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Enhancing power allocation efficiency of NOMA aided-MIMO downlink VLC networks
Optics Communications 454 (2020) 124497
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Enhancing power allocation efficiency of NOMA aided-MIMO downlink VLC networks Heran Wang a , Fasong Wang a ,∗, Rui Li b a b
The School of Information Engineering, Zhengzhou University, Zhengzhou, 450 0 01, Henan, China The School of Science, Henan University of Technology, Zhengzhou, 450 0 01, Henan, China
ARTICLE
INFO
Keywords: Non-orthogonal Multiple Access (NOMA) Visible Light Communication (VLC) Multiple-Input Multiple-Output (MIMO) Power allocation
ABSTRACT In order to enhance the achievable sum rate of indoor non-orthogonal multiple access (NOMA) aided multipleinput multiple-output (MIMO) visible light communication (VLC) downlink networks, in this paper, an efficient low computational complexity power allocation strategy termed as normalized logarithmic gain ratio power allocation (NLGRPA) is proposed, in which the optical channel information of all transmitter light-emitting diodes (LEDs) are exploited and properly ordered to ensure efficient power allocation Numerical results depict that our proposed NLGRPA method exhibits significant improvement in terms of achievable sum rate of NOMA aided MIMO-VLC networks when compared with other conventional power allocation approaches. Specifically, the proposed NLGRPA algorithm attains an achievable sum rate improvement of more than 55% and 33% compared with the gain ratio power allocation (GRPA) method and normalized gain difference power allocation (NGDPA) method in the 4 × 2 MIMO-VLC networks with nine randomly distributed users.
1. Introduction With the explosive growth of Internet-of-Things (IoTs) and portable information terminals, the unprecedented demand for local wireless networks with low latency, massive connectivity, diverse data rates, and low-cost front-ends have been under intensive investigations in the past few years. Although existing radio frequency (RF) based wireless communication has been widely commercially utilized, some bottlenecks have been arrived to meet these demands for various reasons, such as a shortage of RF spectra and severe power consumption. New wireless commutations alternatives are urgently demanded. In these contexts, light-emitting diode (LED) aided visible light communication (VLC), with its unique features such as license-free spectrum, low-cost front-ends, immunity to electromagnetic interference, natural confidentiality, low energy consumption, and the potential of spatial reuse of frequency bands in adjacent optical attocells, has been emerged as an alternative and complementary candidate for high-speed and shortrange to RF-based wireless communication. As a promising small cell technique, indoor VLC can be connected to the existing networks and constitutes an integral part of the upcoming ubiquitous fifth generation (5G) and beyond communication systems [1,2]. Nonetheless, the main challenge to exploiting VLC technology is the limited modulation bandwidth of off-the-shelf LEDs, which acts as a barrier to realize the envisioned VLC system with full potentials. Therefore, some techniques have been proposed in the efficient development of boosting the capacity of VLC system, such as optical multiple-input
multiple-output (MIMO), advanced optical modulation, and multiple access schemes and so on [2,3]. By virtue of its inherent broadcast nature, one transmitter LED is generally expected to support massive connectivity, and admit multiple users to access the same wireless resource. To this end, multiple access is one key technology in the multiuser VLC networks, and various optical multiple access schemes have been proposed in addressing this challenge in the open literature. Conventional orthogonal multiple access (OMA) schemes have already attracted attention in VLC networks, such as orthogonal frequency division multiple access (OFDMA) [4], code division multiple access (CDMA) [3], and space division multiple access (SDMA) [5]. In these OMA schemes, multiple users are separately allocated to orthogonal wireless resource to mitigate mutual interference. Nevertheless, these strategies cannot be applied to VLC systems directly for the intensity modulation and direct detection (IM/DD), and furthermore, these OMA aided techniques cannot yet sufficient to support massive connectivity because of the limited wireless resources. Due to its superior spectral efficiency compared to OMA schemes, non-orthogonal multiple access (NOMA) has recently been proposed to the forthcoming 5G wireless communication systems, which allows multiple users to utilize the entire available time and frequency band resources simultaneously in the power domain at the transmitter by superposition coding and multiuser detection at the receiver by successive interference cancellation (SIC) [3,6]. It has been demonstrated
∗ Corresponding author. E-mail addresses: [email protected] (H. Wang), [email protected] (F. Wang), [email protected] (R. Li).
https://doi.org/10.1016/j.optcom.2019.124497 Received 19 June 2019; Received in revised form 1 August 2019; Accepted 28 August 2019 Available online 3 September 2019 0030-4018/© 2019 Elsevier B.V. All rights reserved.
H. Wang, F. Wang and R. Li
Optics Communications 454 (2020) 124497
However, perfect SIC cannot always be guaranteed in practical NOMAbased VLC systems and imperfect SIC will cause error propagation and decrease system performance [19,20]. Several enhanced NOMA schemes have already been reported in NOMA aided VLC literature. In [19], a flexible-rate SIC-free NOMA technique for downlink VLC systems is proposed based on constellation partitioning coding and uneven constellation demapping techniques. Also, symmetric superposition coding and symmetric SIC decoding are proposed for downlink NOMA-based VLC network to overcome error propagation problem to increase the BER performance in [20]. Yet, in this paper, we focus on the efficiency of the power allocation problem in NOMA aided MIMOVLC networks, the perfect SIC will be considered, just like most existed power allocation approach in NOMA aided VLC systems [9,15,17,18]. In this paper, an efficient and low complexity power allocation strategy is proposed in NOMA aided indoor downlink MIMO-VLC networks, termed as normalized logarithmic gain ratio power allocation (NLGRPA), which can be utilized efficiently when the randomly distributed user’s number is more than 5. The achievable sum rate is evaluated by the proposed NLGRPA power allocation approach via numerical simulations. Numerical results depict that our proposed NLGRPA approach exhibits significant improvement in terms of achievable sum rate of the considered NOMA aided MIMO-VLC networks when compared with the other two conventional power allocation approaches: GRPA and NGDPA.
that NOMA can outperform conventional OMA in terms of sum rate and outage probability [6]. It should be noted that the power domain aided NOMA scheme has the lowest computational complexity among the code domain, power domain, and the combined code-power domain [7]. Meanwhile, the computational complexity of SIC-based NOMA message decoding is acceptable when utilizing current and upcoming processors for ubiquitous wireless sensor networks [8]. Hence, efficient low complexity power allocation approach is highly desirable in NOMA based 5G networks. For NOMA aided wireless communication, the system can perform significant performance gains in high signal-to-noise ratio (SNR) scenarios, which is a typical case in indoor VLC applications due to the dominant line-of-sight (LOS) channel gain and the short distance between the transmitter and the receiver. Furthermore, in NOMA, SIC is exclusively dependent on the channel state information at the transceivers to determine the decoding order and power allocation strategy of all users. This is in line with VLC systems, where the optical channel gains remain constants until the locations of the users change or parameters of transceivers vary [1,3]. Consequently, implementing NOMA is a promising choice in indoor downlink VLC networks with multiple users. The performance of NOMA aided VLC systems has been widely studied in [9]. As an efficient approach to increase system capacity, MIMO has been extensively applied in VLC by exploiting equipped LEDs. Nevertheless, the utilization of NOMA to MIMO-VLC networks has not been widely investigated. Moreover, existing power allocation approaches for a single LED NOMA aided VLC system cannot be directly implemented in NOMA aided MIMO-VLC networks with multiple LEDs. Although some power allocation methods have been proposed for NOMA aided RF-MIMO systems in literature, these methods cannot yet be applied to NOMA aided MIMO-VLC networks for the high computational complexity and the special characteristics of VLC transmitted signals. Actually, efficient power allocation approaches with low computational complexity in NOMA aided MIMO-VLC networks are of great concern for the potential applications. In VLC society, power allocation has been investigated in some respects, such as user fairness [10], channel allocation [11], users scheduling [4], energy efficiency [12], quality of service (QoS) requirement [13], and sum rate maximization [14]. At the time of writing, most of the NOMA aided VLC treatises about optimal power allocation can be categorized as numerical search and strategy design approach. Specifically, the authors of [3,15] proposed a gain ratio power allocation (GRPA) approach, where the optical channel gains of all users were utilized to assign the power. As a result, GRPA was shown to perform better than the so-called fixed power allocation method. Then, by maximizing system’s sum rate with any given required SINR of each user, the power allocation problem for an OFDM NOMA VLC system with an arbitrary number of multiplexed users was addressed in [16]. Furthermore, a downlink power allocation strategy for NOMA aided VLC system was investigated, where the maximize sum throughput of multiuser was considered subject to both user fairness and optical intensity constraints for IM/DD [10]. For a single NOMA aided VLC cell, Tao et al. proposed a GRPA strategy to enhance average user data rate and an alternative lower bound for comparability was also presented in [17]. Another GRPA strategy was proposed to enhance the NOMA aided VLC throughput, and an asymptotic lower bound based on special VLC channel model was derived to facilitate throughput comparisons in [18]. Additionally, a normalized GRPA method, termed as normalized gain difference power allocation (NGDPA), was proposed by exploiting channel conditions in a MIMO-VLC system in [9], unfortunately, the simulation results are demonstrated for the cases with uniformly distributed users’ locations and the user’s number is limited to 2 and 3, which are not practical in reality applications. It should be noted here that the majority of reported contributions on NOMA aided VLC systems assume perfect SIC [9,15,17,18].
2. System model The downlink of a NOMA aided indoor MIMO-VLC networks with multiple LEDs simultaneously serving 𝐾 users is considered. We assume that the LED transmitter is installed on the ceiling, which has 𝑁 down-facing LEDs and communicates with 𝐾 users, each user has 𝐽 upfacing photo-detectors (PDs). The parameters of all LEDs and PDs are assumed to be identical in this paper. Therefore, the system considered represents a typical MIMO-VLC channel model. The network model is illustrated in Fig. 1, in which multiple PDs are equipped with each NOMA user who can utilize the entire available modulation bandwidth of LEDs. According to the NOMA principle, the 𝑖th transmitter LED simultaneously transmits the message data 𝑠𝑖 to all 𝐾 users by using all the bandwidth through a superposition coding technique at the transmitter side. In addition, 4 QAM based DC-biased optical OFDM modulation is adopted in the considered NOMA aided MIMO-VLC downlink networks. Therefore, after DC-biased optical OFDM modulation, the transmitted signal of the 𝑖th LED is the combination signals of 𝐾 users, which can be expressed as 𝑥𝑖 =
𝐾 ∑ √ 𝜅𝑖𝑘 I 𝑠𝑖𝑘 + 𝐼DC
(1)
𝑘=1
where I is the overall electrical power of the 𝑖th transmitter LED, 𝜅𝑖𝑘 is the power allocation factor for the 𝑘th user in the 𝑖th transmitter LED, 𝑠𝑖𝑘 is the modulated message intended for the 𝑘th user in the 𝑖th transmitter, which is assumed to be with zero mean. 𝐼DC is a DC-offset of the 𝑖th transmitter LED for adjusting the illumination level of LEDs. To guarantee overall electrical power for the 𝑖th transmitter LED, the following constraint is proposed 𝐾 ∑
𝜅𝑖𝑘 = 1
(2)
𝑘=1
After going through a free-space optical wireless channel, the optical intensity signal is converted at the PD receivers of the 𝑘th user into a current signal via photoelectric conversion, and further, the constant DC-offset 𝐼DC is removed in the electrical domain. In general, noise is assumed to be introduced in the electrical domain [1,2]. Hence the observation at the receiver of the 𝑘th user in the electrical domain is the combination of all signals transmitted from LED transmitters, which can be given by 𝐲𝑘 = 𝜆𝑃O 𝜉𝐇𝑘 𝐱 + 𝐧𝑘 2
(3)
H. Wang, F. Wang and R. Li
Optics Communications 454 (2020) 124497
Fig. 1. NOMA aided MIMO-VLC networks consisting of four transmitters, K users and all receivers are equipped with 2 PDs each. Fig. 2. Geometric model of LOS transmission.
where 𝜆 is the responsivity of the PD, 𝑃O is the output optical power 𝑗=1,…,𝐽 𝐽 ×𝑁 is the of the LED, 𝜉 is the modulation index, 𝐇𝑘 = [ℎ(𝑘) 𝑗𝑖 ]𝑖=1,…,𝑁 ∈ channel matrix of the 𝑘th user, 𝐱 is the transmitted electrical signal vector from LEDs and 𝐧𝑘 denotes the additive real-valued Gaussian noises with zero mean and variances 𝜎𝑘2 containing shot noise and thermal noise contributions. Assuming each transmitter LED follows a Lambertian radiation pattern and only the LOS signal is considered for the power of the reflected signal is much weaker than the LOS one. The channel gain of the optical link between the 𝑖th LED and the 𝑗th PD of the 𝑘th user, denoted as ℎ(𝑘) 𝑗𝑖 , is given by ℎ(𝑘) 𝑗𝑖 =
(𝑚 + 1)𝐴 (𝑘) (𝑘) (𝑘) )2 cos(𝜙𝑖 )𝑇 (𝜓𝑗𝑖 )𝑔(𝜓𝑗𝑖 ) cos(𝜓𝑗𝑖 ) ( (𝑘) 2𝜋 𝑑𝑗𝑖
Following the same idea as in [9], the decreasing order with respect to the 𝑖th LED is then determined to be 𝑖,1 < 𝑖,2 < ⋯ < 𝑖,𝐾
Then, according to this order, the 𝑘th user can accurately decode the signals of all users with lower decoding order. The signals from users of higher decoding order are treated as noise, which cannot be eliminated. In this paper, we assume that perfect SIC is involved without signal detection error propagations. In this way, the instantaneous signal-tointerference-plus-noise ratio (SINR) of 𝑘th user in the 𝑗th PD can be presented as
(4)
(𝑘) is the LOS distance between the 𝑖th LED and the 𝑗th PD of where 𝑑𝑗𝑖 the 𝑘th user, 𝑚 = −1∕ log2 (cosΦ1∕2 ) is the order of Lambertian emission with half irradiance at semi-angle 𝛷1∕2 , which is measured from the optical axis of the LED, 𝐴 denotes the active detection area of the PD, 𝜙𝑖 is the angle of irradiance of the LED, 𝜓𝑗𝑖(𝑘) is the angle of incidence of the optical link from the 𝑖th LED and the 𝑗th PD of the 𝑘th user, which is measured from the axis perpendicular to the receiver surface, 𝑇 (𝜓𝑗𝑖(𝑘) ) represents the gain of the optical filter, 𝑔(𝜓𝑗𝑖(𝑘) ) is the nonimaging concentrator with refractive index 𝑛, which can be expressed by
⎧ 𝑛2 , ⎪ 𝑔(𝜓𝑗𝑖(𝑘) ) = ⎨ sin2 (𝛹𝑐 ) ⎪0, ⎩
0 ≤ 𝜓𝑗𝑖(𝑘) ≤ 𝛹𝑐
𝛾𝑘,𝑗 =
𝑗=1
ℎ𝑗𝑖,1 >
𝐽 ∑ 𝑗=1
𝐽 ∑
ℎ𝑗𝑖,𝐾
( )2 𝜅𝑛𝑘 I 𝜆2 𝑃O2 𝜉 2 𝐇𝑘 𝑗,𝑛 ( )2 ∑𝐾 2 2 2 2 𝑘′ =𝑘+1 𝜅𝑛𝑘′ I 𝜆 𝑃O 𝜉 𝐇𝑘 𝑗,𝑛 + 𝜎𝑗
(8)
( )2 where 𝐇𝑘 𝑗,𝑛 denotes the 𝑗th row and 𝑛th column element in the optical channel matrix 𝐇𝑘 . 𝑘′ th user is higher than 𝑘th user in the decoding order. Then, after optical to electrical conversion, the achievable data rate of 𝑘th user can be expressed as ⎧ ⎪1 ⎪2 ⎪ ⎪ 𝑅𝑘 = ⎨ ⎪1 ⎪ ⎪2 ⎪ ⎩
(5)
𝜓𝑗𝑖(𝑘) > 𝛹𝑐
ℎ𝑗𝑖,2 > ⋯ >
𝑁 ∑ 𝑛=1
where 𝛹𝑐 is the concentrator FOV semi-angle. The geometric model of LOS transmission is demonstrated in Fig. 2. For the transmitter with a single LED, SIC technique at users is applied to eliminate the inter-user interference. By performing SIC, the decoding order is determined by the order of increasing the channel gains of 𝐾 users. However, different from the single LED transmitter, multiple LEDs in NOMA aided MIMO-VLC system are involved in this paper. Hence, another improved decoding order should be developed. Unlike single LED NOMA aided VLC system, where individual optical channel gains of each user are adopted for the ordering, we utilize the sum of the optical channel gains of each LED with respect to all users to sort the channel gains of all LEDs. As done in [9], assuming that the sum optical channel gains of 𝐾 users with respect to the 𝑖th LED are sorted in the decreasing order as follows 𝐽 ∑
(7)
( )2 𝑁 ⎛ ⎞ 𝜅𝑛𝑘 I 𝜆2 𝑃O2 𝜉 2 𝐇𝑘 𝑗,𝑛 ∑ ⎟, log2 ⎜1 + ( ) ∑ 2 𝐾 ⎜ 2⎟ 2 2 2 𝑛=1 ⎝ 𝑘′ =𝑘+1 𝜅𝑛𝑘′ I 𝜆 𝑃O 𝜉 𝐇𝑘 𝑗,𝑛 + 𝜎𝑗 ⎠ 𝑘 = 1, … , 𝐾 − 1 ( ) 𝑁 ∑ ( )2 I log2 1 + 𝜅𝑛𝑘 𝜆2 𝑃O2 𝜉 2 𝐇𝑘 𝑗,𝑛 , 2 𝑛=1 𝜎𝑗 𝑘=𝐾
(9)
where the scaling factor 1∕2 is due to the Hermitian symmetry in optical OFDM [21]. Furthermore, the achievable sum rate of the considered NOMA aided MIMO-VLC networks can be given by ⎧ ⎪1 ⎪2 ⎪ 𝐾 ∑ ⎪ = 𝑅𝑘 = ⎨ ⎪1 𝑘=1 ⎪ ⎪2 ⎪ ⎩
(6)
( )2 𝑁 ⎛ ⎞ 𝜅𝑛𝑘 I 𝜆2 𝑃O2 𝜉 2 𝐇𝑘 𝑗,𝑛 ∑ ⎟, ⎜ log2 1 + ( ) ∑ 2 𝐾 ⎜ 2⎟ 2 2 2 𝑘=1 𝑛=1 ⎝ 𝑘′ =𝑘+1 𝜅𝑛𝑘′ I 𝜆 𝑃O 𝜉 𝐇𝑘 𝑗,𝑛 + 𝜎𝑗 ⎠ 𝑘 = 1, … , 𝐾 − 1 ( ) 𝐾 𝑁 ∑ ∑ ( )2 I log2 1 + 𝜅𝑛𝑘 𝜆2 𝑃O2 𝜉 2 𝐇𝑘 𝑗,𝑛 , 2 𝑘=1 𝑛=1 𝜎𝑗 𝑘=𝐾 𝐾 ∑
(10)
𝑗=1
3
H. Wang, F. Wang and R. Li
Optics Communications 454 (2020) 124497
3. Normalized logarithmic gain ratio power allocation method
Table 1 Simulation parameters.
As a flexible management strategy of all user rates, NOMA can provide an efficient way to improve the achievable sum rate of MIMOVLC networks by adjusting power allocation coefficients. Therefore, power allocation is one of the key challenges and plays an important role in MIMO-VLC networks. In this paper, the primary objective is to evaluate the achievable sum rate of the NOMA aided MIMO-VLC networks by enhanced low-complexity power allocation approach. It should be noted that, for the deterministic nature of indoor VLC system, the channel gains remain constants for fixed transmitter LEDs and receiver users, which make the channel gains estimation more simply according to the locations of transceivers. As an efficient power allocation strategy for NOMA aided system, GRPA has been proposed for SISO and MIMO multiuser NOMA VLC systems, and the performance has also been analyzed in [15]. Specifically, for GRPA approach proposed in [15], the power allocation strategy is determined by the optical channel gains of users compared to the gain of the first sorted user. According to the decoding order in (7), for the 𝑖th LED, the electrical powers relationship allocated to the 𝑘th user and (𝑘 + 1)th user can be expressed as [15] )𝑘+1 ( ∑𝐽 𝑗=1 ℎ𝑗𝑖,𝑘+1 𝜌𝑖,𝑘+1 (11) 𝜌𝑖,𝑘 = ∑𝐽 𝑗=1 ℎ𝑗𝑖,1
Simulation setup Room size (𝐿 × 𝑊 × 𝐻) Number of LEDs LEDs height Receiver height Location of LED 1 Location of LED2 Location of LED 3 Location of LED 4
5 × 5 × 3 m3 4 3 m 0.85 m (1.5, 1.5) m (1.5, 3.0) m (3.0, 3.0) m (3.0, 1.5) m
Transmitter parameters Semi-angle at half power (𝛷1∕2 ) Optical power/electric conversion efficiency (𝜂) Modulation index (𝛼)
60◦ 0.853 μW/mA 0.1
Receiver parameters Refractive index(𝛽) Physical area of a PD (𝐴PD ) Receiver FoV semi-angle (𝛹FoV ) PD responsivity (𝜆)
1.5 1.0 cm2 72◦ 0.53 A/W
Thus the electrical power assigned to the 𝑘th user decreases with the ∑ increase of 𝐽𝑗=1 ℎ𝑗𝑖,𝑘+1 . Aided by the dynamic power allocation strategy GRPA, to further improve the achievable sum rate of the considered NOMA aided MIMOVLC downlink networks, an efficient power allocation approach termed as NGDPA is proposed in [9], where the electrical powers relationship allocated to the 𝑘th user and (𝑘 + 1)th user can be described as ( ∑𝐽 )𝑘 ∑𝐽 𝑗=1 ℎ𝑗𝑖,1 − 𝑗=1 ℎ𝑗𝑖,𝑘+1 𝜌𝑖,𝑘 = 𝜌𝑖,𝑘+1 (12) ∑𝐽 𝑗=1 ℎ𝑗𝑖,1 As can be seen from (11) and (12), the sum of the optical channel gains in (11) is replaced by the difference of the sum of optical channel gains in (12), and furthermore, the power of the ratio is changed from 𝑘 + 1 to 𝑘. Inspired by this innovative procedure, to further improve the achievable sum rate of the considered NOMA aided MIMO-VLC downlink networks by further exploiting the channel gain difference, we propose a more efficient power allocation strategy. Specifically, for the 𝑁 × 𝐽 NOMA aided MIMO-VLC networks, utilizing the decoding order proposed in (7) and the electrical power allocated to the first sorted user, the relationship between the power allocated to the 𝑘th user and (𝑘 + 1)th user in the 𝑖th transmitter LED can be described as ( ) | log ∑𝐽 ℎ | | 𝑗𝑖,𝑘+1 | 𝑗=1 | | 𝜌𝑖,𝑘 = | (13) (∑ ) | 𝜌𝑖,𝑘+1 | | 𝐽 | log | ℎ 𝑗=1 𝑗𝑖,1 | |
Fig. 3. Achievable sum rate of NLGRPA versus GRPA and NGDPA under different normalized offsets with two users.
4. Numerical results In this section, to validate the efficiency of the proposed NLGRPA strategy on NOMA aided indoor MIMO-VLC networks, we provide numerical experiments for an indoor MIMO-VLC networks environment having the dimensions of [5×5×3] m3 , represented by a threedimensional (3D) Cartesian coordinate system [OX , OY , OZ ] with the origin being in one corner of the room. Again, the transmitter LEDs are assumed to be fixed on the ceiling and down-facing to the users perpendicularly. Similarly, the PDs of receiver users are located at a height of 0.85 m from the floor, which are assumed to be perpendicular to the floor and facing the ceiling. Eventually, the vertical distance between transmitters and the receiving PDs plane is 2.15 m. Unless specially noted, we assume that the positions of LEDs are those presented in Table 1. The half-illuminance semi-angle of LED 𝛷1∕2 is set as 60◦ , which is a typical value for commercially available high-brightness LEDs. All users’ PDs have a 72◦ FoV (semi-angle), the distance between two PDs of each user is set as 4 cm and the area of each PD is 𝐴𝑃 𝐷 = 1 cm2 , the responsivity is 𝜆 = 100 μA/mW/cm2 [22]. For convenience, all the parameters involved in our simulations are summarized in Table 1. The distance from user 1 (with the largest channel gain sum) to the user 𝐾 (with the smallest channel gain) is fixed as 𝑟(m), and the maximum distance from user 1 to the edge of the cell is 𝑅(m). Then, as done in [9], we specify a normalized offset of user 𝐾 with respect user 1 as 𝑟∕𝑅, and the normalized offset of user 𝑘 with respect user 1 (𝑘−1)𝑟 can be obtained as (𝐾−1)𝑅 . Furthermore, we assume that all users are
where, by definition, we have 𝜌𝑖,1 + 𝜌𝑖,2 + ⋯ + 𝜌𝑖,𝐾 = 1 and 0 ≤ 𝜌𝑖,𝑘 ≤ 1, 𝑖 ∈ 1, … , 𝑁, 𝑘 ∈ 1, … , 𝐾. Inherited from this, as an enhanced edition of (13), the power allocation relationship of the 𝑖th LED to the ordered user 𝑘 and user 𝑘 + 1 termed as NLGRPA is formulated as follows (∑ ) | | 𝐽 | | log | | 𝑗=1 ℎ𝑗𝑖,𝑘+1 | | 𝜌𝑖,𝑘 = | (14) | 𝜌𝑖,𝑘+1 (( ) ) ( ) 2 2 |1 | ∑𝐽 ∑𝐽 | log | ℎ − ℎ |2 | 𝑗=1 𝑗𝑖,1 𝑗=1 𝑗𝑖,𝑘+1 | | Observe from (14) that the assigned electrical power increases as the decreasing order of 𝑖,𝑘 in (7) according to the 𝑖th LED. Based on the above, the main motivations behind the proposed NLGRPA approach lies in two aspects: (1) Small fraction electrical power will be sufficient for users with better optical channel conditions to decode the corresponding signal in NOMA aided MIMO-VLC networks. (2) The channel conditions in the considered NOMA aided MIMO-VLC networks are further exploited to ensure efficient power allocation. 4
H. Wang, F. Wang and R. Li
Optics Communications 454 (2020) 124497
distributed uniformly in the considered service area. For comparisons to the proposed NLGRPA method, two other popular power allocation methods for NOMA aided VLC systems termed as GRPA [15] and NGDPA [9] are presented. The achievable sum rate versus the normalized offset in the considered NOMA aided 4 × 2 MIMO-VLC networks are demonstrated in Fig. 3 with 2 users and Fig. 4 with 3 users, respectively. As can be seen in Fig. 3, in the case of two users, when the normalized offset is less than 0.7, the achievable sum rates of the three methods are almost equal. When the normalized offset is bigger than 0.7, the drop speed of the achievable sum rate of GRPA algorithm is the largest, meanwhile, the drop speeds of NGDPA and NLGRPA methods are less than GRPA, and the achievable sum rates are also bigger than GRPA. When the normalized offset reaches 1, the achievable sum rate of the GRPA algorithm declines to 192.74 Mbit/s, while NLGRPA and NGDPA methods achieve 250.2 Mbit/s and 249.8 Mbit/s, respectively. Furthermore, in the case of 3 users, when the normalized offset is less than 0.6, the achievable sum rates of all the three methods are almost the same. When the normalized offset is greater than 0.7, the achievable sum rate of GRPA algorithm drops quickly than that of NGDPA and NLGRPA methods. Furthermore, the achievable sum rate of the NLGRPA always achieves the highest. When the normalized offset is 1, the NLGRPA is 16.2% higher than that of the GRPA, 4% higher than that of the NGDPA, and reaches 250.1 Mbit/s. It can be observed that the proposed NLGRPA approach outperforms the other two considered methods in most situations, which demonstrates that, among all these three methods: GRPA, NGDPA and NLGRPA, the NLGRPA algorithm is the best choice of the power allocation strategy of NOMA aided MIMO-VLC networks when users are uniformly distributed. In order to validate the efficiency of our proposed NLGRPA algorithm with a different number and randomly distributed users, where the NOMA aided 4 × 2 MIMO-VLC networks are utilized, we select 20 random generated Poisson Point Process distribution locations of users for different user number, and then take the average achievable sum rate values, the results compared with GRPA [15] and NGDPA [9] are depicted in Fig. 5. Meanwhile, we present the achievable rate of each
Fig. 4. Achievable sum rate of NLGRPA versus GRPA and NGDPA under different normalized offsets with three users.
Fig. 5. Achievable sum rate of NLGRPA versus GRPA and NGDPA with a different user number.
Fig. 6. Average achievable rate of NLGRPA versus GRPA and NGDPA of (a) LED 1; (b) LED 2; (c) LED 3; (d) LED 4.
5
H. Wang, F. Wang and R. Li
Optics Communications 454 (2020) 124497
Table 2 The achievable sum rate comparisons of three different power allocation methods when FoVs of PDs equal 15◦ . Number of users
Different methods (Mbit/s) GRPA
NGDPA
NLGRPA
The gain of NLGRPA over GRPA
The gain of NLGRPA over NGDPA
2 3 4 5 6 7 8 9 10
324.45 307.89 282.88 282.97 267.93 262.92 262.07 261.98 261.96
324.63 349.29 297.18 313.18 312.03 313.04 315.50 299.6 260.01
349.88 349.86 314.46 314.45 314.42 314.38 350.54 350.53 282.07
7.84% 13.63% 11.16% 11.13% 17.35% 19.58% 33.76% 33.80% 7.67%
7.78% 0.16% 5.81% 0.40% 0.77% 0.43% 11.10% 17.00% 8.48%
Table 3 The achievable sum rate comparisons of three different power allocation methods when FoVs of PDs equal 30◦ . Number of users
Different methods (Mbit/s) GRPA
NGDPA
NLGRPA
The gain of NLGRPA over GRPA
The gain of NLGRPA over NGDPA
2 3 4 5 6 7 8 9 10
284.10 269.56 258.50 255.55 222.04 220.27 220.05 220.03 220.02
284.83 309.29 260.13 269.87 267.50 266.06 272.48 254.68 211.66
309.87 309.84 274.25 274.21 274.12 273.94 310.91 310.88 241.35
9.07% 14.94% 6.09% 7.30% 23.45% 24.37% 41.29% 41.29% 9.70%
8.79% 0.18% 5.43% 1.61% 2.47% 2.96% 14.10% 22.07% 14.03%
Table 4 The achievable sum rate comparisons of three different power allocation methods when FoVs of PDs equal 72o . Number of Users
Different methods (Mbit/s) GRPA
NGDPA
NLGRPA
Percentage higher than GRPA
Percentage higher than NGDPA
2 3 4 5 6 7 8 9 10
238.78 231.16 225.96 209.08 172.75 172.29 172.24 172.23 172.23
241.95 266.06 228.38 218.15 217.08 213.56 221.15 201.47 163.56
266.64 266.64 230.27 230.12 229.67 228.90 268.14 268.02 196.01
11.67% 15.35% 1.91% 10.06% 32.95% 32.86% 55.67% 55.61% 13.81%
10.21% 0.22% 0.82% 5.49% 5.80% 7.18% 21.25% 33.03% 19.84%
LED in Fig. 6, which is the sum achievable rate of all users that are served by the corresponding LED. As can be seen from Fig. 5, the average achievable sum rate of the proposed NLGRPA method always has the best performance in most cases. Specifically, for the cases of 2 and 3 users, the average achievable sum rate of NLGRPA is a bit higher than NGDPA and is apparently bigger than that of GRPA. When the user number changes from 4 to 7, the average achievable sum rate of GRPA and NGDPA decline dramatically, especially that of GRPA, however, the average achievable sum rate of NLGRPA is almost constant 230 Mbit/s and apparently higher than GRPA and NGDPA. When the user number is more than 6, the average achievable sum rate of GRPA drops to 172.7 Mbit/s and then remains constant. When the user’s number changes from 7 to 9, the average achievable sum rate of NLGRPA reaches 268.1 Mbit/s and is much bigger than that of GRPA and NGDPA, which is up to 55.7% higher than GRPA and 33.0% higher than NGDPA, respectively. In all three power allocation methods, our proposed NLGRPA algorithm has the best performance in most cases when the locations of all users are randomly distributed. As can be seen from Fig. 6(a) to Fig. 6(d), the average achievable rates of LED 1 to LED 3 is relatively more stable of NLGRPA than the other two approaches in most cases. Specifically, when the user number changes from 2 to 10, the bit rate of LED1 is maintained between 60 and 60.7 Mbit/s with NLGRPA method, which is higher than that of the other two methods. In Fig. 6(d), in the case of 9 users, the average achievable rates of LED4 with NLGRPA can be 60% and 160% higher than that of GRPA and NGDPA, respectively.
Moreover, the average achievable sum-rate performance of the considered system is investigated by tuning FOVs of receivers’ PDs. In Table 2, the average achievable sum rate of the proposed NLGRPA method is compared with GRPA and NGDPA methods when FOVs of receivers’ PDs are equal to 15◦ . Similarly, comparisons are drawn in Tables 3 and 4, when 𝛹FoV equals 30◦ and 72◦ , respectively. As shown in Table 2, the average achievable sum rate of NLGRPA based system is always higher than GRPA and NGDPA aided systems. Specifically, it is at least 7.67% higher than GRPA. When the users are more than 8, the proposed approach can obtain at least 8.48% gain than NGDPA. Similar comparison results can be concluded from Tables 3 and 4. Especially, in Table 4, the average achievable sum rate gain of the proposed NLGRPA over GRPA and NGDPA are respectively more than 55% and 33% when the user number is 9. 5. Conclusions In this paper, a novel normalized logarithmic gain ratio power allocation (NLGRPA) approach is proposed to enhance the achievable sum rate for indoor non-orthogonal multiple access (NOMA) aided multiple-input multiple-output (MIMO) visible light communication (VLC) downlink networks, in which the optical channel information of all transmitter LEDs are exploited and properly ordered to ensure efficient power allocation. Numerical results depict that our proposed NLGRPA exhibits appropriate improvement in terms of achievable sum rate of the considered NOMA aided MIMO-VLC networks when compared with other conventional power allocation approaches, termed as GRPA and NGDPA. 6
H. Wang, F. Wang and R. Li
Optics Communications 454 (2020) 124497
Acknowledgments
[11] L. Lei, D. Yuan, C.K. Ho, S. Sun, Power and channel allocation for non-orthogonal multiple access in 5G systems: tractability and computation, IEEE Trans. Wireless Commun. 15 (12) (2016) 8580–8594. [12] F. Fang, H. Zhang, J. Cheng, V.C. Leung, Energy-efficient resource allocation for downlink non-orthogonal multiple access network, IEEE Trans. Commun. 64 (9) (2016) 3722–3732. [13] N.T. Le, Y.M. Jang, Resource allocation for multichannel broadcasting visible light communication, Opt. Commun. 355 (2015) 451–461. [14] H. Shen, Y. Wu, W. Xu, C. Zhao, Optimal power allocation for downlink two-user non-orthogonal multiple access in visible light communication, J. Commun. Inf. Netw. 2 (4) (2017) 57–64. [15] H. Marshoud, V.M. Kapinas, G.K. Karagiannidis, S. Muhaidat, Non-orthogonal multiple access for visible light communications, IEEE Photon. Technol. Lett. 28 (1) (2016) 51–54. [16] Y. Fu, Y. Hong, L.K. Chen, C.W. Sung, Enhanced power allocation for sum rate maximization in OFDM-NOMA VLC systems, IEEE Photon. Technol. Lett. 30 (13) (2018) 1218–1221. [17] S. Tao, H. Yu, Q. Li, Y. Tang, Performance analysis of gain ratio power allocation strategies for non-orthogonal multiple access in indoor visible light communication networks, EURASIP J. Wireless Commun. Netw. 2018 (2018) 1–14. [18] S. Tao, H. Yu, Q. Li, Y. Tang, Strategy-based gain ratio power allocation in non-orthogonal multiple access for indoor visible light communication networks, IEEE Access 7 (2019) 15250–15261. [19] C. Chen, W. Zhong, H. Yang, P. Du, Y. Yang, Flexible-rate SIC-free NOMA for downlink VLC based on constellation partitioning coding, IEEE Wireless Commun. Lett. 8 (2) (2019) 568–571. [20] H.Y. Li, Z.T. Huang, Y. Xiao, S. Zhan, Y.F. Ji, Solution for error propagation in a NOMA based VLC network: symmetric superposition coding, Opt. Express 25 (24) (2017) 29856–29863. [21] L. Yin, W.O. Popoola, X.P. Wu, H. Haas, Performance evaluation of nonorthogonal multiple access in visible light communication, IEEE Trans. Commun. 64 (12) (2016) 5162–5175. [22] F. Wang, C. Liu, Q. Wang, J. Zhang, R. Zhang, L.L. Yang, L. Hanzo, Optical jamming enhances the secrecy performance of the generalized space shift keying aided visible light downlink, IEEE Trans. Commun. 66 (9) (2018) 4087–4102.
This research was funded by The National Natural Science Foundation of China (NSFC) under grant number 61401401 and The National Natural Science Foundation of Henan Province, China under grant number 192102210088. References [1] D. Karunatilaka, F. Zafar, V. Kalavally, R. Parthiban, LED Based indoor visible light communications: state of the art, IEEE Commun. Surv. Tutor. 17 (3) (2015) 1649–1678. [2] S. Wu, H. Wang, C. Youn, Visible light communications for 5G wireless networking systems: from fixed to mobile communications, IEEE Netw. 28 (6) (2014) 41–45. [3] H. Marshoud, S. Muhaidat, P.C. Sofotasios, S. Hussain, M.A. Imran, B.S. Sharif, Optical non-orthogonal multiple access for visible light communication, IEEE Wirel. Commun. 25 (2) (2018) 82–88. [4] X. Zhang, Q. Gao, C. Gong, Z. Xu, User grouping and power allocation for NOMA visible light communication multi-cell networks, IEEE Commun. Lett. 21 (4) (2017) 777–780. [5] X. Zhao, H. Chen, J. Sun, On physical-layer security in multiuser visible light communication systems with non-orthogonal multiple access, IEEE Access 6 (2018) 34004–34017. [6] Z. Ding, Z. Yang, P. Fan, H.V. Poor, On the performance of non-orthogonal multiple access in 5G systems with randomly deployed users, IEEE Signal Process. 21 (12) (2014) 1501–1505. [7] M. Moltafet, N. Mokari, M.R. Javan, H. Saeedi, H. Pishro-Nik, A new multiple access technique for 5G: power domain sparse code multiple access (PSMA), IEEE Access 6 (2018) 747–759. [8] A. Anwar, B.C. Seet, Z. Ding, Non-orthogonal multiple access for ubiquitous wireless sensor networks, Sensors 18 (2) (2018) 516. [9] C. Chen, W.D. Zhong, H. Yang, P. Du, On the performance of MIMO-NOMA based visible light communication systems, IEEE Photon. Technol. Lett. 30 (4) (2018) 307–310. [10] Z. Yang, W. Xu, Y. Li, Fair non-orthogonal multiple access for visible light communication downlinks, IEEE Wireless Commun. 6 (1) (2017) 66–69.
7
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Optics Communications journal homepage: www.elsevier.com/locate/optcom
Enhancing power allocation efficiency of NOMA aided-MIMO downlink VLC networks Heran Wang a , Fasong Wang a ,∗, Rui Li b a b
The School of Information Engineering, Zhengzhou University, Zhengzhou, 450 0 01, Henan, China The School of Science, Henan University of Technology, Zhengzhou, 450 0 01, Henan, China
ARTICLE
INFO
Keywords: Non-orthogonal Multiple Access (NOMA) Visible Light Communication (VLC) Multiple-Input Multiple-Output (MIMO) Power allocation
ABSTRACT In order to enhance the achievable sum rate of indoor non-orthogonal multiple access (NOMA) aided multipleinput multiple-output (MIMO) visible light communication (VLC) downlink networks, in this paper, an efficient low computational complexity power allocation strategy termed as normalized logarithmic gain ratio power allocation (NLGRPA) is proposed, in which the optical channel information of all transmitter light-emitting diodes (LEDs) are exploited and properly ordered to ensure efficient power allocation Numerical results depict that our proposed NLGRPA method exhibits significant improvement in terms of achievable sum rate of NOMA aided MIMO-VLC networks when compared with other conventional power allocation approaches. Specifically, the proposed NLGRPA algorithm attains an achievable sum rate improvement of more than 55% and 33% compared with the gain ratio power allocation (GRPA) method and normalized gain difference power allocation (NGDPA) method in the 4 × 2 MIMO-VLC networks with nine randomly distributed users.
1. Introduction With the explosive growth of Internet-of-Things (IoTs) and portable information terminals, the unprecedented demand for local wireless networks with low latency, massive connectivity, diverse data rates, and low-cost front-ends have been under intensive investigations in the past few years. Although existing radio frequency (RF) based wireless communication has been widely commercially utilized, some bottlenecks have been arrived to meet these demands for various reasons, such as a shortage of RF spectra and severe power consumption. New wireless commutations alternatives are urgently demanded. In these contexts, light-emitting diode (LED) aided visible light communication (VLC), with its unique features such as license-free spectrum, low-cost front-ends, immunity to electromagnetic interference, natural confidentiality, low energy consumption, and the potential of spatial reuse of frequency bands in adjacent optical attocells, has been emerged as an alternative and complementary candidate for high-speed and shortrange to RF-based wireless communication. As a promising small cell technique, indoor VLC can be connected to the existing networks and constitutes an integral part of the upcoming ubiquitous fifth generation (5G) and beyond communication systems [1,2]. Nonetheless, the main challenge to exploiting VLC technology is the limited modulation bandwidth of off-the-shelf LEDs, which acts as a barrier to realize the envisioned VLC system with full potentials. Therefore, some techniques have been proposed in the efficient development of boosting the capacity of VLC system, such as optical multiple-input
multiple-output (MIMO), advanced optical modulation, and multiple access schemes and so on [2,3]. By virtue of its inherent broadcast nature, one transmitter LED is generally expected to support massive connectivity, and admit multiple users to access the same wireless resource. To this end, multiple access is one key technology in the multiuser VLC networks, and various optical multiple access schemes have been proposed in addressing this challenge in the open literature. Conventional orthogonal multiple access (OMA) schemes have already attracted attention in VLC networks, such as orthogonal frequency division multiple access (OFDMA) [4], code division multiple access (CDMA) [3], and space division multiple access (SDMA) [5]. In these OMA schemes, multiple users are separately allocated to orthogonal wireless resource to mitigate mutual interference. Nevertheless, these strategies cannot be applied to VLC systems directly for the intensity modulation and direct detection (IM/DD), and furthermore, these OMA aided techniques cannot yet sufficient to support massive connectivity because of the limited wireless resources. Due to its superior spectral efficiency compared to OMA schemes, non-orthogonal multiple access (NOMA) has recently been proposed to the forthcoming 5G wireless communication systems, which allows multiple users to utilize the entire available time and frequency band resources simultaneously in the power domain at the transmitter by superposition coding and multiuser detection at the receiver by successive interference cancellation (SIC) [3,6]. It has been demonstrated
∗ Corresponding author. E-mail addresses: [email protected] (H. Wang), [email protected] (F. Wang), [email protected] (R. Li).
https://doi.org/10.1016/j.optcom.2019.124497 Received 19 June 2019; Received in revised form 1 August 2019; Accepted 28 August 2019 Available online 3 September 2019 0030-4018/© 2019 Elsevier B.V. All rights reserved.
H. Wang, F. Wang and R. Li
Optics Communications 454 (2020) 124497
However, perfect SIC cannot always be guaranteed in practical NOMAbased VLC systems and imperfect SIC will cause error propagation and decrease system performance [19,20]. Several enhanced NOMA schemes have already been reported in NOMA aided VLC literature. In [19], a flexible-rate SIC-free NOMA technique for downlink VLC systems is proposed based on constellation partitioning coding and uneven constellation demapping techniques. Also, symmetric superposition coding and symmetric SIC decoding are proposed for downlink NOMA-based VLC network to overcome error propagation problem to increase the BER performance in [20]. Yet, in this paper, we focus on the efficiency of the power allocation problem in NOMA aided MIMOVLC networks, the perfect SIC will be considered, just like most existed power allocation approach in NOMA aided VLC systems [9,15,17,18]. In this paper, an efficient and low complexity power allocation strategy is proposed in NOMA aided indoor downlink MIMO-VLC networks, termed as normalized logarithmic gain ratio power allocation (NLGRPA), which can be utilized efficiently when the randomly distributed user’s number is more than 5. The achievable sum rate is evaluated by the proposed NLGRPA power allocation approach via numerical simulations. Numerical results depict that our proposed NLGRPA approach exhibits significant improvement in terms of achievable sum rate of the considered NOMA aided MIMO-VLC networks when compared with the other two conventional power allocation approaches: GRPA and NGDPA.
that NOMA can outperform conventional OMA in terms of sum rate and outage probability [6]. It should be noted that the power domain aided NOMA scheme has the lowest computational complexity among the code domain, power domain, and the combined code-power domain [7]. Meanwhile, the computational complexity of SIC-based NOMA message decoding is acceptable when utilizing current and upcoming processors for ubiquitous wireless sensor networks [8]. Hence, efficient low complexity power allocation approach is highly desirable in NOMA based 5G networks. For NOMA aided wireless communication, the system can perform significant performance gains in high signal-to-noise ratio (SNR) scenarios, which is a typical case in indoor VLC applications due to the dominant line-of-sight (LOS) channel gain and the short distance between the transmitter and the receiver. Furthermore, in NOMA, SIC is exclusively dependent on the channel state information at the transceivers to determine the decoding order and power allocation strategy of all users. This is in line with VLC systems, where the optical channel gains remain constants until the locations of the users change or parameters of transceivers vary [1,3]. Consequently, implementing NOMA is a promising choice in indoor downlink VLC networks with multiple users. The performance of NOMA aided VLC systems has been widely studied in [9]. As an efficient approach to increase system capacity, MIMO has been extensively applied in VLC by exploiting equipped LEDs. Nevertheless, the utilization of NOMA to MIMO-VLC networks has not been widely investigated. Moreover, existing power allocation approaches for a single LED NOMA aided VLC system cannot be directly implemented in NOMA aided MIMO-VLC networks with multiple LEDs. Although some power allocation methods have been proposed for NOMA aided RF-MIMO systems in literature, these methods cannot yet be applied to NOMA aided MIMO-VLC networks for the high computational complexity and the special characteristics of VLC transmitted signals. Actually, efficient power allocation approaches with low computational complexity in NOMA aided MIMO-VLC networks are of great concern for the potential applications. In VLC society, power allocation has been investigated in some respects, such as user fairness [10], channel allocation [11], users scheduling [4], energy efficiency [12], quality of service (QoS) requirement [13], and sum rate maximization [14]. At the time of writing, most of the NOMA aided VLC treatises about optimal power allocation can be categorized as numerical search and strategy design approach. Specifically, the authors of [3,15] proposed a gain ratio power allocation (GRPA) approach, where the optical channel gains of all users were utilized to assign the power. As a result, GRPA was shown to perform better than the so-called fixed power allocation method. Then, by maximizing system’s sum rate with any given required SINR of each user, the power allocation problem for an OFDM NOMA VLC system with an arbitrary number of multiplexed users was addressed in [16]. Furthermore, a downlink power allocation strategy for NOMA aided VLC system was investigated, where the maximize sum throughput of multiuser was considered subject to both user fairness and optical intensity constraints for IM/DD [10]. For a single NOMA aided VLC cell, Tao et al. proposed a GRPA strategy to enhance average user data rate and an alternative lower bound for comparability was also presented in [17]. Another GRPA strategy was proposed to enhance the NOMA aided VLC throughput, and an asymptotic lower bound based on special VLC channel model was derived to facilitate throughput comparisons in [18]. Additionally, a normalized GRPA method, termed as normalized gain difference power allocation (NGDPA), was proposed by exploiting channel conditions in a MIMO-VLC system in [9], unfortunately, the simulation results are demonstrated for the cases with uniformly distributed users’ locations and the user’s number is limited to 2 and 3, which are not practical in reality applications. It should be noted here that the majority of reported contributions on NOMA aided VLC systems assume perfect SIC [9,15,17,18].
2. System model The downlink of a NOMA aided indoor MIMO-VLC networks with multiple LEDs simultaneously serving 𝐾 users is considered. We assume that the LED transmitter is installed on the ceiling, which has 𝑁 down-facing LEDs and communicates with 𝐾 users, each user has 𝐽 upfacing photo-detectors (PDs). The parameters of all LEDs and PDs are assumed to be identical in this paper. Therefore, the system considered represents a typical MIMO-VLC channel model. The network model is illustrated in Fig. 1, in which multiple PDs are equipped with each NOMA user who can utilize the entire available modulation bandwidth of LEDs. According to the NOMA principle, the 𝑖th transmitter LED simultaneously transmits the message data 𝑠𝑖 to all 𝐾 users by using all the bandwidth through a superposition coding technique at the transmitter side. In addition, 4 QAM based DC-biased optical OFDM modulation is adopted in the considered NOMA aided MIMO-VLC downlink networks. Therefore, after DC-biased optical OFDM modulation, the transmitted signal of the 𝑖th LED is the combination signals of 𝐾 users, which can be expressed as 𝑥𝑖 =
𝐾 ∑ √ 𝜅𝑖𝑘 I 𝑠𝑖𝑘 + 𝐼DC
(1)
𝑘=1
where I is the overall electrical power of the 𝑖th transmitter LED, 𝜅𝑖𝑘 is the power allocation factor for the 𝑘th user in the 𝑖th transmitter LED, 𝑠𝑖𝑘 is the modulated message intended for the 𝑘th user in the 𝑖th transmitter, which is assumed to be with zero mean. 𝐼DC is a DC-offset of the 𝑖th transmitter LED for adjusting the illumination level of LEDs. To guarantee overall electrical power for the 𝑖th transmitter LED, the following constraint is proposed 𝐾 ∑
𝜅𝑖𝑘 = 1
(2)
𝑘=1
After going through a free-space optical wireless channel, the optical intensity signal is converted at the PD receivers of the 𝑘th user into a current signal via photoelectric conversion, and further, the constant DC-offset 𝐼DC is removed in the electrical domain. In general, noise is assumed to be introduced in the electrical domain [1,2]. Hence the observation at the receiver of the 𝑘th user in the electrical domain is the combination of all signals transmitted from LED transmitters, which can be given by 𝐲𝑘 = 𝜆𝑃O 𝜉𝐇𝑘 𝐱 + 𝐧𝑘 2
(3)
H. Wang, F. Wang and R. Li
Optics Communications 454 (2020) 124497
Fig. 1. NOMA aided MIMO-VLC networks consisting of four transmitters, K users and all receivers are equipped with 2 PDs each. Fig. 2. Geometric model of LOS transmission.
where 𝜆 is the responsivity of the PD, 𝑃O is the output optical power 𝑗=1,…,𝐽 𝐽 ×𝑁 is the of the LED, 𝜉 is the modulation index, 𝐇𝑘 = [ℎ(𝑘) 𝑗𝑖 ]𝑖=1,…,𝑁 ∈ channel matrix of the 𝑘th user, 𝐱 is the transmitted electrical signal vector from LEDs and 𝐧𝑘 denotes the additive real-valued Gaussian noises with zero mean and variances 𝜎𝑘2 containing shot noise and thermal noise contributions. Assuming each transmitter LED follows a Lambertian radiation pattern and only the LOS signal is considered for the power of the reflected signal is much weaker than the LOS one. The channel gain of the optical link between the 𝑖th LED and the 𝑗th PD of the 𝑘th user, denoted as ℎ(𝑘) 𝑗𝑖 , is given by ℎ(𝑘) 𝑗𝑖 =
(𝑚 + 1)𝐴 (𝑘) (𝑘) (𝑘) )2 cos(𝜙𝑖 )𝑇 (𝜓𝑗𝑖 )𝑔(𝜓𝑗𝑖 ) cos(𝜓𝑗𝑖 ) ( (𝑘) 2𝜋 𝑑𝑗𝑖
Following the same idea as in [9], the decreasing order with respect to the 𝑖th LED is then determined to be 𝑖,1 < 𝑖,2 < ⋯ < 𝑖,𝐾
Then, according to this order, the 𝑘th user can accurately decode the signals of all users with lower decoding order. The signals from users of higher decoding order are treated as noise, which cannot be eliminated. In this paper, we assume that perfect SIC is involved without signal detection error propagations. In this way, the instantaneous signal-tointerference-plus-noise ratio (SINR) of 𝑘th user in the 𝑗th PD can be presented as
(4)
(𝑘) is the LOS distance between the 𝑖th LED and the 𝑗th PD of where 𝑑𝑗𝑖 the 𝑘th user, 𝑚 = −1∕ log2 (cosΦ1∕2 ) is the order of Lambertian emission with half irradiance at semi-angle 𝛷1∕2 , which is measured from the optical axis of the LED, 𝐴 denotes the active detection area of the PD, 𝜙𝑖 is the angle of irradiance of the LED, 𝜓𝑗𝑖(𝑘) is the angle of incidence of the optical link from the 𝑖th LED and the 𝑗th PD of the 𝑘th user, which is measured from the axis perpendicular to the receiver surface, 𝑇 (𝜓𝑗𝑖(𝑘) ) represents the gain of the optical filter, 𝑔(𝜓𝑗𝑖(𝑘) ) is the nonimaging concentrator with refractive index 𝑛, which can be expressed by
⎧ 𝑛2 , ⎪ 𝑔(𝜓𝑗𝑖(𝑘) ) = ⎨ sin2 (𝛹𝑐 ) ⎪0, ⎩
0 ≤ 𝜓𝑗𝑖(𝑘) ≤ 𝛹𝑐
𝛾𝑘,𝑗 =
𝑗=1
ℎ𝑗𝑖,1 >
𝐽 ∑ 𝑗=1
𝐽 ∑
ℎ𝑗𝑖,𝐾
( )2 𝜅𝑛𝑘 I 𝜆2 𝑃O2 𝜉 2 𝐇𝑘 𝑗,𝑛 ( )2 ∑𝐾 2 2 2 2 𝑘′ =𝑘+1 𝜅𝑛𝑘′ I 𝜆 𝑃O 𝜉 𝐇𝑘 𝑗,𝑛 + 𝜎𝑗
(8)
( )2 where 𝐇𝑘 𝑗,𝑛 denotes the 𝑗th row and 𝑛th column element in the optical channel matrix 𝐇𝑘 . 𝑘′ th user is higher than 𝑘th user in the decoding order. Then, after optical to electrical conversion, the achievable data rate of 𝑘th user can be expressed as ⎧ ⎪1 ⎪2 ⎪ ⎪ 𝑅𝑘 = ⎨ ⎪1 ⎪ ⎪2 ⎪ ⎩
(5)
𝜓𝑗𝑖(𝑘) > 𝛹𝑐
ℎ𝑗𝑖,2 > ⋯ >
𝑁 ∑ 𝑛=1
where 𝛹𝑐 is the concentrator FOV semi-angle. The geometric model of LOS transmission is demonstrated in Fig. 2. For the transmitter with a single LED, SIC technique at users is applied to eliminate the inter-user interference. By performing SIC, the decoding order is determined by the order of increasing the channel gains of 𝐾 users. However, different from the single LED transmitter, multiple LEDs in NOMA aided MIMO-VLC system are involved in this paper. Hence, another improved decoding order should be developed. Unlike single LED NOMA aided VLC system, where individual optical channel gains of each user are adopted for the ordering, we utilize the sum of the optical channel gains of each LED with respect to all users to sort the channel gains of all LEDs. As done in [9], assuming that the sum optical channel gains of 𝐾 users with respect to the 𝑖th LED are sorted in the decreasing order as follows 𝐽 ∑
(7)
( )2 𝑁 ⎛ ⎞ 𝜅𝑛𝑘 I 𝜆2 𝑃O2 𝜉 2 𝐇𝑘 𝑗,𝑛 ∑ ⎟, log2 ⎜1 + ( ) ∑ 2 𝐾 ⎜ 2⎟ 2 2 2 𝑛=1 ⎝ 𝑘′ =𝑘+1 𝜅𝑛𝑘′ I 𝜆 𝑃O 𝜉 𝐇𝑘 𝑗,𝑛 + 𝜎𝑗 ⎠ 𝑘 = 1, … , 𝐾 − 1 ( ) 𝑁 ∑ ( )2 I log2 1 + 𝜅𝑛𝑘 𝜆2 𝑃O2 𝜉 2 𝐇𝑘 𝑗,𝑛 , 2 𝑛=1 𝜎𝑗 𝑘=𝐾
(9)
where the scaling factor 1∕2 is due to the Hermitian symmetry in optical OFDM [21]. Furthermore, the achievable sum rate of the considered NOMA aided MIMO-VLC networks can be given by ⎧ ⎪1 ⎪2 ⎪ 𝐾 ∑ ⎪ = 𝑅𝑘 = ⎨ ⎪1 𝑘=1 ⎪ ⎪2 ⎪ ⎩
(6)
( )2 𝑁 ⎛ ⎞ 𝜅𝑛𝑘 I 𝜆2 𝑃O2 𝜉 2 𝐇𝑘 𝑗,𝑛 ∑ ⎟, ⎜ log2 1 + ( ) ∑ 2 𝐾 ⎜ 2⎟ 2 2 2 𝑘=1 𝑛=1 ⎝ 𝑘′ =𝑘+1 𝜅𝑛𝑘′ I 𝜆 𝑃O 𝜉 𝐇𝑘 𝑗,𝑛 + 𝜎𝑗 ⎠ 𝑘 = 1, … , 𝐾 − 1 ( ) 𝐾 𝑁 ∑ ∑ ( )2 I log2 1 + 𝜅𝑛𝑘 𝜆2 𝑃O2 𝜉 2 𝐇𝑘 𝑗,𝑛 , 2 𝑘=1 𝑛=1 𝜎𝑗 𝑘=𝐾 𝐾 ∑
(10)
𝑗=1
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H. Wang, F. Wang and R. Li
Optics Communications 454 (2020) 124497
3. Normalized logarithmic gain ratio power allocation method
Table 1 Simulation parameters.
As a flexible management strategy of all user rates, NOMA can provide an efficient way to improve the achievable sum rate of MIMOVLC networks by adjusting power allocation coefficients. Therefore, power allocation is one of the key challenges and plays an important role in MIMO-VLC networks. In this paper, the primary objective is to evaluate the achievable sum rate of the NOMA aided MIMO-VLC networks by enhanced low-complexity power allocation approach. It should be noted that, for the deterministic nature of indoor VLC system, the channel gains remain constants for fixed transmitter LEDs and receiver users, which make the channel gains estimation more simply according to the locations of transceivers. As an efficient power allocation strategy for NOMA aided system, GRPA has been proposed for SISO and MIMO multiuser NOMA VLC systems, and the performance has also been analyzed in [15]. Specifically, for GRPA approach proposed in [15], the power allocation strategy is determined by the optical channel gains of users compared to the gain of the first sorted user. According to the decoding order in (7), for the 𝑖th LED, the electrical powers relationship allocated to the 𝑘th user and (𝑘 + 1)th user can be expressed as [15] )𝑘+1 ( ∑𝐽 𝑗=1 ℎ𝑗𝑖,𝑘+1 𝜌𝑖,𝑘+1 (11) 𝜌𝑖,𝑘 = ∑𝐽 𝑗=1 ℎ𝑗𝑖,1
Simulation setup Room size (𝐿 × 𝑊 × 𝐻) Number of LEDs LEDs height Receiver height Location of LED 1 Location of LED2 Location of LED 3 Location of LED 4
5 × 5 × 3 m3 4 3 m 0.85 m (1.5, 1.5) m (1.5, 3.0) m (3.0, 3.0) m (3.0, 1.5) m
Transmitter parameters Semi-angle at half power (𝛷1∕2 ) Optical power/electric conversion efficiency (𝜂) Modulation index (𝛼)
60◦ 0.853 μW/mA 0.1
Receiver parameters Refractive index(𝛽) Physical area of a PD (𝐴PD ) Receiver FoV semi-angle (𝛹FoV ) PD responsivity (𝜆)
1.5 1.0 cm2 72◦ 0.53 A/W
Thus the electrical power assigned to the 𝑘th user decreases with the ∑ increase of 𝐽𝑗=1 ℎ𝑗𝑖,𝑘+1 . Aided by the dynamic power allocation strategy GRPA, to further improve the achievable sum rate of the considered NOMA aided MIMOVLC downlink networks, an efficient power allocation approach termed as NGDPA is proposed in [9], where the electrical powers relationship allocated to the 𝑘th user and (𝑘 + 1)th user can be described as ( ∑𝐽 )𝑘 ∑𝐽 𝑗=1 ℎ𝑗𝑖,1 − 𝑗=1 ℎ𝑗𝑖,𝑘+1 𝜌𝑖,𝑘 = 𝜌𝑖,𝑘+1 (12) ∑𝐽 𝑗=1 ℎ𝑗𝑖,1 As can be seen from (11) and (12), the sum of the optical channel gains in (11) is replaced by the difference of the sum of optical channel gains in (12), and furthermore, the power of the ratio is changed from 𝑘 + 1 to 𝑘. Inspired by this innovative procedure, to further improve the achievable sum rate of the considered NOMA aided MIMO-VLC downlink networks by further exploiting the channel gain difference, we propose a more efficient power allocation strategy. Specifically, for the 𝑁 × 𝐽 NOMA aided MIMO-VLC networks, utilizing the decoding order proposed in (7) and the electrical power allocated to the first sorted user, the relationship between the power allocated to the 𝑘th user and (𝑘 + 1)th user in the 𝑖th transmitter LED can be described as ( ) | log ∑𝐽 ℎ | | 𝑗𝑖,𝑘+1 | 𝑗=1 | | 𝜌𝑖,𝑘 = | (13) (∑ ) | 𝜌𝑖,𝑘+1 | | 𝐽 | log | ℎ 𝑗=1 𝑗𝑖,1 | |
Fig. 3. Achievable sum rate of NLGRPA versus GRPA and NGDPA under different normalized offsets with two users.
4. Numerical results In this section, to validate the efficiency of the proposed NLGRPA strategy on NOMA aided indoor MIMO-VLC networks, we provide numerical experiments for an indoor MIMO-VLC networks environment having the dimensions of [5×5×3] m3 , represented by a threedimensional (3D) Cartesian coordinate system [OX , OY , OZ ] with the origin being in one corner of the room. Again, the transmitter LEDs are assumed to be fixed on the ceiling and down-facing to the users perpendicularly. Similarly, the PDs of receiver users are located at a height of 0.85 m from the floor, which are assumed to be perpendicular to the floor and facing the ceiling. Eventually, the vertical distance between transmitters and the receiving PDs plane is 2.15 m. Unless specially noted, we assume that the positions of LEDs are those presented in Table 1. The half-illuminance semi-angle of LED 𝛷1∕2 is set as 60◦ , which is a typical value for commercially available high-brightness LEDs. All users’ PDs have a 72◦ FoV (semi-angle), the distance between two PDs of each user is set as 4 cm and the area of each PD is 𝐴𝑃 𝐷 = 1 cm2 , the responsivity is 𝜆 = 100 μA/mW/cm2 [22]. For convenience, all the parameters involved in our simulations are summarized in Table 1. The distance from user 1 (with the largest channel gain sum) to the user 𝐾 (with the smallest channel gain) is fixed as 𝑟(m), and the maximum distance from user 1 to the edge of the cell is 𝑅(m). Then, as done in [9], we specify a normalized offset of user 𝐾 with respect user 1 as 𝑟∕𝑅, and the normalized offset of user 𝑘 with respect user 1 (𝑘−1)𝑟 can be obtained as (𝐾−1)𝑅 . Furthermore, we assume that all users are
where, by definition, we have 𝜌𝑖,1 + 𝜌𝑖,2 + ⋯ + 𝜌𝑖,𝐾 = 1 and 0 ≤ 𝜌𝑖,𝑘 ≤ 1, 𝑖 ∈ 1, … , 𝑁, 𝑘 ∈ 1, … , 𝐾. Inherited from this, as an enhanced edition of (13), the power allocation relationship of the 𝑖th LED to the ordered user 𝑘 and user 𝑘 + 1 termed as NLGRPA is formulated as follows (∑ ) | | 𝐽 | | log | | 𝑗=1 ℎ𝑗𝑖,𝑘+1 | | 𝜌𝑖,𝑘 = | (14) | 𝜌𝑖,𝑘+1 (( ) ) ( ) 2 2 |1 | ∑𝐽 ∑𝐽 | log | ℎ − ℎ |2 | 𝑗=1 𝑗𝑖,1 𝑗=1 𝑗𝑖,𝑘+1 | | Observe from (14) that the assigned electrical power increases as the decreasing order of 𝑖,𝑘 in (7) according to the 𝑖th LED. Based on the above, the main motivations behind the proposed NLGRPA approach lies in two aspects: (1) Small fraction electrical power will be sufficient for users with better optical channel conditions to decode the corresponding signal in NOMA aided MIMO-VLC networks. (2) The channel conditions in the considered NOMA aided MIMO-VLC networks are further exploited to ensure efficient power allocation. 4
H. Wang, F. Wang and R. Li
Optics Communications 454 (2020) 124497
distributed uniformly in the considered service area. For comparisons to the proposed NLGRPA method, two other popular power allocation methods for NOMA aided VLC systems termed as GRPA [15] and NGDPA [9] are presented. The achievable sum rate versus the normalized offset in the considered NOMA aided 4 × 2 MIMO-VLC networks are demonstrated in Fig. 3 with 2 users and Fig. 4 with 3 users, respectively. As can be seen in Fig. 3, in the case of two users, when the normalized offset is less than 0.7, the achievable sum rates of the three methods are almost equal. When the normalized offset is bigger than 0.7, the drop speed of the achievable sum rate of GRPA algorithm is the largest, meanwhile, the drop speeds of NGDPA and NLGRPA methods are less than GRPA, and the achievable sum rates are also bigger than GRPA. When the normalized offset reaches 1, the achievable sum rate of the GRPA algorithm declines to 192.74 Mbit/s, while NLGRPA and NGDPA methods achieve 250.2 Mbit/s and 249.8 Mbit/s, respectively. Furthermore, in the case of 3 users, when the normalized offset is less than 0.6, the achievable sum rates of all the three methods are almost the same. When the normalized offset is greater than 0.7, the achievable sum rate of GRPA algorithm drops quickly than that of NGDPA and NLGRPA methods. Furthermore, the achievable sum rate of the NLGRPA always achieves the highest. When the normalized offset is 1, the NLGRPA is 16.2% higher than that of the GRPA, 4% higher than that of the NGDPA, and reaches 250.1 Mbit/s. It can be observed that the proposed NLGRPA approach outperforms the other two considered methods in most situations, which demonstrates that, among all these three methods: GRPA, NGDPA and NLGRPA, the NLGRPA algorithm is the best choice of the power allocation strategy of NOMA aided MIMO-VLC networks when users are uniformly distributed. In order to validate the efficiency of our proposed NLGRPA algorithm with a different number and randomly distributed users, where the NOMA aided 4 × 2 MIMO-VLC networks are utilized, we select 20 random generated Poisson Point Process distribution locations of users for different user number, and then take the average achievable sum rate values, the results compared with GRPA [15] and NGDPA [9] are depicted in Fig. 5. Meanwhile, we present the achievable rate of each
Fig. 4. Achievable sum rate of NLGRPA versus GRPA and NGDPA under different normalized offsets with three users.
Fig. 5. Achievable sum rate of NLGRPA versus GRPA and NGDPA with a different user number.
Fig. 6. Average achievable rate of NLGRPA versus GRPA and NGDPA of (a) LED 1; (b) LED 2; (c) LED 3; (d) LED 4.
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H. Wang, F. Wang and R. Li
Optics Communications 454 (2020) 124497
Table 2 The achievable sum rate comparisons of three different power allocation methods when FoVs of PDs equal 15◦ . Number of users
Different methods (Mbit/s) GRPA
NGDPA
NLGRPA
The gain of NLGRPA over GRPA
The gain of NLGRPA over NGDPA
2 3 4 5 6 7 8 9 10
324.45 307.89 282.88 282.97 267.93 262.92 262.07 261.98 261.96
324.63 349.29 297.18 313.18 312.03 313.04 315.50 299.6 260.01
349.88 349.86 314.46 314.45 314.42 314.38 350.54 350.53 282.07
7.84% 13.63% 11.16% 11.13% 17.35% 19.58% 33.76% 33.80% 7.67%
7.78% 0.16% 5.81% 0.40% 0.77% 0.43% 11.10% 17.00% 8.48%
Table 3 The achievable sum rate comparisons of three different power allocation methods when FoVs of PDs equal 30◦ . Number of users
Different methods (Mbit/s) GRPA
NGDPA
NLGRPA
The gain of NLGRPA over GRPA
The gain of NLGRPA over NGDPA
2 3 4 5 6 7 8 9 10
284.10 269.56 258.50 255.55 222.04 220.27 220.05 220.03 220.02
284.83 309.29 260.13 269.87 267.50 266.06 272.48 254.68 211.66
309.87 309.84 274.25 274.21 274.12 273.94 310.91 310.88 241.35
9.07% 14.94% 6.09% 7.30% 23.45% 24.37% 41.29% 41.29% 9.70%
8.79% 0.18% 5.43% 1.61% 2.47% 2.96% 14.10% 22.07% 14.03%
Table 4 The achievable sum rate comparisons of three different power allocation methods when FoVs of PDs equal 72o . Number of Users
Different methods (Mbit/s) GRPA
NGDPA
NLGRPA
Percentage higher than GRPA
Percentage higher than NGDPA
2 3 4 5 6 7 8 9 10
238.78 231.16 225.96 209.08 172.75 172.29 172.24 172.23 172.23
241.95 266.06 228.38 218.15 217.08 213.56 221.15 201.47 163.56
266.64 266.64 230.27 230.12 229.67 228.90 268.14 268.02 196.01
11.67% 15.35% 1.91% 10.06% 32.95% 32.86% 55.67% 55.61% 13.81%
10.21% 0.22% 0.82% 5.49% 5.80% 7.18% 21.25% 33.03% 19.84%
LED in Fig. 6, which is the sum achievable rate of all users that are served by the corresponding LED. As can be seen from Fig. 5, the average achievable sum rate of the proposed NLGRPA method always has the best performance in most cases. Specifically, for the cases of 2 and 3 users, the average achievable sum rate of NLGRPA is a bit higher than NGDPA and is apparently bigger than that of GRPA. When the user number changes from 4 to 7, the average achievable sum rate of GRPA and NGDPA decline dramatically, especially that of GRPA, however, the average achievable sum rate of NLGRPA is almost constant 230 Mbit/s and apparently higher than GRPA and NGDPA. When the user number is more than 6, the average achievable sum rate of GRPA drops to 172.7 Mbit/s and then remains constant. When the user’s number changes from 7 to 9, the average achievable sum rate of NLGRPA reaches 268.1 Mbit/s and is much bigger than that of GRPA and NGDPA, which is up to 55.7% higher than GRPA and 33.0% higher than NGDPA, respectively. In all three power allocation methods, our proposed NLGRPA algorithm has the best performance in most cases when the locations of all users are randomly distributed. As can be seen from Fig. 6(a) to Fig. 6(d), the average achievable rates of LED 1 to LED 3 is relatively more stable of NLGRPA than the other two approaches in most cases. Specifically, when the user number changes from 2 to 10, the bit rate of LED1 is maintained between 60 and 60.7 Mbit/s with NLGRPA method, which is higher than that of the other two methods. In Fig. 6(d), in the case of 9 users, the average achievable rates of LED4 with NLGRPA can be 60% and 160% higher than that of GRPA and NGDPA, respectively.
Moreover, the average achievable sum-rate performance of the considered system is investigated by tuning FOVs of receivers’ PDs. In Table 2, the average achievable sum rate of the proposed NLGRPA method is compared with GRPA and NGDPA methods when FOVs of receivers’ PDs are equal to 15◦ . Similarly, comparisons are drawn in Tables 3 and 4, when 𝛹FoV equals 30◦ and 72◦ , respectively. As shown in Table 2, the average achievable sum rate of NLGRPA based system is always higher than GRPA and NGDPA aided systems. Specifically, it is at least 7.67% higher than GRPA. When the users are more than 8, the proposed approach can obtain at least 8.48% gain than NGDPA. Similar comparison results can be concluded from Tables 3 and 4. Especially, in Table 4, the average achievable sum rate gain of the proposed NLGRPA over GRPA and NGDPA are respectively more than 55% and 33% when the user number is 9. 5. Conclusions In this paper, a novel normalized logarithmic gain ratio power allocation (NLGRPA) approach is proposed to enhance the achievable sum rate for indoor non-orthogonal multiple access (NOMA) aided multiple-input multiple-output (MIMO) visible light communication (VLC) downlink networks, in which the optical channel information of all transmitter LEDs are exploited and properly ordered to ensure efficient power allocation. Numerical results depict that our proposed NLGRPA exhibits appropriate improvement in terms of achievable sum rate of the considered NOMA aided MIMO-VLC networks when compared with other conventional power allocation approaches, termed as GRPA and NGDPA. 6
H. Wang, F. Wang and R. Li
Optics Communications 454 (2020) 124497
Acknowledgments
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