A Clustered PD-NOMA in an Ultra-Dense Heterogeneous Network with Improved System Capacity and Throughput

Abstract

In the current era of exponentially growing demand for user connectivity, spectral efficiency (SE), and high throughput, the performance goals have become even more challenging in ultra-dense 5G networks. The conventional orthogonal frequency division multiple access (OFDMA) tech-niques are mature but have not proven sufficient to address the growing user demand for high data rates and increased capacity. Therefore, to achieve an improved throughput in an ultra-dense 5G network with an expanded network capacity, the unified non-orthogonal multiple access (NOMA) technique is considered to be a more promising and effective solution. Throughput can be im-proved by implementing PD-NOMA, as the interference is managed with the successive inter-ference cancellation (SIC) technique, but the issue of increased complexity and capacity with compromised data rate persists. This study implements the clustered PD-NOMA algorithm to enhance user association and network performance by managing the users in clusters with fewer users per cluster with the implementation of the cooperative PD-NOMA within the clusters. In this study, we enhanced the user association in a network and ultimately improved the throughput, sum rate, and system capacity in an ultra-dense heterogeneous network (HetNet). By imple-menting the proposed clustered PD-NOMA scheme, the system throughput has improved by 23% when compared to the unified PD-NOMA scheme and 65% when compared to the OFDMA scheme with a varied number of randomly deployed users, along with an improvement in system capacity of 8% as compared to the unified PD-NOMA and almost 80% as compared to the conventional OFDMA scheme in a randomly deployed ultra-dense multi-tier heterogeneous network. Thus, we improved the network performance with the proposed algorithm and achieved increased capacity, throughput, and sum rate by outperforming the unified PD-NOMA scheme in an ultra-dense heterogeneous network.

1. Introduction

5G networks are widely deployed with the orthogonal frequency division multiple access (OFDMA) technique to achieve efficient resource allocation and user association. This multi-access technique is more commonly implemented with fractional frequency reuse, multi-cell architectures, clustering techniques, etc. However, considering a proficient multi-tier dense heterogeneous network deployment, clustering has proven to be a noticeable way to manage the linkages among the randomly deployed base stations with reduced network overhead; multi-tier HetNets consist of macro base stations (MBS) and small cell base stations (SBS) [1,2,3]. In addition, for efficient user association in such ultra-dense heterogeneous networks, the conventional OFDMA techniques have not proven to be sufficient enough to accommodate users’ ever-increasing high data rate demand. Eventually, this results in poor data rates and underprovided network performance and capacity. As shown in [2], the author has improved user association and data rate with increased density but with a highly complex solution using the cluster-based OFDMA technique.

Moreover, in OFDMA, each sub-channel can serve only one user at a definite time slot, frequency band, or code to avoid interference and enable single-user detection under a simple receiver scheme. Ultimately, it is not expected to provide an adequate spectrum efficiency. Therefore, a less complex mechanism is required with which efficient spectrum use can be achieved along with improved fairness, high data rate, increased capacity, and enhanced user connectivity. This could be achieved by simultaneously serving multiple receivers with various channel conditions as with the non-orthogonal multiple access (NOMA) technique.

Researchers have widely used NOMA schemes because of their competence in increasing the system capacity and accommodating the network requirement of increased spectral efficiency (SE) and throughput with low complexity measures. NOMA is implemented as either a power domain (PD-NOMA) scheme or a code domain (CD-NOMA) scheme; in this paper, we considered PD-NOMA. In PD-NOMA, different users are assigned different power coefficients under the respective channel conditions to attain improved system performance. This scheme has a simple implementation, does not require considerable changes to the existing network architecture, and does not require additional bandwidth to improve the SE [4].

In addition, according to some researchers, within the ultra-dense heterogeneous networks, the incorporation of the power domain non-orthogonal multiple access (PD-NOMA) technique, orthogonal multiple access (OFDMA) techniques has been identified to provide an improved solution to achieve proficient resource allocation with enhanced capacity and load balancing in ultra-dense heterogeneous networks [5]. The PD-NOMA scheme superposes coding at the transmitter, and the base stations transmit superposed signals to multiple users in the power domain. In addition, PD-NOMA does not require significant alterations to the existing 3GPP LTE architecture, which helps in achieving the implementation of low-complexity solutions.

PD-NOMA implements successive interference cancellation (SIC) [6] to decode the signal one by one and concurrently yield a high SE while allowing some degree of multiple access interference at the receivers. The downlink PD-NOMA with SIC enhances the network performance, but the complexity associated with both the capacity and user throughput still continues with the increased network densities, as each user has to decode the neighboring user signal, which increases the computational complexity and leads to longer delays with increased channel state information feedback overhead at the BS. Thus, the PD-NOMA scheme also shows several challenges requiring mitigation through efficient solutions [7].

1.1. Prior Work

In [8], the authors implemented the OFDMA scheme and proposed a joint user association and power allocation algorithm to obtain an energy-efficient HetNet environment. The authors achieved an energy-efficient solution with compromised performance and smaller power constraints for the sub-channel allocations. In OFDMA, a frequency resource is allocated to each user, even to a receiver with relatively low SE and throughput. In addition, with conventional methods that introduce scheduling, a receiver with a fair channel condition has a higher chance of being considered than one with a diminished channel condition. This leads to fairness problems with increased latency. PD-NOMA assigns the same frequency resource to multiple users to improve the SE. In addition, multiuser detection (MUD) with SIC is implemented at the user end to manage interference. However, in [9] the researchers presented a resource-allocation scheme under distributed clustering with OFDMA and PD-NOMA schemes. The authors have worked on various cluster sizes and analyzed with numerical and simulation results that large clusters can provide better performance in terms of better spectral efficiency. In addition, considering user association, they discussed the importance of both schemes in achieving improved gains for both uplink and downlink communication, though more work could also be performed to show the overall improvement in the system capacity and throughput with the proposed cluster formations and user association under the PD-NOMA scheme.

PD-NOMA has gained considerable research interest in HetNets and has been implemented as an efficient resource allocation strategy compared to the conventional OFDMA technique. As in [10], a distributed resource allocation is presented for a self-backhauled small-cell network in full-duplex mode. The authors of this paper contributed to joint user scheduling, mode selection, and power allocation in a two-tier network, intending to maximize the network sum rate and the quality of service (QoS) and capacity constraints by implementing PD-NOMA over the small-cell network in the full-duplex mode. However, the authors did not study increased capacity with ultra-dense random user deployments.

In [11], PD-NOMA is utilized for user association and resource allocation in a dense heterogeneous network and improved connectivity in 5G systems. This work is presented by considering various case studies to demonstrate the effectiveness of PD-NOMA in ultra-dense networks. It emphasizes that the development of techniques that offer robust connectivity of massively deployed devices to improve energy efficiency with managed user deployments through increased network capacity with various distant user allocations has not been taken under consideration. In [12], PD-NOMA was implemented with beamforming to gain energy-efficient resource allocation and user association. The network is considered to be an ultra-dense user-centric heterogeneous network. In addition, in [13], the authors deemed multi-access edge computing and worked on offloading techniques to improve the performance in heterogeneous networks by reducing delays and achieving user association and resource sharing through a game-based algorithm.

Moreover, in [14], the complete details of the PD-NOMA scheme and its practical implementation are discussed in detail. In [14], the analysis and discussion of PD-NOMA were mainly performed as an efficient future radio multi-access technique. In [15], the author conducted a comprehensive survey on PD-NOMA and analyzed it as a proficient scheme to enhance the network capacity with efficiency and ultimately improve the network performance along with a few future research directions in the said domain by combining PD-NOMA with other schemes.

Moreover, in [5], Cirine Chaeib et al. utilized PD-NOMA for user association and sub-channel assignment to accomplish an effective radio resource management strategy. In addition, the authors implemented OFDMA and NOMA in a hybrid manner, and the results proved that the hybrid technique outperformed the results achieved with standalone OFDMA or NOMA for efficient user association.

Similarly, in [16], the author considered the gained sum rate of NOMA over OFDMA for uplink transmission with a single antenna, multiple antennas, and massive multiple antennas and proved with analytical results the accuracy of the gain achieved with the proposed technique. In [17], the authors showed with simulation results that NOMA can be a solution to increase the cell capacity without compromising the network performance for 5G networks, eventually satisfying users’ ever-increasing data rate demands.

The benefits of both OFDMA and NOMA schemes cannot be ignored for 5G ultra-dense heterogeneous networks. PD-NOMA has been suggested for user association as a technique for achieving a reliable and efficient solution with improved network capacity.

Therefore, it can be concluded from the above-discussed literature that PD-NOMA has gained great significance in radio resource management and user association in heterogeneous networks. However, it still has to mitigate a few challenges with ultra-dense heterogeneous network deployments.

Other popular techniques are used with PD-NOMA, including the cooperative NOMA and cognitive radio with the NOMA technique. In cooperative NOMA, the relaying function is performed by the near user to reduce the outage probability and can virtually extend the coverage area of the base station, and the relaying function can be performed under various techniques to achieve the desired results of improved network performance [18]. Further, in [19] the author presented a detailed critical overview of current research methods in cooperative PD-NOMA (PD-CNOMA) and also discussed the implementation of PD-CNOMA with other techniques such as cognitive radio, energy harvesting, and full duplex 5G technologies. Further, in [20], the author has explored energy harvesting assisted cooperative NOMA with underlay cognitive radio networks. The presented methodology has high complexity, and the impacts of power transmission, energy harvesting co-efficient, and imperfect SIC was also analyzed with simulation and analytical results. Thus, it can be concluded that by using cooperative PD-NOMA, the performance of 5G networks can further be improved, i.e., by implementing better techniques for deploying relays and by selecting significant values of transmission power, SIC strategies, and other performance parameters.

In cognitive radio with NOMA, on the other hand, the far user is considered the primary user if the target rate conditions are satisfied with the far user. Thus, more power is allocated to the far user, and remaining power is allocated to the secondary user; the coverage probability can be improved with this scheme, but with high signal to noise ratio (SNR) values, the system performance declines [21].

Hence, with the above-mentioned schemes, the user association can be improved, but still the complexity of the SIC process at the receiver’s end persists. With clustering, the complexity of the SIC process can be reduced, and thus the chances of errors during the SIC process can be reduced [22,23]. In this paper, we proposed the clustered PD-NOMA technique and implemented it with the previously applied interference managed hybrid clustering (IMHC) scheme [1] and found that with the proposed PD-NOMA scheme, the interference among the users was further reduced because with the clustered PD-NOMA, the frequency band was shared with a lower number of users due to clustering. Hence, we could achieve improved throughput and channel capacity with the proposed scheme due to effectively reduced interference among the associated users and high channel gain differences.

The literature analyzed in

Table 1. Existing literature performed with PD-NOMA.

Research Work	Contribution	Sum Rate	Capacity	Clustering	Ultra-Dense HetNet	User Association
[11]	Proposed a unified NOMA framework for user association and resource allocation to achieve massive connectivity.				✓	✓
[12]	Energy efficiency maximization is achieved by proposing a joint optimization framework of PD-NOMA and beam forming.					✓
[17]	System level performance analysis with hybrid PD-NOMA and OFDMA schemes.		✓		✓
[24]	PD-NOMA, game theory algorithms are proposed based on QoS threshold to improve user association and power allocation.	✓			✓	✓
[22]	Proposed a cluster specific beam-forming algorithm to maximize sum-throughput.	✓		✓	✓

and discussed above shows that the performance of PD-NOMA with massive deployments, specifically if the nodes are deployed over more considerable distances, needs to be addressed. However, despite the remarkable capabilities of PD-NOMA, only a few studies has been performed to address this issue with clustering methods to achieve improved user association, system capacity, and sum rate in ultra-dense heterogeneous networks.

1.2. Challenges of PD-NOMA

NOMA faces a few challenges with the increased number of users; considering an ultra-dense network deployed with the PD-NOMA scheme, energy consumption at the user end becomes high due to extensive SIC calculations. As each user has to decode all other users' information associated with the same BS, if an error occurs in decoding any one user’s information, then all additional decoding will therefore have an impact and eventually will harm the system level performance, specifically in achieving an efficient sum rate and capacity [23]. Thus, the computational complexity and power consumption will be increased at the receiver’s end. The channel gain information is sent back to the BS, resulting in remarkable channel state information overhead. In addition, in downlink NOMA, for an arbitrary user ‘k’, it decodes the user signals with lower channel gain and processes the user signals with a relatively high channel gain as noise [25,26].

1.3. Motivation

In PD-NOMA, decoding and SIC implementation complexity has always been a vital concern; SIC with increased complexity in ultra-dense networks also increases the chances of error and eventually affects the network’s performance, resulting in throughput deprivation. Therefore, limiting the number of interference cancellations is essential, i.e., the number of users associated with each small cell base station (SBS) [15,27].

Clustering is a solution to the problem mentioned above, i.e., by forming users into clusters and reducing the number of messages decoding SIC at the user end, the SIC complexity and the chances of errors will be reduced [22,28]. When there will be fewer users associated with SBS, the interference among users will also be reduced.

Therefore, the issues can be managed when PD-NOMA is implemented on a dense network, with a reduced number of users associated with the SBS, within a densely deployed SBSs heterogeneous network to improve user association. The PD-NOMA limitations can be addressed by implementing a clustering technique. PD-NOMA can achieve efficient results by keeping the reasonably low number of associated users linked with the SBSs in every cluster, since, based on clustering, we can have more power controlling the supervision on the related users, and consequently, the system interference can be reduced, resulting in enhanced system capacity and user association.

1.4. Contribution

Our work in this paper extended our previously performed study in [1]. In this study, we proposed a clustered PD-NOMA scheme that contributes by implementing a randomly deployed ultra-dense heterogeneous network to improve user association, the overall system capacity, and throughput.

Requiring the number of users associated with SBSs should be limited to gain considerable channel gain; a clustered PD-NOMA is implemented with hybrid clusters for improved user association and resource allocation at multiple tiers of the proposed architecture.

The user association and power allocation is performed to maximize user connectivity and network capacity. By implementing the proposed clustered PD-NOMA on multi-tier ultra-dense HetNet, we improved the throughput gain due to the reduced interference with the proposed scheme as compared to the IMHC scheme.

We implemented the cooperative network scheme applied on users within the PD-NOMA clusters. In the proposed scheme, we considered users with strong signals as relays for the users with low channel condition to improve the throughput gain and capacity in the clustered network. Furthermore, we achieved the results with significantly improved throughput in comparison with the technique presented in [1] and the conventional OFDMA scheme. The proposed technique was verified through simulation results to maximize user connectivity and ensure the improved capacity and sum rate in an ultra-dense HetNet.

1.5. Organization

The rest of the paper is organized as follows: Section 2 presents the detailed description and functionality of PD-NOMA. Section 3 presents the system model comprising the user association and power allocation scheme, Section 4 discusses the simulation results, and Section 5 concludes the paper.

2. Power Domain-NOMA

Generally, PD-NOMA has achieved improved spectral efficiency (SE), enabling users to share resources efficiently. More commonly, a basic two-user downlink NOMA scheme is considered in much of the research, where two users are allocated such that the user U1 is deployed near the base station with high channel gain and U2 is far from the base station, experiencing a relatively low channel gain. Different powers are superimposed upon each other at the transmitter’s end for users U1 and U2 as shown in Figure 1. The transmitter assigns high power to the weak user due to its high path loss component and comparatively low power to the strong user. The strong signal receiver will have a higher signal-to-noise ratio than the weak user, implying that the strong user can decode and subtract its signal more efficiently. The robust user’s signal at the weak side is considered noise, as its transmission power is lower than the weak user’s signal. Therefore, the weak user can decode its signal without performing SIC.

Thus, grouping or clustering active users in the same resource block is necessary in PD-NOMA and is usually performed as two or multiple users per cluster. The selection in the basic NOMA scheme, with single-antenna BS and users, depends on the rapid channel gains, and the users are ranked accordingly to allow proper SIC decoding, which tends to improve as the channel gain increases, unless the channel gain of the weak user is minimal [29]. Overall, the optimal user clustering requires a thorough search and might not be reasonable for practical systems and networks with many users [30]. Therefore, researchers resort to low complexity solutions to solve the user clustering problem through heuristic algorithms, leading to unexpected results. Instead, the NOMA clustering problem includes the following [29]: A large number of user decoding is considered to be complex, and therefore it is required to limit the exhaustive search to a much smaller region of the achievable set; this will simplify the problem and can lead to the optimum result.

3. System Model

Consider a hybrid clustered multi-tier network with a single macro base station (MBS) and randomly deployed clustered small-cell base stations (SBSs) under a Poisson distribution. The SBSs are laid as high-power small-cell base stations (HSBS) and low-power small-cell base stations (LSBS) over tier-2 and tier-3, respectively. The SBSs are located at the center of the cluster with radius ‘r’, with ‘n’ number of users deployed within each SBS cluster. It was assumed that users with considerable correlations were grouped into a cluster. Figure 2 illustrates the system model considered in this study, which is comprised of a 3-tier heterogeneous network. MBSs are deployed at tier-1, pico BSs are deployed at tier-2, and femto BSs are deployed at tier-3. Hybrid clustering is performed at tier-2 and tier-3 to manage interference and improve the system throughput [1]. PD-NOMA is implemented at the user side UE at tier-2 and tier-3.

According to the Interference Managed Hybrid Clustering (IMHC) algorithm proposed in [1], the system interference is reduced by deploying the SBSs using a hybrid clustering technique, where SBS are deployed in a more decentralized manner. In addition, a power control algorithm is implemented on the clustered SBSs based on the threshold interference value and are categorized as either a low-power small-cell base station (LSBS) or high-power small-cell base station (HSBS). Therefore, LSBSs and HSBSs will form clusters to serve their relative associated users. The author has considered the Pico BSs as HSBS and Femto BSs as LSBSs. The results in [1] show that higher data rates are achieved with HSBS than with the LSBS.

3.1. Clustered PD-NOMA

Step 1.

The user will send their respective channel state information (CSI) to the corresponding SBS, and the SBS forms the CSI set ‘I’, within the threshold value ‘T’, where T ≥ 1.

Step 2.

The SBS finds the channel gain difference based on the correlation between the users linked with the same SBS.

Step 3.

The SBS calculates the distance d_j,n as the channel gain difference between the jth and kth user.

I_j,k = {d_j,k → ||h_j| − |h_k||; corresponding _(j,n) → (|h_j·h_k|/|h_j||h_k|) ˃ ρ},

Where ‘ρ’ represents a pre-defined real value (0 ≤ ρ ≤ 1).

Step 4.

The SBS forms the cluster with users having the maximum channel gain difference.

(j,k)* = argmax {d_j,k}, T = T − (d_j,k) until the difference with the nth user is computed.

Step 5.

Among the residual users, users with the most significant channel gain difference will be selected by the SBS, eventually improving system capacity. Ɐ(j,k)_n the users will be evaluated based on the respective channel gain difference.

The SBSs share the bandwidth ‘W’ using the OFDMA scheme. Assuming downlink transmission, let U_s ⊃ (U_H ∪ U_L), where U_s represents the set of all SBS users sharing ‘W’ under the NOMA scheme, and U_H and U_L represent the categorization of users of HSBS and LSBS, respectively.

Let S ⊃ (S_H ∪ S_L) denote the set of all SBSs, with S_H = {1, 2,…, S_H} as a set of HSBS, and S_L = {1, 2,…, S_L} representing the set of LSBS.

Consider C_s ⊃ (C_H ∪ C_L) as the set of sub-channels, where C_H = {1, 2,…, C_n} and C_L = {1, 2,…, C_n} represent the sub-channels assigned to the S_H and S_L, respectively. Considering only the small-cell network, each user is connected to either an HSBS or an LSBS, as U_s and C_s represent the set of SBS users linked with the set of sub-channels, respectively. Let P_uc be the power allocated to user u on sub-channel c, and h_uc be the channel gain between the SBS s and user u on sub channel c, where P_uc > 0. Therefore, the SINR of user u on sub-channel c can be given as:

$$SIN{R}_{uc}=\frac{p_{uc}{h}_{uc }}{{{\displaystyle \sum }}_{i\in U_s }{p}_{uc}{h}_{uc}+No}$$

(1)

where i represent the interfering signals intended for users belonging to set U_s, and h_uc represents the channel gain. If ‘X’ (where X = x_usc) represents the user association matrix, such that, Ɐ s Є S, u Є U_s, and c Є C_s, then

$$x_{usc}= {\{}_{0, otherwise}^{1, if ‘s’ is transmitted to ‘u’ over ‘c’}$$

(2)

The user association ‘X’ should guarantee that the total number of associated users has increased, and the sub channels are efficiently allocated, as shown in Figure 3. The user interference is managed using the SIC technique at the receiver’s side [7,31]. The optimal decoding in the downlink channel can be attained by organizing users according to the normalized channel gain |h_usc|²/σ², where σ² is the variance of the additive white Gaussian noise (AWGN), and |h_usc| is the modulus of channel gain between user ‘u’ and SBS ‘s’.

SIC is used for detection and decoding in the accompanying NOMA scheme with a normalized channel gain. NOMA reduces the inter-user interference that occurs when densely deployed BSs and users operate in the same vicinity. Received signals at u₁, u₂,…, u_n presented within the cth sub channel can be given by

$$y_{c,1}=h_{c,1 }\sqrt{{\alpha }_{c,1}{p}_{c,1}}+h_{c,1 }{{\displaystyle \sum }}_{t=1}^{n-1}\sqrt{{\alpha }_{c,1}{p}_{c,t}}+N_o$$

(3)

$$y_{c,2}=h_{c,2 }\sqrt{{\alpha }_{c,2}{p}_{c,2}}+h_{c,2 }{{\displaystyle \sum }}_{t=1}^{n-1}\sqrt{{\alpha }_{c,2}{p}_{c,t}}+N_o$$

(4)

$$y_{c,n}=h_{c,n }\sqrt{{\alpha }_{c,n}{p}_{c,n}}+h_{c,n }{{\displaystyle \sum }}_{t=1}^{n-1}\sqrt{{\alpha }_{c,n}{p}_{c,t}}+N_o$$

(5)

where ‘α’ is the power co-efficient for the user, ‘h’ is the corresponding channel gain, and ‘p’ is the received power at the receiver end. Thus, after implementing SIC at the receiver’s end, the SNR can be expressed as:

$$SN{R}_{c,1}=\frac{{\alpha }_{c,1 }p{\left|h_{c,1}\right|}^2}{N_o}$$

(6)

$$SN{R}_{c,2}=\frac{{\alpha }_{c,2 }p{\left|h_{c,2}\right|}^2}{N_o+{\alpha }_{c,1 }p{\left|h_{c,1}\right|}^2}$$

(7)

$$SN{R}_{c,n}=\frac{{\alpha }_{c,n }p{\left|h_{c,n}\right|}^2}{N_o+{{\displaystyle \sum }}_{t=1, t\ne n}^{n-1}({\alpha }_{c,t }p{\left|h_{c,n}\right|}^2)}$$

(8)

SNR_c,1 is received at u_c,1, and it is considered to be closest to s as it applies SIC to eliminate interference occurring from other users i; therefore, the SNR in Equation (5) consists of average noise without any interference, whereas u_c,2 is relatively far from s, and u_c,n is the farthest. User u_c,n cannot implement SIC to cancel the weak signals of other users, as its received power ‘p’ is not strong; therefore, the SNR in Equation (7) consists of average noise along with the interfering signals.

Moreover, as NOMA is implemented within the dense s-comprised clusters, the maximum number of users will be close to some ‘s’ and receive adequate ‘p’ to improve the data rate. However, users at the edges of the cluster may experience strong interference from neighboring users. In addition, it is assumed that there will be a limited number of users within the defined clusters. The achievable data rate over a sub channel ‘c’ from SBS ‘s’ transmitted to user ‘u’ will be given as:

$$R_{usc}=wlo{g}_2(1+SN{R}_{usc})$$

(9)

3.2. Power Allocation

The power allocation in NOMA differs from that in OFDMA; for sub-channels, assume a single beam scenario with (c = 1); let, mathematically, h₁ > h₂ > … > h_n be the channel condition for users 1, 2, 3,…, n.

Considering the user deployments as given in Figure 1, there will be two users, u₁ and u₂, where u₁ is the near user, and u₂ is the far user. The user rate for the two users will be given as:

$$R_{u1}=lo{g}_2(1+{\alpha }_{u1}{\left|h_{u1}\right|}^{2}p)$$

(10)

$$R_{u2}=lo{g}_2(1+\frac{{\alpha }_{u2}{\left|h_{u2}\right|}^{2}p}{{\alpha }_{u1}{\left|h_{u2}\right|}^{2}p+1})$$

(11)

where α_u1+ α_u2 = 1

If the total sum rate is defined as R_n = R_u1 + R_u2.

Furthermore, R_n represents the sum rate.

Maximize ‘R_n’,

Subject to:

$${{\displaystyle \sum }}_{k=1}^n{\alpha }_{k}p \le p$$

(12a)

$${\alpha }_{k}p>0$$

(12b)

where

$$R_n={{\displaystyle \sum }}_{k=1}^{n}lo{g}_2(1+\frac{{\alpha }_{k}p {\left|h_{k }\right|}^2}{N_o+{{\displaystyle \sum }}_{t=1, t\ne k}^{n-1}{\alpha }_{t }p|h_k{|}^2}) > R_{min}$$

(12c)

where R_min is the minimum required sum rate by the system. The power allocation is carried out so that the power is allocated to each user if the preceding user has been assigned the power [27,32]. Therefore, if ‘k’ is a user in the tagged cluster nearest to the SBS, therefore:

α_{k + 1}p > 0 only if α_k p > 0

(13)

It can be concluded from the above-given expression that an improved sum rate is achieved by increasing the power of every proceeding user in comparison to the succeeding one. Thus, shifting the power from farther to closer users will improve the system capacity. The shifting process continues until the farthest user reaches its minimum threshold ‘τ_min’ [27,32]. However, the nearest user should not obtain power more than the maximum defined threshold ‘τ_max’. The power shifting process is repeated from the farther user to the closer user as follows:

$$u_1\left\{{\alpha }_{1}p\right\} \leftarrow u_2\left\{{\alpha }_{2}p\right\} \leftarrow \cdots u_k\left\{{\alpha }_{k}p\right\}$$

(14)

As MBS employs OFDMA and SBS NOMA to achieve considerable connectivity in the proposed network, the received power approach is incorporated to regulate user association. Figure 3 plots the user association probability of the unified NOMA-enabled dense network with three layers. However, it is assumed that NOMA users prefer HSBS or MBS if LSBS availability is relatively low. With the densification of HSBS and LSBS, NOMA users show a great possibility of being associated with the SBSs deployed within the clusters.

However, it is also assumed that NOMA-associated users have a higher probability of being associated with LSBS, even though HSBS transmits at a higher power level, due to the close deployment of LSBS within the clusters, and reveals the effectiveness and benefits of densely deploying LSBSs in the clustered HetNets.

3.3. Cooperated Clustered PD-NOMA

In wireless communication, transmitting more than one copy of a signal is an encouraging technique to reduce the effects of fading. Among the range of existing schemes, the cooperative network is considered to be a better scheme. The cooperative network helps in achieving improved reliability by transmitting multiple signals through relaying. Moreover, for users with bad channel conditions located at farther distances, where a direct link between BS and a user could be established, relaying proves to be the solution. In general, relaying is preferred because it is relatively closer to the BS and therefore requires less power at BS to transmit the signal at relay. It determines that relay networks have more benefits in terms of reliability, extensive coverage area, and power saving [19,33]. As with the PD-NOMA in the cooperative network, the receiver’s SNR can be improved significantly over a restricted distance. NOMA enhances with relaying the system’s throughput. The spectral efficiency of PD-NOMA improves by relaying signals and backing the cell-edge users. Therefore, it is necessary to consider the cooperation in PD-NOMA-based communication systems. Two types of cooperation in the downlink scenario are possible, namely cooperation between the PD-NOMA users/BSs and cooperation by using fixed relays [19,34,35].

In this article, we considered cooperation within the PD-NOMA clusters among users, as shown in Figure 4a. The basic design and working of cooperative PD-NOMA is similar to the function of SIC. According to the working principle of SIC, the users with strong channel conditions perform the decoding, and thus the messages of the weak user will be decoded first by the users with the better channel condition. Therefore, the users with the good channel condition exploit this information by working as relays for other users with weak channel states and improving the reliability of users with weak channel states. We considered a multi-user downlink cooperative PD-NOMA with a single SBS and two or more end users. For two users, the downlink transmission will be performed in two time slots as shown in Figure 4b, i.e., the direct phase and the cooperative phase. In the direct phase, a superposed message of both users U1 and U2 will be broadcasted by the SBS.

Consider a scenario where the channel state of U1 is supposed to be strong, so SIC will be implemented at U1. Considering the working principal of SIC, U1 decodes the message of U2 before decoding its own message, while in the second time slot, U1 will function as a relay and forwards the former decoded information of U2. With this cooperation scheme, two copies of signals will be received at U2 via different paths. This cooperation is important and much needed for weak users, since the throughput of weak users would suffer due to the interference from the strong user.

Therefore, the signal reception of the farther user will be improved by having two copies of a message. For larger distances, this cooperation would require additional spectral resources. However, it can be recompensed by working with shorter distances, which is achievable with the formed PD-NOMA clusters. The other method to implement cooperative PD-NOMA is with dedicated relays, which can be considered in future research.

4. Results and Discussion

Numerical analysis by performing Monte Carlo simulations was performed in this section to verify the accuracy of the proposed algorithm. To perform simulations, we used MATLAB tools. The overall simulation setup is summarized in

Table 2. Simulation parameters.

Parameters	Values
Sub Carrier Bandwidth	5 MHz
System Bandwidth (W)	10 MHz
Transmission Power of Pico BSs (HSBS)	25 dBm
Transmission Power of Femto BSs (LSBS)	10 dBm
Channel Gain (MBS)	14 dBi
Channel Gain (SBS)	7 dBi
Indoor/Outdoor Path Loss Coefficient	2
Radius of MBS (Macro BS)	500 m
Radius of HSBS (Pico BS)	25 m
Radius of LSBS (Femto BS)	10 m
No. of HSBS	10
No. of LSBS	30
No. of Users	2–60
No. of Sub-Carriers NOMA	5
AWGN	169 dBm/Hz
Fading	Rayleigh

; the values were selected based on the 3GPP standards. Simulations were performed on SBS-associated users considering both indoor and outdoor small cell users. All active SBS nodes were randomly deployed using a Poisson random distribution within a macro cell area, giving the targeted region′s coverage probability as shown in Figure 5. The power coefficient ‘α’ range was from 0 ≤ 1, and the simulations were performed to evaluate and give a comparative system capacity with the implementation of OFDMA, PD-NOMA, and the proposed clustered PD-NOMA techniques.

Figure 6 shows the channel capacity comparison by comparing the user rate of u1 and u2 achieved with unified PD-NOMA and clustered PD-NOMA in Mbps. It can be seen in the results that the region covered by clustered PD-NOMA was considerably more significant than the unified PD-NOMA scheme due to the increased channel gain difference achieved with the clustered PD-NOMA.

Figure 7 shows the throughput gain achieved with the increased number of users associated per cell; it can be seen that 4% more throughput gain was achieved with clustered PD-NOMA (without cooperative PD-NOMA) than the unified PD-NOMA scheme. In addition, it can be analyzed from the results that the throughput gain achieved with unified PD-NOMA was 11% improved as that achieved with the conventional OFDMA scheme, and it was enhanced by 15% with the clustered PD-NOMA as compared to the traditional PD-NOMA scheme.

After implementing the cooperative method on clustered PD-NOMA, the throughput further improved. Figure 8 shows the comparative analysis of throughput gain achieved with the proposed clustered PD-NOMA with cooperative nodes, the throughput achieved with the IMHC scheme [1], and the results achieved with unified PD-NOMA and OFDMA techniques. With the proposed scheme, the throughput gain improved by 23, 29, and almost 65% as compared to the unified PD-NOMA scheme, IMHC clustering scheme, and the conventional OFDMA scheme, respectively.

Results showed that the throughput efficiency improved remarkably for a varied number of users when implemented with the proposed clustered PD-NOMA scheme, whereas the number of users associated per cluster would be based on maximum channel gain difference between the associated users for the clustered PD-NOMA.

The throughput gain improved with the clustered PD-NOMA due to low interference values and cooperative user implementation within the PD-NOMA clusters, as interference was mitigated by applying SIC, and as the clusters were formed, the distance of users from the SBS also decreased; therefore, the inter-cluster interference also decreased. Moreover, due to the high channel gain difference, the number of users per cluster would be low and thus would result in low interference and eventually improved throughput gain.

Figure 9 shows that by implementing clustered PD-NOMA in an ultra-dense HetNet, the overall system capacity improved remarkably compared to the capacity achieved by implementing a unified PD-NOMA and the OFDMA scheme in an ultra-dense heterogeneous network. On performing the analysis, it was found that the overall system capacity with clustered PD-NOMA improved by 8% compared to the unified PD-NOMA scheme and more than 80% compared with the conventional OFDMA scheme. Thus, the proposed clustered PD-NOMA algorithm improved the system capacity by grouping the base stations and user associations with satisfactory data rates, although with clustered PD-NOMA as the average SINR increased, system capacity also improved.

The potential reason for increased system capacity is the increased channel gain difference due to cluster formations with a lower number of users along with the basic functionality of the PD-NOMA scheme. Thus, with clustered PD-NOMA, the system capacity further improved and eventually will improve the coverage probability in ultra-dense heterogeneous networks.

Figure 10 shows an improved sum rate achieved with the proposed algorithm of the clustered PD-NOMA scheme, which hence improved the overall sum rate versus the increased density of associated users within the targeted cell area and eventually resulted in an improved system sum rate achieved with the increased user density, as compared to the sum rate achieved with the unified PD-NOMA and the conventional OFDMA schemes for the same number of users. The results show that the proposed clustered PD-NOMA scheme improved the sum rate by 4 and 14% compared to the unified PD-NOMA and conventional OFDMA scheme, respectively. Therefore, an improved sum rate with an increased system capacity was achieved with the clustered PD-NOMA scheme in an ultra-dense HetNet.

Figure 11 and Figure 12 show the CDF generated to validate the results achieved with the clustered PD-NOMA, showing improvements in throughput and capacity, respectively.

5. Conclusions

This article implemented a clustered PD-NOMA scheme on an ultra-dense heterogeneous clustered network at tier-2 and tier-3 small cell users, i.e., HSBS and LSBS users, respectively. The proposed clustered PD-NOMA algorithm was proved to be a promising solution to achieve an efficient user association with an improved data rate for an ultra-dense 5G network. The results achieved in this article with the proposed algorithm outperformed the overall system capacity, throughput gain, and sum rate achieved with both the unified PD-NOMA and OFDMA schemes. With the proposed method, we improved various performance parameters simultaneously in a randomly deployed ultra-dense HetNet, as the system capacity and the throughput gain improved by 8 and 23%, respectively, as compared to the unified PD-NOMA scheme, and by 80% and 65%, respectively, when compared to the conventional OFDMA scheme, with significant improvement in sum-rate achieved with clustered PD-NOMA implementation. In the future, different cooperative PD-NOMA implementations will be explored, and their impacts on load balancing and system capacity will be studied. In addition, based on the existing literature, there are still so many ways in which PD-NOMA could be implemented to improve the user association and spectral efficiency.