Game Theory Based Delta-OMA Scheme for VLC Networks

This paper proposes a delta-orthogonal multiple access (D-OMA) scheme-based visible light communications (VLC) network to enhance spectral efficiency and massive connectivity in the indoor environment. The D-OMA scheme is an advanced version of the non-orthogonal multiple access (NOMA) scheme. D-OMA allows the partial overlapping of the in-band NOMA clusters to achieve the benefits of a massive in-band NOMA scheme with low power consumption and less complexity. In this work, the massive in-band NOMA scheme is used as a special case of the proposed D-OMA scheme. Game theory is employed for the user grouping mechanism, which enhances the sum rate of the proposed network. Closed-form expressions for the bit error rate (BER) and outage probability of the proposed network are derived. Further, downlink transmission power optimization is performed using Karush-Kuhn Tucker (KKT) conditions to improve the outage performance of the proposed D-OMA VLC network. The presented numerical results show the effect of optical filter gain and field of view (FoV) in indoor communication. Further, it is noted that the BER performance of the D-OMA scheme outperforms the massive in-band NOMA scheme due to the cluster sizes which control the interference in the D-OMA scheme. Moreover, the sum rate of the proposed network is significantly improved using the preference relation algorithm (PRA) compared to the random NOMA scheme.

white LED is an essential factor to consider in VLC communication. In [4] the frequency response of UXEON3020 LED has been measured and shows low pass characteristics with a 3 dB bandwidth of 1.47 MHz. Moreover, the DC bias current of a VLC transmitter affects the magnitude of the frequency response. The magnitude of the frequency response reduces with the reduction of the DC bias current. Whereas the magnitude of the frequency response increases with the DC bias current at a higher frequency due to the higher optical power detected at the receiver.
In fact, the VLC technique has several advantages when compared to RF communication. For instance, it has high spatial reuse characteristics due to its signal isolation which provides secure communication. Since the VLC is a non-coherent communication system, the transmit and receive front-ends do not require many complex signal processing units, unlike the RF receiver circuits. Inherently, VLC networks achieve a high data rate due to the large Terahertz spectrum, and it operates with simple transmission techniques such as intensity modulation/direct detection (IM/DD). In the recent surveys, it was identified that many of the people and their services mainly depend on the indoor environment; therefore, VLC will be a more demanded one in the upcoming year [5].
It is noteworthy that the Doppler effect does not exhibit in the VLC channel. Hence it is easy to model as a time-invariant channel in the indoor environment [6]. For the given setup, such as room shape, user/node location, and light source type, the VLC channel is simply modeled as a deterministic direct current (DC) channel. Further, VLC signals inherently provide a high signal-to-noise ratio (SNR) due to their dominant line of sight (LOS) path and short distances of users/nodes [7]. However, the VLC links can also be modeled using the reflections, refraction, and diffusion components [8].
The main challenges in the VLC networks arise from the fact of limitation of the modulation bandwidth with respect to the LED characteristics. Hence VLC support only a limited data rate. In this scenario, the multiple access (MA) scheme is identified as a suitable method to enhance the data rate of the VLC networks. In particular, frequency division multiple access (FDMA) and orthogonal frequency division multiple access (OFDMA) is the preferred multiple access schemes to achieve high spectral efficiency in the VLC networks. However, these multiple access techniques have limitations, such as the DC biasing and signal clipping requirement to convert the signal values as real and non-negative [9]. Therefore, VLC networks need a new promising multiple access scheme requirement to enhance their performance.

A. REVIEW ON MULTIPLE ACCESS TECHNIQUES IN VLC
An optical OFDM scheme is initially employed in the VLC networks to achieve a high data rate. However, it leads to the peak-to-average power ratio (PAPR) problem due to the non-linearity behavior of the LEDs [10]. Hence, the single carrier frequency division multiple access (SC-FDMA) scheme is proposed for the VLC network [11], which significantly reduces the PAPR level. Basically, SC-FDMA can be modeled as a fast-Fourier transform (FFT) precoded OFDM scheme, which achieves the benefits of OFDMA. In fact, SC-FDMA outperforms the OFDMA scheme due to the frequency diversity gain [12]. However, the joint equalization process in the SC-FDMA scheme is the critical one that increases the receiver complexity [13]. On the other hand, OFDMA supports dynamic resource allocation and scheduling. Hence it works well on the medium access control (MAC) protocol [14]. Practically, OFDMA is used in the long-term evaluation (LTE) downlink and SC-FDMA is used in the LTE uplink.
Recently, a new multiple access scheme known as the non-orthogonal multiple access (NOMA) scheme has been proposed for RF-based fifth-generation (5G) wireless networks to improve spectral efficiency and massive connectivity. Generally, the NOMA scheme is easily adopted with downlink transmission [15], [16]. However, the end-to-end transmission of the NOMA wireless network is established by combining the physical-layer network coding (PLNC) scheme as in [17] and [18]. Inherently, the NOMA scheme is well suited for the VLC networks due to the quality of channel state information (CSI), which makes successive interference cancellation (SIC) operations more flexible. Therefore, the NOMA scheme is highly recommended for the VLC networks.
In the NOMA scheme, getting a perfect SIC operation is practically difficult because there will be a SIC residual error leading to an error propagation to the successive symbols. In this scenario, an adaptive modulation scheme based on NOMA-VLC networks is proposed as in [19], which gives SIC-free operation with respect to the channel conditions. Further, in the NOMA scheme, users are ordered based on channel conditions, and this ordering can be used for decoding, power allocation, and grouping. In the realistic wireless environment, CSI information is not always perfect, and therefore, it introduces CSI errors which will degrade the performance of the VLC networks. In such a scenario, the performance of the NOMA-VLC networks is improved using hybrid RF/VLC links [20].
Moreover, power optimization is another way to improve the performance of the NOMA wireless networks [21]. Particularly, optimal power allocation at the base stations (BS) or access points (AP) will enhance the sum rate of the NOMA-VLC networks under LED light constraints [22]. Mostly, on-off keying (OOK) modulation is preferred in the VLC networks [23] due to its easy implementation with LED. However, in [24] and [25], higher-order modulation is also considered to improve the reliable data rate in the VLC networks.

B. REVIEW ON CLUSTERING IN VLC
User clustering in NOMA-based wireless networks is another challenging issue and using such suitable clustering algorithms the sum rate of the NOMA wireless network is significantly improved. In this direction, the game theory approach to employed for user clustering in NOMA wireless network to enhance the sum rate [26]. User grouping using the preference relation algorithm (PRA) is proposed for the NOMA wireless networks, and the Shapley value is calculated to allocate the payoff to each user such that the sum rate is improved in the VLC network [27]. Also, low complexity sub-optimal user clustering algorithm is proposed for uplink and downlink NOMA systems using channel gain differences in [28]. Further, the system capacity of the device-to-device VLC network is improved by selecting the optimum communication mode using the game theory approach in [29]. Similarly, user grouping in the VLC networks is performed based on the user's location in [30]. Therefore, the game theory-based VLC networks with the D-OMA scheme is the promising optical wireless network model and will fill the gap in the existing indoor wireless networks.

C. MOTIVATION
In the future, it is expected that new multiple access schemes with white LED sources will brighten the VLC technology. Moreover, multiplexing and micro LEDs can play a vital role in upcoming VLC wireless networks [31]. Significant requirements of sixth-generation (6G) communication include ubiquitous mobile ultra-broadband (uMUB), ultra-high-speed with low-latency communications (uHSLLC), massive machine-type communications (mMTC), and ultra-high data density (uHDD). Powerdomain NOMA solves the small bandwidth modulation problems in the VLC networks. Thereby, it achieves a high data rate in indoor communication. However, the NOMA scheme has some drawbacks, such as the SIC complexity and power allocation problem. Therefore, VLC networks need an advanced multiple access scheme beyond the NOMA scheme to support such massive connections with less complexity and low power consumption.
More recently, another multiple access scheme called delta-orthogonal multiple access (D-OMA) schemes have been proposed for RF-based 6G wireless networks [32]. D-OMA scheme allows the partial overlapping of in-band NOMA clusters under distributed large coordinated multipoint (CoMP) environment. Similarly, in the in-band NOMA scheme, the total bandwidth is divided into a number of subbands, and each sub-band operates with a unique NOMA scheme. Due to the partial overlapping of the D-OMA scheme, the accessibility of the D-OMA scheme is higher when compared to the in-band NOMA scheme. Further, since the D-OMA scheme allows overlapping, it is unavoidable for the sub-bands to overlap interferences. However, it can be mitigated by reducing the cluster size without affecting the network performance.
By considering the accessibility and the rate issues in the VLC networks, in this paper, a new D-OMA scheme-based VLC network is proposed for indoor applications. It will meet one of the major requirements of the 6G networks, that is mMTC [33].

D. CONTRIBUTIONS
The main contributions of this paper are summarized as follows.
• Proposal of novel indoor VLC network model using D-OMA scheme. It supports massive access in the indoor environment with low complexity.
• Game theory-based user clustering is considered in this proposed D-OMA VLC network to enhance the sum rate.
• Transmission power optimization is performed under QoS, outage, and dimming control constraints. It ensures the QoS of all the users within the clusters.
• BER and outage probability analytical expressions of the proposed network are derived. The remaining part of the paper is arranged as follows: In section II, the system model of the proposed D-OMA VLC network and user clustering are discussed. The achievable rates, BER and the outage probability of the proposed network are discussed in section III. Two users' cluster-based D-OMA downlink transmission is discussed in section IV. Downlink transmission power optimization of the proposed network is explained in section V. Numerical results are presented in section VI, and the concluding remarks are given in section VII.

II. SYSTEM MODEL
Consider the downlink transmission of a VLC attocell where LED is mounted on the ceiling of the room and N users are distributed uniformly inside the room as shown in the circular area (coverage area of the LED) of Fig. 1. In this model, D-OMA is applied as a special MA scheme to serve all the users simultaneously with sub-band overlapping. Basically, in the D-OMA scheme, the entire bandwidth W is divided into M number of sub-bands and partially overlapped with allowable interference. Then, each sub-band is allocated a group of users and operates with the NOMA scheme as depicted in Fig. 2. Therefore, within the allocated bandwidth, the number of users using the D-OMA scheme is greater than the non-overlapping massive in-band NOMA scheme. In this model, all the users are grouped into several subsets of users. Therefore we refer to the subset of users as a NOMA cluster. Further, the number of sub-bands is equal to the number of NOMA clusters such that each sub-band is allocated to one NOMA cluster. User grouping is performed using the coalitional game theory approach, which is discussed in detail in the next subsection. Generally, user grouping is performed by pairing the near user and the far user. Thereby, the sum rate of the wireless network can be increased [33]. Therefore, for the user grouping, we initially adopted with basic user grouping algorithm as in [33]. During the user grouping, it is assumed that the perfect CSI is known at the BS (i.e., LED transmitter) and the users, and it is modeled as a static or quasi-static.   and Bδ r m , respectively. Therefore, the effective bandwidth of each sub-band becomes B m = B(1 − (δ l m + δ r m )). Note that, when δ l m = δ r m = 0, the overlapped amount of sub-bands is 0 and this corresponds to massive in-band NOMA scheme thus partial overlapping inter-cluster interference (PICI) is neglected. However, when δ l m = δ r m = 1, the adjacent bands are overlapped and PICI is maximum. The allocated power to the U m,k is denoted as P m,k , and the power allocation is based on the channel conditions, g m,k of the users. Without loss generality, let us assume g m,1 < g m,2 < . . . , < g m,K m , then the allocated powers becomes P m,1 > P m,2 > . . . , > P m,K m .

A. OPTICAL TRANSMISSION POWER
Let us consider the transmit electrical signal at the LED is x(t) ∈ (0, +1) for on-off keying (OOK) modulation. Then the transmitted optical signal at the BS (i.e., LED) can be given as where P LED is the LED power at the BS in W /A, and I DC is the added DC bias at the BS to obtain non-negative signals, i.e. x(t) + I DC ≥ 0. Due to the illumination and safety requirements, I DC is chosen between 0 ≤ I DC ≤ P a , where P a is the permissible average optical power and E[x s ] ≤ P a .

B. VLC CHANNEL MODEL
In this work, we assumed that the communication between the LED and a user is carried out only through the LOS path. The LOS direct current (DC) channel gain in VLC, g m,k from the BS to the user U m,k is given by [2] where A m,k , m,k and φ m,k , denote the photodetector (PD) area, the field of view (FoV) of the PD and the angle of incidence of the user U m,k , respectively. Further, the parameters d m,k is the distance from the LED to U m,k , υ is the path loss exponent, ϕ m,k is the angle of irradiation of the transmitter LED and T (φ m,k ) is the gain of the optical filter. Also, the parameter R 0 (ϕ m,k ) is the Lambertian radiant intensity of the LED transmitter and it can be expressed as where µ represents the order of Lambertian emission which is given as µ = − ln(2)/ ln[cos(ϕ 1/2 )], in this ϕ 1/2 denotes the transmitter LED semi-angle at half power (half irradiation) of the BS. In addition, G(φ m,k ) is the gain of the optical concentrator of the PD and it can be expressed as G(φ m,k ) = ν 2 / sin 2 ( m,k ) where ν is the refractive index. By substituting (3) into (2), LOS VLC channel gain can be expressed as where C is a constant given by

C. USERS CLUSTERING: COALITIONAL GAME APPROACH
In this section, user clustering within each sub-band of the VLC network is discussed. Users are clustered according to their channel conditions such that the sum rate of the proposed network is enhanced. It is noted that users are cooperative with each other within the cluster using the NOMA scheme. Each user has a non-transferable utility (NTU), and it is treated as a random NOMA. Further, the orthogonal multiple access (OMA) scheme is used if only one user is located inside the cluster. Consider there is N number of users distributed in the attocell and form the M coalitions. Therefore, the number of coalitions is equal to the number of sub-bands. Let C be the initial coalitions of this game, and the sum of the cardinality of all the coalitions is equal to N. Each coalition within the attocell can satisfy the condition as given by where ∅ is the null set, let the l th partition of the game is ξ l ∈ , 1 ≤ l ≤ O, in this O is total number of partitions and is the set of all possible partitions. The utility i.e., data rate of the n th user in the C i coalition and ξ l partition is denoted as a n (C i , ξ l ). Assume coalition C i has two users, u 1 , u 2 ∈ C i and their channel coefficients satisfy the condition |h 1 | 2 < The utility or payoff of the k th user with weak channel condition in coalition C i is expressed as where I ICI is the intra-cluster interference, I PICI is the partial overlapping inter-cluster interference, and σ 2 m,k is the effective noise variance and it is explained in section III-A. Similarly, the utility of the K th user with strong channel condition in coalition C i is given by Then, the sum payoff of the coalition C i and partition ξ l is determined as Coalition game-based user clustering in downlink NOMA is a cooperative game with non-transferable utility (NTU). Hence, it is necessary to convert the game from NTU into a transferable utility (TU) to facilitate user clustering. In this direction, the Shapley value calculation is applied to assign the payoff to each user with respect to coalitions. Therefore, the payoff i.e., Shapley value of the n th user in coalition C i and partition ξ l can be written as where c k is the subset of C i , i.e., c k ⊆ C i , 1 ≤ k ≤ Q, in this Q is the total number of subsets and the first term in (10) expresses the probability of the n th user contribution and the second term is the n th user marginal contribution. Using Shapley value, the sum payoff of the coalition C i and partition ξ l is computed as

D. PREFERENCE RELATION ALGORITHM (PRA)-TYPE I CLUSTERING
In this algorithm, each user checks their contribution while joining the new coalition; if the coalition value increases, then the user leaves the current coalition and joins the new coalition; otherwise, the user stays in the same coalition. Consider the two partitions ξ 1 and ξ 2 ∈ and assume coalition C i present in both partition. In this situation, the preference of the user is decided using the relation given below

Algorithm 1 Preference Relation Algorithm-Type I Initial state
Game start from the initial partition where the notation ⪯ n denote the preference of the n th user. In the above expression (12), if the condition is satisfied then n th user will move to partition ξ 2 . Alternatively, the user's preference is decided within the same partition with different coalitions. Let C 1 and C 2 are the two clusters, then the condition for user preference is given by In PRA, the user coalition is initiated from the weak user, and it is selected by arranging the users in ascending order. Assume n th user as a weak user want to join into m th target coalition. Before joining the new coalition, the n th user compares the sum rate with the current coalition and the m th coalition using strict PRA. If the sum rate is improved, then the n th user leaves the current coalition and joins into the m th target coalition otherwise, the n th user stays in the current coalition and then restart the joining process with the next target coalition and this process is continued until checking with all target coalitions. The second step in PRA is that if the n th user is moved successfully into the target coalition or else cannot be moved anywhere, then the n th user stops its process and then the next user will start the coalition process. This operation is repeated until checking with the last user. Now, the new partition structure is formed after one cycle of operation. Then, again the coalition process started with a new partition structure and repeated. If the users are not allowed to move into any target coalitions, then the process is stopped and the current partition structure will be considered as the desired partition. The procedures of PRA type-I are given in the algorithm. 1 Using the above theory, the n th user decides its coalition to improve the sum rate, thus the strict preference relation of the n th user is expressed as (14) E. PRA-TYPE II CLUSTERING Type II is similar to type I, except in type II the sum payoff is calculated without considering the partition. Thus, in type II the sum payoff improvement is achieved by simply swapping users between clusters, and user preference is decided by comparing the sum payoff of all users of those swapped clusters. Mathematical expression for the preference of the n th user is given by payoff of all users in cluster C i which is similar to (11) except including the partition parameter ξ l . PRA type II procedures is given in algorithm 2. This algorithm is similar to the PRA type-I except in this game, only residual users play a game while a new coalition is leaving the game. Thus, the complexity of this game is less when compared to the PRA. Let the initial partition ξ ini = {C 1 , C 2 , . . . , C M } and assume one of the users start the game and leave from the current coalition and form a new coalition. Note that this user is allowed to form a new coalition only after all other users in this game can accept this proposal otherwise user can return to the current coalition. After this game, a new coalition is formed and then it leaves the game. Then, the game can be started with residual users and this process is continued until all the users joined into the new coalition. Finally, a new partition structure is formed which reaches the Nash equilibrium stable state.
Let us consider the current partition structure as given by When the user starts the proposal in this sequencing game then a new partition is formed and it is expressed as The detailed procedure of the sequence game is given in algorithm 3.

Algorithm 3 Sequence Game Based Algorithm
Initial state Game start players {1, 2, . . . N } and n,m ∈ N Initial partition In the preference relation type -1 algorithm, the user migration from one coalition to the other is decided by the strict preference condition which always increases the sum rate of the proposed network. Further, the sum rate due to the movement of the user is calculated by considering all the user's in the structure instead of users only in the specific coalitions. Also, in this case, the user follows the compare-and-swap operation and the final partitions are formed with the finite set. This final partition is converged into Nash-equilibrium stable state.
Similarly in the preference relation type-II algorithm, the user's migration between the coalitions is performed by compare-and-swap operation and the sum rate is calculated by considering only user's in the specific coalitions. Therefore, in this case, when the user moves to the new coalition the payoff of the users in the particular group only contributes to the improvement in the sum rate.
In sequence game algorithm, players move to the new coalition and the partition structure changed. Then, the game continues with residual players and the final partition is not always Nash's stable state. If the final partition is not Nash stable, then the player from the previous coalition starts the proposal and tries to form the final partition which satisfies the Nash stable state.

2) COMPLEXITY ANALYSIS
The computational complexity of the preference relation algorithm is based on how many times the compare-andswap operations are performed by the users to reach the final partitions. Each user needs (N-1) time compare-andswap operation therefore total N(N-1) times compare-andswap operations are required for N users.
In sequence relation operation, the complexity is less due to limited compare-and-swap operation by the users because in this algorithm once the new coalition is formed it can leave the game, and swap operation is required only for the residual users. Each user needs (N-1) times compare-andswap operation however, the total number of compare-andswap operations is less than N(N-1).

III. PERFORMANCE ANALYSIS: D-OMA-VLC NETWORK
This section analyzes performance metrics of the proposed D-OMA VLC network, such as achievable rates, BER, and outage probability.

A. ACHIEVABLE RATES
Let us assume that the continuous data symbol is fed into the power amplifier which is denoted by s m,k with E{s m,k } = 0, variance E{|s m,k | 2 } = ε m,k , −A < ε m,k < A where A is the peak amplitude. After removing the DC bias, the received signal at U m,k can be expressed as in (16), shown at the bottom of the page, and η is the photo-detector responsivity in A/W , g m,k is the LoS VLC channel gain and ω m,k ∼ CN (0, σ 2 m,k ) is the variance of additive white Gaussian noise (AWGN) at U m,k which is a combination of thermal and shot noise.
The variance σ 2 m,k of the noise can be expressed as The shot noise in the optical communication can be modeled as where q is the electronic charge, I back is the background current and I N is the noise bandwidth factor. Similarly, the variance of the thermal noise in the VLC network can be expressed as [2] where K is the Boltzmann's constant, T k is the absolute temperature, G is the open-loop voltage gain, C is the fixed capacitance of the PD per unit area, is the field-effect transistor (FET) channel noise factor, g m is the FET trans conductance and I 3 = 0.0868 [2]. The signal-to-interference plus noise ratio (SINR) for decoding its own messages at U m,k can be given as where σ m,k is the effective variance of AWGN due to the expansion of bandwidth of the sub-band, i.e. σ m,k = σ m,k (1+ δ l m + δ r m ). Also, the interference due to the signal of users in the same cluster is called intra-cluster interference (ICI), and the interference due to the signal of users in neighbor clusters is called as I PICI are expressed as  VOLUME 11, 2023 and Finally, the achievable rates of the users belong to the attocell of BS is obtained through the lower bound of the capacity and it can be expressed as

B. BIT ERROR RATES
In this sub-section, the bit error rate (BER) expressions of the proposed D-OMA-based VLC networks are derived using uni-polar OOK modulation. As in Fig. 2, a network with M clusters is considered and each cluster consists of K m users. By applying maximum likelihood (ML) decoding, the m th cluster k th user U m,k can decode its message in the presence of the interferences. Mathematically, it can be written aŝ Assume that m th cluster k th user, U m,k decoded previous user's messages successfully i.e., s m,1 , . . . , s m,k−1 , thus SIC error is omitted. 1 The conditional error probability of the m th cluster k th user, U m,k when the transmitted OOK symbol s m,k = 0 is written as where P s = (ηP LED |g m,k |) 2 P m,k is the estimated desired signal power, N (µ, σ m,k ) denote the mean and variance of the Gaussian random variable y m,k . After integrating the probability density function (PDF) of y m,k , the error probability of the m th cluster k th user, U m,k can be expressed as [23] p e|s m, Similarly, the conditional error probability of the k th user, U m,k when the transmitted OOK symbol s m,k = 1 is given by After some mathematical manipulations, the conditional error probability becomes Using the identity 1 − Q(x) = Q(−x), the conditional error probability of m th cluster and k th user, U m,k can be further simplified as Proposition 1: In the proposed D-OMA scheme, the desired signal is affected by ICI and PICI thereby the effect of interference is more when compared to the massive in-band NOMA scheme where ICI only present. However, it is noteworthy that while reducing the cluster size in the D-OMA scheme the effect of ICI is significantly reduced and thus D-OMA scheme achieves similar performance to massive in-band NOMA. For example, consider six users with two clusters then massive in-band NOMA allows three users in each cluster and ICI comes from the two users in each cluster. At the same time, in the D-OMA scheme due to partially overlapping one more cluster is formed within the allocated bandwidth, therefore, two users are allocated to each cluster thus ICI comes from only one user in each cluster.

C. OUTAGE PROBABILITY
For the VLC downlink communication, if the user U m,k , k = 1, . . . , K m is failed to decode the signals of user U m,i , i = k, . . . , K m , then the user communication is failed and tend to the outage. Let us assume the target data rate at U m,k is ℜ m,k and then corresponding SINR can be written as m,k = 2 2ℜ m,k /B m − 1. The outage probability of the user U m,k can be expressed as By substituting from (20) into (30), we can further obtained the outage probability as where As the users are distributed randomly and uniformly within the circular coverage area of the atto cell, the PDF of r m,k is given by f r m,k (r m,k ) = 2r m,k /r 0 . The PDF of |g m,k | 2 is given as [34] where boundaries of the variable x is given as Let us take ϵ * m,k = max{ϵ m,1 , ϵ m,2 , . . . , ϵ m,k }. The outage probability can be given as By considering two users cluster, a closed-form expression for the outage probability of the downlink VLC network can be obtained which is given in (40) and (41).

IV. D-OMA FOR VLC DOWNLINK COMMUNICATION
In downlink VLC networks, when the D-OMA scheme is employed, it can achieve better network performance when compared to the massive in-band NOMA. However, due to the overlapping of sub-bands, it can introduce the interference I PICI which degrades the performance of the VLC network. Therefore, in order to reduce both I PICI and I ICI interference, we can design the D-OMA scheme with a smaller cluster size, preferably with two users clusters, so that the D-OMA scheme reduces the I PICI interference. In this direction, all the N users are formed into a number of clusters, and each cluster consists of two users according to the game theory. Hence the SINR of FU and NU of the m th NOMA cluster, respectively, can be given as and γ m,n = (ηP LED |g m,n |) 2 P m,n With two users clustering, the BER of the k th user when the transmitted OOK symbol s m,k = 0 can be expressed as where m,f = (ηP LED |g m,f |) 2 P m,f and m,n = (ηP LED |g m,f |) 2 P m,n are the desired signal and ICI. Similarly, the BER of the k th user when the transmitted OOK symbol s m,k = 1 is written as Similarly, the outage probability of the FU and NU in the m th NOMA cluster, respectively, can be given as and where and

V. TRANSMISSION POWER MINIMIZATION
In this Section, we minimize the total transmission power of a NOMA cluster, under the QoS requirements, outage constraints, and dimming control. In dimming control, the average optical power is controlled as per the illumination requirements of the environment. The average optical power P avg o = I DC = τ P T , where τ is the dimming level and P T is the maximum optical power. Also, to ensure eye safety, the maximum permissible current of the LED, I H should be limited as P m,k A + I DC ≤ I H . The optimization problem can be expressed as The outage probability constraint is also taken into the optimization problem and ϱ o m,k is the outage probability limit for successful communication between U m,k and the BS. In the proposed D-OMA for VLC communication, users are grouped to have only two users in a NOMA cluster i.e. two user clustering. Hence the allocated power for the NU and FU, respectively, can be expressed as α m P N and (1 − α m )P N , where α m is the power allocation coefficient of the m th NOMA cluster and P N is the maximum power allocated for a sub-band. Therefore, the optimization problem can be reformulated as Since the Hessian matrix of the objective function is positive and semi-definite, the optimization problem is convex under the considered constraints. Therefore, the Lagrange function of the above problem can be expressed as is the total transmission power of the m th NOMA cluster and λ i , i ∈ {1, . . . , 6} are the Lagrange multiplier. By taking the derivations of (44) and applying Karush-Kuhn Tucker (KKT) conditions, optimal solutions for α m and I DC can be obtained. Consequently, the derivatives of (44) with respect to α m , I DC , and λ i , respectively, can be given as By applying KKT conditions, the optimal solutions of α m and I DC , respectively, can be obtained.
and where,

VI. RESULTS AND DISCUSSION
In this section, the sum rate, BER, and outage probability of the proposed D-OMA-VLC network are analyzed. In all the simulations, the VLC downlink channel is used as a DC channel and OOK modulation is considered. The proposed D-OMA VLC network is compared with massive in-band NOMA. The simulation parameters are listed in the Table. 1. The sum-rate performance of the proposed D-OMA-VLC network is shown in Fig. 3. In this simulation, four users are considered for the clustering. In PRA, users are not classified as near and far users and grouping is formed using Shapley value calculation. In random NOMA, grouping is performed using near-user and far-user channel conditions. Further, two sets of distances are considered to analyze the sum-rate variation due to distances. It is noted that the sum rate of the proposed D-OMA-VLC network is significantly improved compared to the random NOMA because each user's payoff depends on the users' coalition. However, the sum rate of the random NOMA is better than the existing OMA scheme. Also, it is observed that the sum rate of the network using the clustering algorithm is improved with respect to the distance. Particularly, the sum-rate improvement is achieved when the distance is decreased.
Sum-rate performance of the proposed D-OMA-VLC network using type-I PRA is compared with type-II PRA in Fig. 4. Shapley value calculation is employed in both type-I and type-II PRA methods. It is noted that type-I PRA achieves a better sum rate when compared to the type-II PRA because, in the type-I coalition, user preference is decided along with their type of partition. Therefore, coalition value is improved  when compared to the users swapping among the clusters without considering the type of partitions. Fig. 5 shows the sum-rate performance of the proposed D-OMA VLC network with different users. In this simulation, clustering is formed using four users and six users. All the simulation setup are considered as in the previous figure. It is noted that the improvement in the users clustering is achieved when the number of users is increased within the cluster. Also, it is noted that user clustering does not improve the performance of the network while operating with the OMA scheme.
BER performance of the proposed D-OMA VLC network is shown in Fig. 6. The following simulation parameters are considered: the I ICI power is 0 dB, I PICI power is −10 dB [32], the distance of the near user taken as 2 m and far user is 4 m. Simulation results are plotted to validate the analytical results. It is observed that when increasing the optical filter gain, the BER performance of the downlink D-OMA VLC network is significantly improved. Therefore, the optical filter gain is identified as one of the main factors in improving the performance of the VLC networks.    7 shows the BER performance of the downlink D-OMA VLC network. Distances of near and far users are taken as in the attocell dimensions. In this simulation, the I ICI power is considered as 0 dB and I PICI power is −10 dB. The distances of the far users are considered as 2 m, 4 m, and 6 m. It is observed that the proposed D-OMA user with the distance of 2 m achieves around 5 dB SNR gain when compared with massive in-band NOMA-VLC networks. Also, it is noted that even with increasing the distance, D-OMA far users still maintain a good SNR gain due to the smaller cluster size.
The BER performance of the proposed D-OMA-VLC network is shown in Fig. 8. In this simulation, two clusters are considered and each cluster consists of one near the user and one far user [33]. The distances of the near user and far user of the first cluster are 1 m and 2 m respectively. Similarly, the distance of the users in the second cluster is 3 m and 6 m. The sub-band overlapping interference I PICI = −10 dB. It is noteworthy that the BER performance of cluster 1 is better than cluster 2. This is because the distances of the users in cluster 1 are small when compared to cluster 2. Also, it is  noted that the cluster near the user has better BER results than the far user. Further, it is interesting to note that even though the proposed D-OMA-VLC network operates with small cluster sizes, it maintains a similar performance to the massive in-band NOMA. Fig. 9 shows the BER performance of the proposed D-OMA-VLC for different FOV. The values of sub-band overlapping parameter δ are 0.01 and 0.001. Two user cluster is considered with the distance of 2 m and 4 m. FOV of LED light varied from 40 • to 90 • . Assumed LOS path between the users and LED. It is noted that when the degree of angle of FOV increases, the BER of the user within the cluster gradually increases. Thus, it gives the idea about the choice of FOV value to get better performance of the VLC wireless network.
The BER performance of the proposed D-OMA-VLC network is shown in Fig. 10 for various values of the photodetector areas, A. In this simulation, FOV values are considered as 40 • , 45 • and 50 • and the sub-band overlapping interference I PICI = −10 dB. It is observed that the BER of the proposed network is decreased when increasing the photodetector area. Also, the impact of the photodetector area on optical light   The spectral efficiency of the proposed D-OMA-VLC network is shown in Fig. 11. For D-OMA, the left side and  right side sub-band overlapping coefficient is taken as δ. Subband overlapping coefficient δ varied from 0 to 0.2 in this simulation. At δ = 0, the proposed network match with a massive in-band NOMA-VLC network. The figure clearly shows the effect of the sub-band overlapping in the proposed D-OMA-VLC network at a high SNR regime. Also, it is noteworthy that the spectral efficiency achieves its highest values at δ = 1. However, increasing the δ results in the highest partial ICI. At δ = 0.1, D-OMA provides better spectral efficiency for the considered allocated power levels. Moreover, it is noted that at the value of δ = 0.1, the network achieves the reasonable spectral efficiency of 20 b/s/Hz. Thus, the proposed network guarantees the network capacity with allowed sub-band overlapping. Fig. 12 shows the comparison of the spectral efficiency of the proposed D-OMA-VLC with a massive in-band NOMA-VLC network. For D-OMA, sub-band overlapping percentage δ is set to 0.1. Clusters with four users, six users, eight users, and ten users are considered for massive in-band NOMA. In the proposed D-OMA, four users cluster is split into two users clusters. Similarly, six users, eight users, and ten users clusters are split into a number of two user clusters. Hence, the spectral efficiency of the proposed D-OMA-VLC network is less when compared with the massive in-band NOMA-VLC network, even though it achieves better reliability and massive connectivity.  The outage probability of the NU and FU of the proposed D-OMA-VLC network for different power allocation schemes is shown in Fig. 13. The optimized values of α and VOLUME 11, 2023 I DC are used to obtain the simulation results. The performance of optimized power allocation is compared with the existing gain ratio power allocation (GRPA) and fixed power allocation. The sub-band overlapping percentage δ is set to 0.1, and the QoS requirement for both NU and FU is set to 0.5 bps/Hz. For optimized power allocation, the outage probability of both NU and FU shows better performance than the GRPA and fixed power allocation. NU performs better outage in all power allocation schemes, especially at a low SNR regime. On the other hand, the performance of the FU is limited due to ICI and PICI at allocated power values. Although the allocated power increases, the outage performance of the FU remains at a fixed value at high allocated power values.

VII. CONCLUSION
A new multiple access schemes D-OMA enabled VLC network model is proposed to enhance the accessibility and rate of indoor wireless networks. The performance of the proposed D-OMA-VLC network is compared with the massive in-band NOMA-VLC network in terms of spectral efficiency, BER, and outage probability. Numerical results conclude that the sum rate of the proposed D-OMA-based VLC network outperforms the existing in-band NOMA scheme. Further, power optimization is performed at the downlink transmission of the proposed network, which ensures the QoS of the users within the clusters of the network. Therefore, the proposed VLC model will support many indoor applications with a high rate and large access.