This article has been accepted for publication in a future issue of this journal, but has not been fully edited. Content may change prior to final publication. Citation information: DOI 10.1109/LCOMM.2016.2642921, IEEE Communications Letters 1 User Grouping and Power Allocation for NOMA Visible Light Communication Multi-cell Networks Xiaoke Zhang, Qian Gao, Chen Gong and Zhengyuan Xu Abstract—To design an efficient multiple access scheme for visible light communication (VLC) multi-cell networks, this letter leverages the non-orthogonal multiple access (NOMA), which has received significant attention in the 5th generation wireless communication. A user grouping based on user locations is proposed to reduce interference for VLC multi-cell networks. With the residual interference from the successive interference cancellation in NOMA taken into account, we optimize the power allocation within each cell to improve the achievable user rate under user quality of service constraint. The performance of the proposed approaches is evaluated by the numerical results. Index Terms—visible light orthogonal multiple access (NOMA), multi-cell networks. communication (VLC), non- I. INTRODUCTION With a rapid growth in portable information terminals, the demand for high rate wireless data communication in local area networks keeps increasing. Although radio frequency (RF) has been widely commercialized for communication purposes because of the wide area coverage and little interfer- ence in frequency band [1], the limited spectrum cannot well accommodate the increasing communication rate requirement. Visible light communication (VLC) has received significant interest due to its advantages in unlicensed spectrum, natu- ral confidentiality, convenient deployment, low energy con- sumption, etc. VLC networks is also considered to be an environmental-friendly solution for smart home networking. Consider the realistic network application where multiple VLC access points (VAPs) are placed in the room ceiling and multiple mobile users are randomly distributed within the circular coverage area underneath. Distinctive from RF communications, in VLC is significantly smaller for the sharp signal attenuation and restricted user field of view (FOV), which brings a big challenge for dealing with the interference in multi-cell networks. A few terminal ac- cess approaches have been proposed. A graph theory based scheduling method is proposed in [2] where the users are the cell This work was supported by National Key Basic Research Program of China (Grant No. 2013CB329201), Key Program of National Natural Science Foun- dation of China (Grant No. 61631018), National Natural Science Foundation of China (Grant No. 61501420), Key Research Program of Frontier Sciences of CAS (Grant No. QYZDY-SSW-JSC003), Key Project in Science and Technology of Guangdong Province (Grant No. 2014B010119001), Shenzhen Peacock Plan (No. 1108170036003286), and the Fundamental Research Funds for the Central Universities. The authors are with Key Laboratory of Wireless-Optical Communications, Chinese Academy of Sciences, University of Science and Technology of China, Hefei, Anhui 230027, China. Z. Xu is also with Shenzhen Grad- uate School, Tsinghua University, Shenzhen 518055, China. Email: zxi- aoke@mail.ustc.edu.cn, {qgao, cgong821, xuzy}@ustc.edu.cn. selected to access the network according to proportional fair- ness priority factor. Furthermore, [3] proposes a user-centric cluster formation technique employing vectored transmission to allow each multiple-access-point cell serving multiple users simultaneously. On the other hand, non-orthogonal multiple access (NOMA) has been recently suggested as a promising solution in the 5th generation (5G) wireless networks [4]. Multiple users are multiplexed in the power domain on the transmitter side by superposition coding and multi-user signal separation is accomplished on the receiver side by successive interference cancellation (SIC) at the receiver side. NOMA is demonstrated to outperform the orthogonal multiple access in terms of the ergodic sum rate and the user outage probability [5]. Due to the limited coverage which well controls limited user number in each cell, the computational complexity of the SIC can be well controlled. Other advantages of NOMA for the VLC network include high signal-to-noise ratio (SNR), easily adjusted optical gains and the slow-fading channel such that the channel state information is available at the transceiver side. With fixed power allocation, the performance of NOMA for a single VAP is investigated in [6]. The channel dependent gain ratio power allocation is proposed in [7] to ensure efficiency and fairness compared to static power allocation approach, where the scenario of two VAPs are considered. In this letter, we propose a user grouping based on user locations for NOMA VLC multi-cell networks, as high precise positioning is feasible in VLC [8]. We also propose two types of quality of service (QoS) guaranteed power allocation within each cell to iteratively optimize the sum user rate or the max- min user rate. The residual interference during the SIC in NOMA is taken into account in the formulated optimization problem. II. NOMA VLC MULTI-CELL NETWORKS A. User grouping in NOMA VLC Multi-cell Networks A typical NOMA VLC network is shown in Figure 1. The red dots denote the VAPs in the network. The coverage area consists of four types. Area type Li; i 2 f1; 2; 3; 4g represents that the corresponding hatched area can receive line of sight (LOS) signal of i VAPs. The neighboring cells are distinguished by solid line and dashed line. The cell size is determined by the user FOV, vertical distance, attenuation coefficient and so on. The interference is influenced by the following factors: 1) User FOV: When the user FOV is sufficiently small, no more than one VAP exists in the FOV which will cer- tainly eliminate the inter-cell interference. Meanwhile, 1089-7798 (c) 2016 IEEE. Personal use is permitted, but republication/redistribution requires IEEE permission. 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This article has been accepted for publication in a future issue of this journal, but has not been fully edited. Content may change prior to final publication. Citation information: DOI 10.1109/LCOMM.2016.2642921, IEEE Communications Letters 2 g„ k” with refractive index n is given by n2sin2„c” if 0 k c and 0 otherwise, where c is the concentrator FOV semiangle [1]. Without loss of generality, assume that the K users in a particular cell are sorted based on the link gain as h1 h2 hK. Let sk denote the message that the VAP delivers to the k th user. According to the NOMA protocol, fsk; k = 1; 2; : : : ; Kg is superposed and transmitted by the VAP as Pelecsi + IDC; (2) K∑ √ x = ai i=1 Fig. 1. NOMA VLC network model this would cause communication failure for the absence of LOS optical signal in coverage holes. 2) User Distribution: While the inter-cell interference can be avoided without co-frequency VAPs working, this condition depends on the time-varying user distribution. 3) Frequency Reuse (FR) Factor: Although FR = 1 can achieve the highest spectrum efficiency, users located in areas L2; L3; L4 in Figure 1 suffer from severe in- terference where sophisticated interference cancellation or user scheduling technique is in need. This situation would be significantly improved when FR = 2 since only users in area type L4 can receive co-frequency interference. To balance the interference management requirements and the frequency efficiency, we adopt FR = 2 in this letter. Based on the user positions, the user grouping for NOMA VLC networks is designed as follows. The users in L1 and L3 are assigned to the VAP without interference. As the probability of users existing in L4 is reasonably small, the users in L4 are allocated with special bandwidth Bi to avoid the interference. Since a user in L2 can select either VAP1 or VAP2 for access without interference, they are scheduled for load balancing among the VAPs and 1d„V APi” may be regarded as the priority, where d„V APi” denotes the number of users connected to VAPi. B. System Model The power of the reflected signal is usually much weaker than that of the LOS signal and thus can be neglected. The VAP is placed at height Lk above the users. The k th user, denoted as Uk, is located on a polar coordinate plane at the distance dk from the light-emitting diode (LED), and the LED irradiance angle and the photodiode (PD) incidence angle are given by ϕk and k, respectively. According to the Lambertian emission model, the channel gain of the optical link between the VAP and the k th user, denoted as hk, is given by cosm„ϕk”T„ k”g„ k” cos„ k”; (1) where A denotes the detection area of the PD, T„ k” represents the gain of the optical filter, m is the order of Lamber- tian emission relying on the transmitter semiangle 12 by m = ln 2ln„cos 12”. The gain of nonimaging concentrator A„m + 1” 2d2 k hk = where IDC is the DC bias added to ensure the positive instan- taneous intensity and ai is the power allocation coefficient for ith user. Therefore, the observation at the k th user is given by K∑ √ yk = hk ai i=1 Pelecsi + nk; (3) where nk denotes the additive real-valued Gaussian noise with zero mean and variance 2 k including the shot noise and the thermal noise [9]. In NOMA, users with lower channel gain will be allocated more power, i.e. a1 a2 aK. At the receiver side, the user would perform SIC [5]. Note that the SIC requires highly accurate channel and signal estimation otherwise the non-negligible residual interference remains. Although optical wireless channel is practically stationary, the channel estima- tion error can still exist due to the feedback delay and user mobility which leads to the residual interference within the process of SIC. Let " represent the fraction of user’s power not cancelled [10] and in the process of SIC, the k th user is supposed to detect the message for the j th (j k) user with the observed signal yk!j, given by „hkai” + " „hkai” + nk : K∑ j1∑ yk!j = (4) i=j i=1 To guarantee the success of SIC, the k th user is supposed to decode the message for the j th (j k) user. The achievable rate of the j th user’s message at user k, denoted as ˜Rk!j, is given by ) ˜Rk!j = K 1 + ∑ i= j +1„hk ai”2+" j k; j , K; ∑ j1 „hK a j”2 „hK ai”2+1 ∑ j1 „hk a j”2 ) 1 + i=1 " i=1 B 2 log2 B 2 log2 „hk ai”2+1 Tj; Tj; j = k = K; (5) where Tj denotes the targeted data rate satisfying the j th user’s QoS requirements, = 2 TSN R, TSN R = PelecN0B denotes the transmitted signal-to-noise ratio (TSNR) [5][6], B denotes the transmission bandwidth, denotes the photoelec- tric conversion efficiency. The scaling factor 12 indicates the spectral efficiency is lost due to the Hermitian symmetry. Note that in Eq. (5), if k1 k2 i, we have ˜Rk1!i ˜Rk2!i ˜Ri where ˜Ri ≜ ˜Ri!i since a1 a2 aK. Therefore, Eq. (5) can be further simplified as k = 1; 2; ; K: ˜Rk Tk; (6) ( ( 8>>>>>><>>>>>>: 1089-7798 (c) 2016 IEEE. Personal use is permitted, but republication/redistribution requires IEEE permission. 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This article has been accepted for publication in a future issue of this journal, but has not been fully edited. Content may change prior to final publication. Citation information: DOI 10.1109/LCOMM.2016.2642921, IEEE Communications Letters 3 k = 1; 2; : : : ; K; (7) = 1; k = 1; 2; : : : ; K: : ˜Rk is a function of fak; ak+1; : : : ; aKg, which Notice that leads to the objective parameters coupling in the original optimization problem and brings difficulty to analysis. Perform i=k a2 variable substitution as pk ≜ ; k = 1; 2; : : : ; K and Eq. i (5) can be equivalently expressed as K maximize s.t. k K k=1 ∑ ˜Rk; ˜Rk Tk; k=1 a2 ak 0; K∑ 8>>><>>>: ∑ ( „1 "”pk + mk („1 "”pK + mK ) ( ∑ h2 k log2 pk+1 "pk + mk k = 1; 2; : : : ; K 1; log2 "pK + mK k = K; ) ) 8>>>>>>>><>>>>>>>>: B 2 B 2 ˜Rk = It can be seen from Eq. (5) and (6) that the power alloca- tion parameters fa1; a2; : : : ; aKg jointly determine each user’s achievable rate and thus may nontrivially affect the corre- sponding modulation and coding scheme for data transmission of each user. As the power allocation plays a key rule in NOMA, we investigate the QoS-guaranteed power allocation strategies for NOMA in Section III. III. QOS-GUARANTEED NOMA POWER ALLOCATION A. QoS-guaranteed Max-Sum Rate Criterion NOMA can support a flexible management of user rate and provide an efficient way to ensure fairness by adjusting power allocation coefficients. We aim to maximize the sum of user achievable rate by optimizing the power allocation while satisfying the basic QoS requirements. With Eq. (6), the corresponding optimization problem is formulated as follows, ≜ Gk„pk; pk+1”; ≜ GK„pK”; ; (8) ; k 2 f1; 2; : : : ; Kg. Then the achiev- where mk = " + 1 able sum rate of users is denoted as ˜Rtot al and transformed k=1 Gk„pk; pk+1” + GK„pK”. K1 into separable form as ˜Rtot al = The constraints in problem Eq. (7) form the feasible region D. Clearly, these constraints are linear and are hence convex. However, the objective function is not convex which is difficult to solve directly using standard optimization solvers. We de- velop a gradient projection (GP) algorithm [11] which includes a gradient descending process and a projection process. Let p denote the variable p = „p2; ; pK”. The gradient descending process iteratively takes steps in the direction of the gradient of the objective function at a given position yielding where the superscript „”„i” denotes the iteration time,ep denotes variableep the variable with step added and i denotes the step size which can be chosen by backtracking line search [11]. When the „i+1” steps out of D, it is mapped into D by finding the nearest feasible point in D. The corresponding projection process is described as a convex optimization problem whose „i” + i @ ˜Rtot al„p” „i+1” = p p=p„i”; ep (9) @p TABLE I SIMULATION PARAMETERS Parameter name, notation VAP height, H User height, z Semi-angle at half power, ϕ12 Information signal power, Pel e c Signal bandwidth, B Noise power spectral density, N0 PD detection area, A PD responsivity, PD FOV, f ov Optical filter gain, T„ ” Refractive index, n Value 3 m 0:85 m 60◦ 1:25 mW 20 MHz 1021 A2/Hz 0:28 A/W 1 cm2 32◦ 1 1:5 solution can be efficiently obtained utilizing the standard solver such as CVX [12] embedded with MATLAB R⃝. B. QoS-guaranteed Max-min Rate Criterion Distinct from the fairness criterion investigated in [13] where the minimum of user achievable rate is maximized, we consider additional QoS requirement of each user and take the residual interference into account. We propose the QoS-guaranteed max-min rate criterion with the associated optimization problem formulated as follows max fa1;a2;:::;aK g min ˜Ri; k = 1; 2; : : : ; K; 8>>>>><>>>>>: K∑ i2f1;2;:::;Kg ˜Rk Tk; a2 ak 0; k=1 k s.t. = 1; k = 1; 2; : : : ; K; (10) (11) With the additional QoS constraints, this problem can still be solved following the searching algorithm in [13] which is time-consuming to obtain a solution with desired accuracy. Instead, we adopt GP algorithm to dynamically adjust the power allocation parameters in a short interval. To overcome the non-differentiability of objective function in Eq. (10), we adopt the following approximation [14], ) i2f1;2;:::;Kg Ri ≃ lim min !+1 1 ln exp„Ri” : (12) ( K∑ i=1 IV. NUMERICAL RESULTS In this section, we evaluate the performance of our proposed NOMA VLC multi-cell network parameterized as in Table I. Assume that the K users simulated are uniformly distributed in the 1:8m1:8m square area illustrated in the upper right corner of Fig. 1. Fig. 2 shows a higher achievable sum user rate can be obtained with NOMA compared to OMA for either FR = 2 or FR = 4. We select 30 random user distributions for each case and take the average value. Adopting FR = 2 will drastically improve the sum user rate for doubled available bandwidth in each cell. Although the residual interference during the SIC can degrade the performance of NOMA, NOMA can still outperform OMA when " = 0:1. A higher user rate can be achieved with smaller " which emphasizes the importance 1089-7798 (c) 2016 IEEE. Personal use is permitted, but republication/redistribution requires IEEE permission. See http://www.ieee.org/publications_standards/publications/rights/index.html for more information. 

This article has been accepted for publication in a future issue of this journal, but has not been fully edited. Content may change prior to final publication. Citation information: DOI 10.1109/LCOMM.2016.2642921, IEEE Communications Letters 4 Fig. 2. The maximized sum user rate comparison for the NOMA VLC network under different user number K when Tk = 3. Fig. 4. The change of the maximized minimum user rate in the process of algorithm iteration when Tk = 3 and K = 5. QoS-guaranteed power allocation within each cell on either max-sum rate criterion or max-min rate criterion. By virtue of the GP algorithm, the power allocation coefficients can be dynamically adjusted. REFERENCES Fig. 3. The effect of parameters on the sum user rate for the NOMA VLC network when Tk = 1 and K = 5. of the channel estimation accuracy. When the user number increases, the sum user rate first grows because the probability of more VAPs in service is improved. Fig. 3 investigates the effect of parameters on the sum user rate of the NOMA VLC multi-cell network. Due to larger FOV, the more overlapping area of cells will enhance the interference which results in the decrease of sum user rate. The sum user rate is drastically increased when N0 is improved by one order of magnitude. We also verify the efficiency of our proposed QoS- guaranteed max-min user rate criterion. Assume 3 users are distributed in a particular cell with channel gains h = »3:683; 4:877; 4:966… 105. The maximized minimum user rate is achieved at R1 = »10:85; 11:26; 11:02… for " = 0:1 and T1 = »10; 10; 10…. When one of the users requests higher transmission rate as T2 = »20; 5; 5…, the power allocation solution achieves a user rate of R2 = »20:00; 6:52; 6:76…. Obviously, the minimum user rate changes from 10:85 to 6:52 due to the QoS constraints. Fig. 4 illustrates the max-min user rate is optimized in the process of iteration. Our adopted Eq. (12) has a good approximation performance. V. CONCLUSION In this letter, the user grouping and the power allocation for NOMA VLC networks are proposed. With residual in- terference during SIC taken into account, we investigate the [1] D. Karunatilaka, F. Zafar, V. Kalavally, and R. Parthiban, “LED based indoor visible light communications: State of the art,” IEEE Commu- nications Surveys Tutorials, vol. 17, no. 3, pp. 1649–1678, thirdquarter 2015. [2] Y. Tao, X. Liang, J. Wang, and C. Zhao, “Scheduling for indoor visible light communication based on graph theory,” Optics express, vol. 23, no. 3, pp. 2737–2752, Feb 2015. [3] X. Li, F. Jin, R. Zhang, J. Wang, Z. Xu, and L. Hanzo, “Users first: User-centric cluster formation for interference-mitigation in visible-light networks,” IEEE Transactions on Wireless Communications, vol. 15, no. 1, pp. 39–53, Jan 2016. [4] Z. Ding, Y. Liu, J. Choi, Q. Sun, M. Elkashlan, C. I, and H. V. 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Boyd, and Y. Ye, “CVX: Matlab software for disciplined University Press, 2004. convex programming,” 2008. 1089-7798 (c) 2016 IEEE. Personal use is permitted, but republication/redistribution requires IEEE permission. See http://www.ieee.org/publications_standards/publications/rights/index.html for more information. 6810122122232425262728User NumberSum User Rate [Mbps](a) FR=4 OMANOMA, ε=0.05NOMA, ε=0.16810124244464850525456User NumberSum User Rate [Mbps](b) FR=2 OMANOMA, ε=0.05NOMA, ε=0.12468101214161820020406080100User Random Distribution CountSum User Rate [Mbps] FOV=32°, N0=10−21A2/HzFOV=40°, N0=10−21A2/HzFOV=32°, N0=10−20A2/Hz05101520253044.555.566.5Iteration TimeUser Rate [Mbp/s] min−function approximation ε=0min−function real ε=0min−function approximation ε=0.1min−function real ε=0.1