cluster are sufficiently different. In practice, due to potential content diversity [17,18,19], user equipment and the corresponding messages may have different priorities. Notice that such content priorities are often defined with specific requirements. For example, in a BS-centric downlink network, devices receiving large-capacity data (such as video) will be sent much higher priorities than the devices receiving text messages to ensure the throughput requirements.

Different from the traditional NCMA system, we consider a content-centric design in PD-NCMA. Device clustering is solved first, and power allocation will be adjusted dynamically based on message priority. In addition, we will allocate more power to users with higher priorities to ensure their communication performance. In other words, users in our scheme need to have priority differences within each cluster. This design ensures that power allocation aligns with service demands rather than channel states, which is particularly advantageous in Internet of Things (IoT) scenarios with diverse QoS requirements.

3.1. Content-Centric Clustering

Due to the potential diversity of the content being transmitted, the BS sorts all M user devices in descending order of their throughput requirements. Then, the BS assigns different message priorities to users according to the sorted results. Devices with high throughput requirements will be set much higher priorities. The sorted results are denoted by $r_1\ge r_2\ge \dots \ge r_M$, where

$$r_m=M-m+1,m=1,2,\dots ,M$$

(4)

represents message priority, i.e., $r_1=M$ and $r_M=1$ denote the highest and lowest message priority, respectively. In order to ensure priority difference within clusters and allocate more power to high-priority messages, we propose two differentiation clustering methods.

• Method 1: User device with message priority $r_m$ forms a cluster with $r_{M-m+1},m=1,2,\dots ,M$. (i.e., the user device with the highest message priority $r_1$ forms a cluster with the lowest one $r_M$). If M is an even number, user devices are clustered pairwise. Nevertheless, a device with the priority $r_{{\displaystyle \frac{M+1}{2}}}$ forms a single-user cluster if M is an odd number.
• Method 2: Two cases are considered in Method 2. If M is an even number, users are first sorted and divided into 2 groups. Group 1 and group 2 are denoted as $\{r_1,r_2,\dots ,r_{{\displaystyle \frac{M}{2}}}\}$ and $\{r_{{\displaystyle \frac{M}{2}}+1},r_{{\displaystyle \frac{M}{2}}+2},\dots ,r_M\}$, respectively. Then, a user device with message priority $r_i$ forms a cluster with $r_{{\displaystyle \frac{M}{2}}+i},i=1,2,\dots ,{\displaystyle \frac{M}{2}}$ (i.e., the user device with message priority $r_1$ forms a cluster with $r_{{\displaystyle \frac{M}{2}}+1}$). If M is an odd number, users are first sorted and divided into 2 groups: $\{r_1,r_2,\dots ,r_{{\displaystyle \frac{M-1}{2}}}\}$ and $\{r_{{\displaystyle \frac{M+3}{2}}},r_{{\displaystyle \frac{M+5}{2}}},\dots ,r_M\}$. Then, a user device with message priority $r_m$ forms a cluster with $r_{{\displaystyle \frac{M+1+2m}{2}}},m=1,2,\dots ,{\displaystyle \frac{M-1}{2}}$. Furthermore, a device with priority $r_{{\displaystyle \frac{M+1}{2}}}$ forms a single user cluster.

Figure 4 demonstrates the clustering results for a six-user system under two schemes. According to the sorting result, user 1 is configured with the highest message priority $r_1=6$, since it posses the highest throughput requirement. The priorities of other users are analogous. User devices then cluster according to the proposed clustering schemes. In a nutshell, the intuitive motivation behind clustering methods is to allocate varying power to users in each cluster and make the power difference large enough. This is because our power allocation in the second stage is related to message priority, so we need to cluster users according to the corresponding priority in the first stage.

3.2. Dynamic Power Allocation

Consider the power allocation problem in cluster i; we assume that the user with higher message priority is A and the other is B. The message priorities of A and B can be denoted as $r_{iA}$ and $r_{iB}$, respectively.

Since users within each cluster have differrent message priorities, we adopt a priority-based power allocation strategy. Users in each cluster will be allocated power based on their priorities as follows:

$$P_i^s={\displaystyle \frac{r_{is}}{r_{iA}+r_{iB}}}{P}_i,$$

(5)

where $s\in \{A,B\}$, $i=1,2,\dots ,N$, $P_i$ represents the total power of cluster i. The superiority of the considered power allocation method is that more power can be allocated to high-priority users to ensure communication performance. Meanwhile, the performance of low-priority user is not significantly degraded thanks to the PNC and bridging operation in NCMA (More details will be illustrated in simulation results). Without the loss of generality, a user will be assigned the total power of one cluster if it forms a single user cluster.

3.3. PHY Layer Processing and Union Bound

As depicted in Figure 5, the received signal is fed into PNC and MUD decoders simultaneously to decode $C_{ij}^A$, $C_{ij}^B$ and $C_{ij}^A\oplus C_{ij}^B$.

First, let us focus on PNC decoder processing. $Y_{ij}^S$ passes through the PNC demodulator to get XOR bits $V_{ij}^A\oplus V_{ij}^B$. Notice that both PNC and MUD demodulators adapt the maximum a posteriori (MAP) method, which is derived in detail in [15]. Then, the standard Viterbi decoder is adopted after the demodulator to obtain packets $C_{ij}^A\oplus C_{ij}^B$.

Suppose that the superposed constellation point $X_{ij}^{AB}=x_k$ is sent ($X_{ij}^{AB}$ is defined in (2)). Thus, the superposed result at the receiver can be denoted as $y_k=x_k+w$, where w is the complex Gaussian noise with variance $N_0$. Similarly to the analysis method in [15], we adopt the unit channel gain to explain the symbol error rate (SER) in simple terms. The SER for the PNC decoder can be expressed as

$$\begin{array}{cc}\hfill P_e^{PNC}\left(x_k\right)& \le \sum _{{\displaystyle \genfrac{}{}{0pt}{}{l=1,l\ne k}{\prod \left(x_k\right)\ne \prod \left(x_l\right)}}}^{K}P\left(∥y_k-x_l∥<∥y_k-x_k∥\right)\hfill \\ \hfill & =\sum _{{\displaystyle \genfrac{}{}{0pt}{}{l=1,l\ne k}{\prod \left(x_k\right)\ne \prod \left(x_l\right)}}}^{K}P\left(∥w+x_k-x_l∥<∥w∥\right)\hfill \\ \hfill & =\sum _{{\displaystyle \genfrac{}{}{0pt}{}{l=1,l\ne k}{\prod \left(x_k\right)\ne \prod \left(x_l\right)}}}^{K}P\left(w>{\displaystyle \frac{d_{kl}}{2}}\right)\hfill \\ \hfill & \le \sum _{{\displaystyle \genfrac{}{}{0pt}{}{l=1,l\ne k}{\prod \left(x_k\right)\ne \prod \left(x_l\right)}}}^{K}Q\left({\displaystyle \frac{d_{kl}}{\sqrt{2N_0}}}\right),\hfill \end{array}$$

(6)

where K denotes all possible superposed constellation points (e.g., for QPSK, $K=16$). $\prod \left(•\right)$ is the PNC mapping operation in [12]. $d_{kl}$ represents the Euclidean distance between superposed constellation points $x_k$ and $x_l$. In consequence, the union bound can be derived by summing over all possible $x_k$:

$$\begin{array}{cc}\hfill P_e^{PNC}& =\sum _{k=1}^{K}P\left(x_k\right)P_e^{PNC}\left(x_k\right)\hfill \\ \hfill & \le {\displaystyle \frac{1}{K}}\sum _{k=1}^K\sum _{{\displaystyle \genfrac{}{}{0pt}{}{l=1,l\ne k}{\prod \left(x_k\right)\ne \prod \left(x_l\right)}}}^{K}Q\left({\displaystyle \frac{d_{kl}}{\sqrt{2N_0}}}\right).\hfill \end{array}$$

(7)

As for the MUD decoder, it follows a similar process to the PNC decoder. $Y_{ij}^S$ passes through the MUD demodulator to get coded bits $V_{ij}^A$ and $V_{ij}^B$. Then, two standard Viterbi decoders are adopted after the MUD demodulator to obtain packets $C_{ij}^A$ and $C_{ij}^B$ for user A and user B, respectively. Similarly, the SER of the MUD decoder can be expressed as

$$P_e^{MUD}\left(x_k\right)\le \sum _{{\displaystyle \genfrac{}{}{0pt}{}{l=1,l\ne k}{\Omega \left(x_k\right)\ne \Omega \left(x_l\right)}}}^{K}Q\left({\displaystyle \frac{d_{kl}}{\sqrt{2N_0}}}\right),$$

(8)

where $\Omega \left(•\right)$ is the MUD demodulation operation. Furthermore, the SER union bound of the MUD decoder is defined as

$$\begin{array}{cc}\hfill P_e^{MUD}& =\sum _{k=1}^{K}P\left(x_k\right)P_e^{MUD}\left(x_k\right)\hfill \\ \hfill & \le {\displaystyle \frac{1}{K}}\sum _{k=1}^K\sum _{{\displaystyle \genfrac{}{}{0pt}{}{l=1,l\ne k}{\Omega \left(x_k\right)\ne \Omega \left(x_l\right)}}}^{K}Q\left({\displaystyle \frac{d_{kl}}{\sqrt{2N_0}}}\right).\hfill \end{array}$$

(9)

The detailed results of the SER union bound will be demonstrated in Section 4.

3.4. Throughput Analysis

The overall throughput for the NCMA system in each simulation is defined as

$$Th=\sum _{i=1}^N(T{h}_i^A+T{h}_i^B)=\sum _{i=1}^N({\displaystyle \frac{L_A\times N_A}{S_A}}+{\displaystyle \frac{L_B\times N_B}{S_B}}),$$

(10)

where $L_A\left(L_B\right)$ is the theoretical number of small packets for user A (or B) to recover one MAC layer message. Thus, $L_A\left(L_B\right)$ is equal to the RS code parameter L. $N_A\left(N_B\right)$ represents the total number of MAC layer messages for user A (or B). $S_A\left(S_B\right)$ denotes the total actual number of small packets for user A (or B) to recover all MAC layer messages.

3.5. Complexity Analysis

The computational complexity comes from two parts. In terms of device clustering, the quick-sort algorithm is adopted to sort users, and the corresponding computational complexity is $\mathcal{O}\left(Mlo{g}_{2}M\right)$. As for power allocation, computational complexity is mainly determined by (5), that is, a small amount of multiplication and addition. Compared with the device clustering part, computational complexity caused by power allocation is negligible. Hence the computational complexity of the algorithm is determined by quick sort $\mathcal{O}\left(Mlo{g}_{2}M\right)$, where M represents the total number of users. Obviously, the proposed method has low computational complexity.

Notice that the computational complexity of the PHY layer is also important to NCMA. The received signal is first fed into PNC and MUD decoders to obtain the soft information. According to the LLR analysis in [15], the computational complexity of the decoder is determined by the modulation orders. If both user A and user B in one cluster adopt M-order modulation (e.g., $M=4$ corresponding to QPSK), the complexity is $\mathcal{O}\left(M^2\right)$. Then the Viterbi decoder is adopted after decoders to obtain packets. The complexity of Viterbi decoding is mainly determined by the constraint length K of the convolutional code and the number of states S, where $S=2^{K-1}$. Its computational complexity is $\mathcal{O}\left(SN\right)$, where N is the length of the received sequence.

4. Simulation Results

In the following experiments, we illustrate numerical results of the proposed PD-NCMA. We compare PD-NCMA with PB-NCMA [13] and PR-NCMA [15]. Notice that we adopt PD-NCMA-1 and PD-NCMA-2 to denote the proposed design, since we consider two different clustering methods in previous section. Similarly, PR-NCMA-1 and PR-NCMA-2 are introduced to represent the PR-NCMA scheme with phase rotations of 25° and 45°, respectively. A phase rotation of 25° is considered, since it was empirically optimized in [13] for PR-NCMA-1 to maximize the minimum Euclidean distance of superimposed constellations and improve decoding reliability. To enable a more comprehensive comparison of PR-NCMA, we additionally include 45° as a comparative parameter for PR-NCMA-2. We summarize the simulation schemes as follows:

• PB-NCMA [13]: Conventional NCMA method with a power-balanced design.
• PR-NCMA-1 [15]: Phase rotation-based NCMA method with a relative phase offset of 25°.
• PR-NCMA-2 [15]: Phase rotation-based NCMA method with a relative phase offset of 45°.
• PD-NCMA-1: Proposed power-diverse NCMA scheme with Clustering Method 1.
• PD-NCMA-2: Proposed power-diverse NCMA scheme with Clustering Method 2.

Furthermore, in Section 4.3, we also derive a specific power allocation coefficient by simulating union bounds and cluster throughput rather than the proposed content-centric design to further demonstrate the performance improvement of power-diverse method.

We consider a NCMA downlink system with 6 users in a Rayleigh channel. The channel coefficients $H_{ij}^s$ are randomly generated according to the distribution $H_{ij}^s\sim \mathcal{CN}(0,1)$ in each independent simulation. All user devices share the same RS code parameter $L=8$. Additionally, the ${[133, 171]}_8$ convolutional code is adopted for all users. Power among clusters is equal. All results are averaged over 6000 Monte Carlo simulations. For the BER performance of the MUD decoder, each simulation is averaged from user A (or B) of all clusters. Since the PNC decoder decodes the XOR packets, each simulation of the PNC decoder is averaged from both user A and B across all clusters.

4.1. BER Performance of PNC and MUD Decoders

First, let us focus on the MUD performance of high-priority users in each cluster. It can be seen from Figure 6 that PD-NCMA and PR-NCMA significantly outperform PB-NCMA. The conventional PB-NCMA can hardly work since the superposition of the same constellation points of user A and B seriously affects the MUD detector. By introducing phase rotation artificially, PR-NCMA alleviates the constellation points’ superposition and improves MUD performance effectively. Besides, the proposed content-centric PD-NCMA adopts a differentiated power configuration. Users with high message priority are allocated more power to boost MUD performance. It is obvious that PD-NCMA-2 is fully ahead of other algorithms, which also reveals that content-centric design improves performance significantly. Nevertheless, PD-NCMA-1 is inferior to PD-NCMA-2 and PR-NCMA at high SNRs since Method 1 in clustering leads to an inconspicuous power difference between users with similar priorities (i.e., user 3 and user 4 in Figure 4). Fortunately, the proposed PD-NCMA-1 still fully outperforms PB-NCMA.

Figure 7 demonstrates the BER performance of the MUD decoder of user B. Since user B is the low-priority user within each cluster, the MUD performance of PD-NCMA-1 is obviously inferior to that of PR-NCMA. However, due to a better power differential clustering design, PD-NCMA-2 shows nearly the same performance as PR-NCMA-1, even surpassing PR-NCMA-2 at high SNRs. In addition, the performance of the proposed PD-NCMA is still much better than that of PB-NCMA.

In Figure 8, the PNC performances of PD-NCMA and PR-NCMA both show degradation, since the minimum distance of different XOR constellations is reduced. Nevertheless, due to the huge improvement in MUD, the performance degradation of the the PNC decoder has a negligible impact on overall performance. This can also be verified in throughput simulation.

4.2. Packets Number Comparison

Figure 9 illustrates the number of packets required to correctly recover message $M_i^A$. Notice that we adopt $L=8$ in the RS code; thus, the minimum number of packets to decode the message is 8. It can clearly been seen that both PR-NCMA and PD-NCMA can reach this lower bound in high-SNR ranges. Furthermore, PD-NCMA is fully ahead of other methods in low-SNR ranges, since the power-diverse design improves MUD performance significantly (Figure 6).

In Figure 10, we compare the number of packets required to correctly recover message $M_i^B$. Interestingly, it is observed that PD-NCMA-2 is still ahead of the other methods in low-SNR ranges, in sharp contrast to the common belief that PR-NCMA-1 should outperform PD-NCMA-2 because of better MUD performance in Figure 7. This observation is because the bridging operations in both the PHY and MAC layer utilize the correctly decoded $M_i^A$ to boost the $M_i^B$ decoding. Therefore, $M_i^B$ decoding will be promoted by the performance of $M_i^A$ decoding, even if $M_i^B$ is allocated less power.

Considering user B (low-power user) in cluster i, we first derive a specific value of power allocation by simulating union bounds and cluster throughput rather than priority. Notice that $P_i^A+P_i^B=P_i=2$ is adopted. As a consequence, $P_i^A$ can be determined when $P_i^B$ is obtained. Notice that it can also start with user A to get $P_i^A$ first. Furthermore, $P_i^B=P_i-P_i^A=2-P_i^A$.

4.3. SER Union Bound and Throughput Performance

Figure 11 demonstrates the SER union bound of the MUD and PNC decoder under different $\sqrt{P_i^B}$. It is worth noting that although PNC and MUD have almost the same SER union bound formulas (refer to (7) and (9)), their results are still quite different. $P_e^{PNC}$ decreases gradually with the increase in power, while $P_e^{MUD}$ decreases first and then increases. The main reason for this phenomenon is that the mapping operation of PNC $\prod \left(•\right)$ is different from that of MUD $\Omega \left(•\right)$, which leads to different Euclidean distance statistics of superimposed constellation points (more details about mapping operation analyses can be found in [12]). Hence, it can be seen from Figure 11 that the specific value of $\sqrt{P_i^B}$ should be between 0.6 and 1.

Then, we determine the specific value according to the throughput results within the cluster. From Figure 12, we can see that the throughput has a relatively stable performance between 0.69 and 0.75. Hence, we set $\sqrt{P_i^B}=0.72$ as the specific value to get better throughput performance. At this point, we have completed power allocation without considering priority. We refer to this approach as PD-NCMA-SV, and it is adopted in each cluster to further compare the overall throughput. Notice that PD-NCMA-SV adopts the same random grouping strategy as PB-NCMA and PR-NCMA; the only difference lies in power allocation.

As shown in Figure 13, the overall throughput performance of PD-NCMA-2 is much higher than that of PB-NCMA and PR-NCMA, especially at low- and medium-SNR ranges. PD-NCMA-1 exhibits similar performance but with reduced performance at high SNRs. The main reason for these results is due to the performance variation in the MUD decoder (Figure 6 and Figure 7). As for PD-NCMA-1, despite its suboptimal performance relative to PD-NCMA-2, it serves an important analytical purpose. It demonstrates that power diversity alone (via extreme priority pairing) yields throughput gains over PB-NCMA, while also revealing that a balanced clustering design is critical for maximizing these benefits. This comparison validates that both the clustering methodology and power allocation strategy contribute to PD-NCMA’s overall performance.

The total throughput of PD-NCMA-SV is still far ahead of PB-NCMA and PR-NCMA, even without considering the content-centric design. It indicates that the performance gain from power allocation in NCMA can not be neglected. However, PD-NCMA-SV needs to find an appropriate value based on the union bound and cluster throughput performance, which vary with SNRs. Therefore, PD-NCMA-SV cannot guarantee global optimality. However, in terms of overall throughput performance, NCMA based on power allocation is clearly far ahead of conventional algorithms. Overall, PD-NCMA can boost throughput dramatically.

To verify the generalization performance of the proposed algorithm, we repeated the simulation with 6, 60 and 300 nodes while keeping the same RS code ($L=8$). As shown in Figure 14, the average throughput gain of PD-NCMA-2 over PR-NCMA-1 18–22% at 8 dB at the scenario of 300 users, which indicates that the algorithm remains applicable in large-scale user scenarios.

Besides, we have performed a comparative simulation of the PD-NCMA method under both the Rayleigh and Rician channels in Figure 15, where the Rician factor $K=5$ is adopted. Other simulation parameters remain unchanged. The proposed algorithm can operate under different channels.

In a single-user cluster, the user has a full power budget and is not affected by superposed constellation points. Its BER and the number of packets required for correct reception will be better than those of paired users. Therefore, its performance will not become a bottleneck for the overall system. Relying on higher power, the MUD detector will exhibit excellent decoding performance in the low-SNR region. We conducted the following simulation.

Figure 16 shows the comparison of BER performance between the user assigned higher power in a normal cluster of PD-NCMA and the user occupying full power. It is obvious that due to the advantage in power, the BER performance of the single user is significantly improved. Similar results can also be observed from the number of required packets to correctly decode the message.

Figure 17 demonstrates the number of packets required to correctly recover the message. In the low-SNR region, the single user requires fewer packets due to the gain brought by occupying the full power. However, thanks to the PHY and MAC layer bridging operations, starting from 8 dB, the performance of both parties basically approaches the lower limit value of the RS code specified in the simulation parameters. We also compared the performance between 5, 6, and 7 users.

As can be seen from Figure 18, the final throughput of systems with different numbers of users approaches the upper limit value. In the low-SNR region, the difference in performance is relatively small.

5. Conclusions

In this paper, we have addressed a critical limitation of conventional NCMA systems by proposing a power-diverse, content-centric framework for downlink multiuser scenarios. The proposed PD-NCMA scheme dynamically clusters users based on message priorities and allocates power proportionally to throughput demands. Our priority-based strategy successfully boosts critical messages while leveraging NCMA’s bridging operations to safeguard low-priority users. Monte Carlo simulations validate that PD-NCMA outperforms PB-NCMA and PR-NCMA, achieving up to 30% reduction in decoding packets. The overall system throughput is also superior to other algorithms. Future work could be generalized to clusters using hierarchical grouping, integrate adaptive modulation and coding for dynamic environments, employ reinforcement learning for real-time priority-power optimization, prototype on SDR platforms for latency validation, and investigate energy–throughput trade-offs for battery-powered IoT devices. These directions will enhance the applicability of PD-NCMA.