Slow Beam Steering for Indoor Multi-User Visible Light Communications

Transcription

1 Slow Beam Steering for Inoor Multi-User Visible Light Communications Yusuf Sai Eroğlu, Chethan Kumar Anjinappa, İsmail Güvenç, an Nezih Pala Department of Electrical an Computer Engineering, North Carolina State University, Raleigh, NC Department of Electrical an Computer Engineering, Floria International University, Miami, FL {yeroglu, canjina, arxiv:5.90v1 [cs.ni] May 01 Abstract Visible light communications VLC) is an emerging technology that enables broaban ata rates using the visible spectrum. VLC beam steering has been stuie in the literature to track mobile users an to improve coverage. However, in some scenarios, it may be neee to track an serve multiple users using a single beam, which has not been rigorously stuie in the existing works to our best knowlege. In this paper, consiering slow beam steering where beam irections are assume to be fixe within a transmission frame, we fin the optimum steering angles to simultaneously serve multiple users within the frame uration. This is achieve by solving a non-convex optimization problem using gri base search an majorization-minimization MM) proceure. Aitionally, we consier multiple steerable beams case with larger number of users in the network, an propose an algorithm to cluster users an serve each cluster with a separate beam. The simulation results show that clustering users can provie higher rates compare to serving each user with a separate beam, an two user clusters maximizes the sum rate in a crowe room setting. Inex Terms Free space optics FSO), Li-Fi, micro-electromechanical systems MEMS), optical wireless communications OWC). I. INTRODUCTION Visible light communications VLC) technology uses light sources such as LEDs for both illumination an wireless ata transfer. In this technology, light-emitting ioes LEDs) act as an antenna an transmit ata to users through moulating light intensity. Due to high frequency of the moulation, the changes in the signal are not perceivable to human eye. Depening on the LED or lens type, VLC light beams can be highly irectional [1], []. Such irectional LEDs can be preferre for proviing higher signal strength at longer istances, ecreasing interference in other irections, or proviing accurate angle of arrival information for localization purposes. VLC networks can provie highly accurate localization information [3], an this location information can be use to steer the light beam towars user location by manipulating the orientation of the light source to further enhance the communications performance. It has been shown in the literature that using a steerable irectional beam maximizes both the overall signal strength an the coverage area []. In [5], tracking users by steering LEDs is shown to provie much higher signal to interference plus noise ratio SINR) in the VLC cell borers, which provies smoother hanovers between ajacent VLC access points APs). However, these stuies assume that each user is tracke with a eicate LED. When the number of users are lower than or equal to the number of steerable beams the steering is relatively simple, because each user can be assigne a single beam that tracks the user. However, it is This work is supporte in part by NSF CNS awar 10. Piezo actuators LED platform Lens a) b) Piezo actuators LED platform Lens Fig. 1: VLC beam steering using piezoelectric actuators. a) The LED an the lens are steere together. b) Only the lens is steere. highly likely that in some cases number of users are higher than the number of steerable beams. In such cases, how to steer the LEDs an istribute time allocation to users is an open problem which has not been aresse in the literature. In this paper, we investigate the optimal beam steering parameters, especially for the case where the number of users are higher than the number of steerable beams. The optimization parameters are the steering angles, the irectivity inex of the LED, an the time allocation of each user. First, we efine the optimization problem for a single LED an more than one user. We propose a near-optimal solution for the nonconvex problem. Secon, we evaluate the case where there are more than one steerable components. As a solution for beam steering an multiple access in this scenario, we propose a k- means clustering base user grouping algorithm. In particular, we cluster the users an assign a single beam to each cluster. Our results show that, clustering an average of two users per beam maximizes the sum rate in a m m room setting with users. II. SYSTEM MODEL In this section, we investigate the methos propose for VLC beam steering with multiple access, an introuce the slow beam steering problem. A. VLC Beam Steering Methos Piezoelectric beam steering is propose in [5] in orer to track the user, improve the signal strength, an provie smoother hanover between ifferent APs. Piezo actuators convert electrical signal into precisely controlle physical isplacement. This property of piezo actuators is use to finely ajust machining tools, camera lenses, mirrors, or other equipment []. Piezoelectric actuators can also be use to tilt LEDs or lenses to steer the beam irection towars user location. In Fig. 1, two ifferent beam steering schemes using

2 a) Single steerable beam. Cluster 1 Cluster b) Multiple steerable beams. Fig. : Steering single an multiple beams to user clusters. piezo actuators are illustrate. In the left figure, whole LED is tilte using a set of piezo actuators, while in the right figure, only the lens is steere. The setup in the right figure makes it possible to change the irectivity of the light beam by shifting the lens to forwar or backwar. In orer to tilt an LED to any angle, two sets of piezo actuators can be use. While one provies steering on one irection, the other provies steering on a perpenicular irection. Another metho to steer LED light is to use micro-electromechanical system MEMS) base mirrors [], [7], [], where irection of beam is controlle by changing the orientation of micro mirrors. In [], a setup with LEDs an MEMS mirrors is presente with steering angles of ±0 with a settling time uner 5 ms, aitionally featuring aaptable beam irectivity. MEMS mirrors are also stuie in the context of steering laser beams for inoor free space optical FSO) communications [9] [11]. In this stuy, without assuming any of the mentione beam steering methos, we consier a VLC AP with limite number of steerable beams that can be steere in a given range. Aitionally, we consier both scenarios where 1) the beam irectivity is fixe, or ) it can be change within a given range. B. Slow Beam Steering for Multiple Access We consier a moel where the beam is steere so that multiple users can access the channel with time ivision multiple access TDMA) without changing the beam orientation every time slot. There are two reasons not to consier changing beam orientation each time slot. The first one is, there will be time loss between each time slot for orientation change. The shortest reporte settling time for LED beam steering is 5 ms [], which is close to the whole TDMA frame length use for Wi-Fi systems. The secon reason is that it is not possible to o such a switching without a flickering effect. Human eye can capture changes up to 00 Hz [1], which means the whole TDMA frame length shoul be uner 5 ms. In this paper we propose a solution where the beam is steere once, an no more steering is neee unless the location an orientation of the users change. If any user movement occurs, new steering parameters are compute an the beam is steere between TDMA frames. Initially, we consier an AP with a single steerable light beam an K users, an Fig. a) shows an example scenario for K = 3. The AP serves all users with TDMA, an kth user is serve with time ratio τ k. We aim at fining the steering angles an LED irectivity inex which maximizes logarithmic sum rate of all users. In 3D moel, we nee two angles to specify the orientation of the beam, which are the elevation an the azimuth angles, enote by α an β, respectively. We can convert these angles to an orientation vector given as n tx = [n xtx), n ytx), n ztx) ] 1) = [cosβ) cosα), sinβ) cosα), sinα)]. The location of the AP is r tx = [x tx, y tx, z tx ]. Likewise, the location an the orientation of the kth user are r k = [x k, y k, z k ], an n k = [n xk), n yk), n zk) ], respectively. Then, the vector from the AP to kth user is v k = r k r tx = [v xk), v yk), v zk) ]. The istance between the LED an the kth user is k = v k. The angle between the LED orientation an v k is enote as φ k, an we can write cosφ k ) = nt txr k r tx ) k = vt k n tx v k. ) The angle between the receiver orientation an v k is θ k, an cosθ k ) = nt k r tx r k ) k = vt k n k v k. 3) We assume a light beam raiation follows the Lambertian pattern [13], with γ being the irectivity inex of the beam. Then, assuming the receiver has a wie fiel of view FOV), we can remove the FOV constraint, an the line-of-sight LOS) channel gain of the kth user can be calculate as h k = γ + 1 π A r cos γ φ k ) cosθ k ) 1 ) k = γ + 1 π = γ + 1 π A r A v T k n tx) γ v T k n k r v k n+3 ) vxk) n xk) + v yk) n yk) + v zk) n zk) ) γ+3 vxk) + v yk) + v zk) v xk) cosβ) cosα) + v yk) sinβ) cosα) + v zk) sinα) ) γ. Then, with a irect current DC) biase Gaussian signal assumption [1], the rate of the kth user is given as R k = B log 1 + rph k) ), 7) where r is the responsivity of photo-ioe an p is the transmit power of the LED, which are both consiere to be constant. The N 0 is the spectral ensity of aitive white Gaussian noise AWGN), an B is the communication banwith. Then the optimal parameters can be foun solving the problem τ, α, β, γ = arg max τ, logτ k R k ), α min α α max, c : 0 β 30, c 3 : γ min γ γ max, c : τ k = 1, where τ = [τ 1,..., τ K ] is the time ivision coefficient vector which sums up to 1. To make sure all users are serve an the resources are istribute fairly, the objective function is the sum of logarithmic rate instea of sum rate [15]. If the logarithm is remove from objective function, a single user gets all time allocation an the beam is steere towars that user, leaving other users unserve. 5) ) )

3 III. PROPOSED SOLUTIONS In this section, we solve the optimization problem in ) for a single steerable beam an multiple users, an subsequently exten the solution to the multiple beams case. A. Solution to the Optimization Problem We can ivie the problem in ) to two sub-problems by separating the objective function as logτ k R k ) = logτ k ) + logr k ). 9) The first problem is τ = arg max τ log K τ k ), subject to c in ). The answer to this trivial problem is τ k = 1/K k. The secon problem is given by α, β, γ = arg max logr k ), ) subject to c 1, c, an c 3 in ). The problem in ) is nonconvex, an any graient base optimization gets stuck in a local optima. This can be seen in the channel gain in ), which has sine, cosine, an exponential functions of optimization parameters. In orer to remove ) from the optimization problem, we follow a gri search base metho an calculate the channel gain for iscrete values of α, β, an γ. To give an example, we separate all available range for α to iscrete values with a small interval δ an α = [α min, α min +δ,..., α max ]. The sizes of α, β an γ are s α, s β, an s γ, respectively. We calculate the channel gain for all possible α, β, an γ combinations an form a column vector h k), whose length is s α s β s γ, an its inices can be mappe back to α, β, an γ. Then, we can impose the optimization problem as ) = arg max log B log 1 +, c : i = 1, 11) i = {0, 1} i, where is a vector same size as h k). The constraints enforce that only one element of is equal to one, an the others are all equal to zero. The vector multiplication results in choosing an element of h. The problem with 11) is the combinatorial nature of the problem ue to the integer constraint i s. In orer to remove the integer constraint, we moify the problem further as ) = arg max log B log 1 + λ 0, 1) i = 1; i 0 where. 0 is the l 0 norm an λ is a positive penalty parameter. Note that the solution set of the optimization problems 11) an 1) are the same. Thus, imposing l 0 penalty still preserves the meaning of the problem, however 1) is still combinatorial ue to l 0 norm. This can be relaxe by replacing l 0 norm with a concave function e.g. l q norm with 0 < q < 1). Upon relaxation, the problem turns out to be non-convex an can be optimize using the majorizationminimization MM) proceure [1] to a near-optimal solution. The basic iea of the MM proceure is to keep the convex part as it is an linearize the concave part of the function aroun a solution obtaine in the previous iteration. The relaxe optimization problem with linearize l q norm is as follows: = arg max log B log 1 + λ γ ) W i t) i, 13) i = 1; i 0, where W i t) = q i + ɛ) q 1 is the weight upate of the majorizer function at iteration t, an ɛ is a small non-negative number ae to overcome the singularity issue; without ɛ, W i t) becomes unefine at i = 0. Intereste reaers may refer [17] an references therein for further etails of MM proceure. Solving 13) returns, an the inex of one in the can be mappe back to the final α, β, an γ values. B. Multiple Steerable Beams In this subsection, we consier a transmitter that can steer multiple beams inepenently, an therefore can track multiple users. In case number of users are higher than the number of beams, users can be separate to clusters, an each cluster can be serve with a single beam as illustrate in Fig. b). In orer to cluster users, we introuce VLC user clustering VUC) algorithm, which is a moifie k-means clustering. Each cluster of users is serve by a single beam, an the VUC algorithm assigns users to the clusters base on the signal strength receive from each beam, an fins the steering parameters for each beam. The algorithm is explaine in etail as follows. We assume there are N steerable beams, an the steering angles an the irectivity inex of nth beam are α n), β n), an γ n), respectively. To initiate the algorithm, we ranomly assign a single user to each cluster i.e. assign first N users to one cluster each). Initially there are some unassigne users, but all users will be assigne to a cluster after the algorithm is complete. We have a total of N clusters, an we repeat the following steps iteratively to fin conclusive clusters an cluster centers. In the first step, we calculate the steering parameters for nth beam, which is α n), β n), an γ n), solving the optimization problem in ) as escribe in Section III.A, for the users in nth cluster. We repeat it for each beam. In the secon step, we assign each user to the cluster whose beam provies the maximum signal strength to the user. We repeat these two steps until the steering parameters stay the same for two consecutive iterations. The clustering process is summarize in Algorithm 1, where Jn) represent the set of users assigne to nth cluster, an h k,n enotes the channel gain between nth beam an kth

4 Sum Rates bps) Sum Rate bps) Sum Rate bps) SBS GA-FBS SBSF GA-FBS an Focus Number of Users a) The AP has a single steerable beam AP Number of Users b) The AP has three inepenently steerable beams. 0 Number of Steerable Beams c) The AP has varying number of steerable beams serving users. Fig. 3: The sum rate of users for single an multiple steerable beams using SBS an SBSF. Algorithm 1 The propose VUC algorithm. 1: Initialize: Assign user n Jn) for n = 1,..., N : repeat 3: for n = 1 to N o : Solve ) for the nth beam an users in Jn) to fin the steering parameters of nth beam α n), β n), an γ n) ). 5: en for : for k = 1 to K o 7: Fin n maximizing h k,n, then assign user k Jn). : en for 9: until Steering parameters stay the same for two consecutive iterations. user. A possible problem with this algorithm is that, a cluster may lose all its users while the algorithm is running. While this is theoretically possible, we i not encounter it in our extensive simulations with up to users an beams. A possible solution to this problem woul be to elete the cluster an leave that LED ile, or assume a ranom orientation for that LED an recalculate the clusters. Restarting algorithm by assigning ifferent initial users to clusters is another solution, since the final clusters epen on the initial cluster centers. IV. SIMULATION RESULTS We conuct computer simulations using MATLAB, where we consier a square room of size m m m. The transmitter is locate in the center at ceiling level, an receivers are istribute at uniformly ranom locations at 0.5 m height, facing upwars. The simulation parameters are as follows: The transmit power p is 1 W, the receiver responsivity r is 1 A/W, the moulation banwith B is 0 MHz, the AWGN spectral ensity N 0 is.5 0 A /Hz, an the receiver surface area A r is 1 cm. Optimization parameter limits are α min = 00, α max = 30, γ min = 1, an γ max = 15, an the q value use for l q norm is 0.1. In Fig. 3a), the sum rate of users are shown when there is only a single steerable beam. We simulate three ifferent scenarios. The first one is labele as, where the beam is not steere an face ownwars with a efault irectivity inex γ = 5. The secon one is labele as slow beam steering SBS), where the beam is steere as escribe in Section II.A. In this scheme we assume the irectivity inex cannot be change, an equal to the efault value. The thir scenario is labele as slow beam steering an focus SBSF), where both beam orientation an irectivity inex are optimize. For comparison, we also consier a genie-aie fast beam steering GA-FBS) approach as an upper boun on the sum rate. In particular, while settling time for steering may be on the orer of 5 ms in practice [], we assume that we can instantaneously steer beams to each scheule user within an iniviual TDMA frame. In this scheme, the LED is completely steere towars a user for the time slot allocate to that user, an we assume steering happens with no time loss. Results in Fig. 3a) shows that when there is a single user, a significant gain on the sum rate can be achieve with steering an focusing. In this case steering angles point to the irection of the user, an the irectivity inex is high, since the user is on the exact irection of the beam. When the number of users increases, the total rate achievable with steering ecreases. The optimization maximizes the sum of logarithm of rates to serve all users simultaneously, therefore the beam orientation oes not point to a single user. Since users are not on the exact irection of the beam, the channel gains of the users ecrease as the number of users increases. The sum rate for GA-FBS schemes o not ecrease, because the LED is steere towars the receiving user at each time interval, an we consier the average rate over large number of user locations. In Fig. 3b), the sum rate of users are shown when the AP has three inepenently steerable beams. The transmit power of these beams are p/3 versus p that was use in Fig. 3a)) for a fair comparison. For this simulation, we consier two ifferent multiple access schemes. The first one is labele as single stream an shown with ashe blue lines, where all beams transmit the same signal to avoi any interference. In this scheme, the signal strength is higher, an the interference is zero. However, all the users are serve with time ivision of a single stream, therefore they are allocate lower amount of time. In the multi-stream scheme shown with soli re lines, all beams transmit a ifferent stream to the users assigne to them. Since Fig. 3b) shows results for an AP with three inepenently steerable beams, multi-stream scheme has three

5 CDF User Rates bps, log scale) Fig. : The CDF of iniviual user rates with three steerable beams an six users. The rates are converte to B scale 0 log R k )). ifferent streams. Users assigne to the same beam are serve with time ivision if the beam is assigne more than a single user. The sum rate ecreases especially for more than three users because each user is not assigne a eicate beam. Due to the use of spatial iversity an higher time allocation to the users, this scheme may offer higher rates than the single stream scheme. As seen in Fig. 3b), the multi-stream beams with focusing ability provie the highest sum rates. The multi-stream beams with no focusing ability o not perform well, especially with lower number of users. In this scheme a beam can cause heavy interference to other users because its irectivity cannot be ajuste as neee. The slight increase in the sum rate with increasing number of users can be explaine by preventing interference by clustering closer users together. With single stream scheme, the sum rate ecreases an approaches to no steering scheme with increasing number of users. Since the ratio of users to the number of beams increases a lot, steering becomes less effective. Note that in Fig. 3b) the sum rates o not ecrease rapily as in Fig. 3a), especially sum rates of multi-stream schemes. This is ue to VUC algorithm clustering users together that can receive high signal strength through a single beam. In Fig., the cumulative istribution function CDF) of user rates are shown for six users an three steerable beams, as in Fig. 3b). The steering provies more uniform istribution of user rates in comparison to no steering scheme, since the optimization problem maximizes the sum of logarithm of rates an provies a fairer resource allocation. In Fig. 3c), the sum rates are shown for users with varying number of inepenently steerable beams. The transmit power of each beam is p/n, where N is the number of beams. SBSF with multi-stream provies the highest sum rate, which is maximize at 5 beams when there are two users per beam on the average. Higher number of beams means better steering accuracy an higher receive signal strength, however it also causes higher interference in multi-stream scheme an lower transmit power per beam. The ieal user count per beam ratio may change base on the size of the room or the total number of users in the room. V. CONCLUSION In this paper we stuy the optimal beam steering parameters for VLC when there are higher number of users than the steerable components. We fin the near-optimal steering angles an LED irectivity for a single LED an multiple users. The results show that steering VLC beams an changing the irectivity can improve the user rates significantly. Although serving a single user maximizes the user rates, multiple users can also be serve using a single steerable beam with a significant sum rate gain over no steering scheme. In case of a multiple steerable beam setting, we cluster users an serve each cluster with a separate beam. This setting allows higher ata rates by clustering close users together an proviing more accurate steering. Future work inclues the transmit power optimization of multiple steerable beams for maximizing the sum rate with a total power limit. REFERENCES [1] Y. S. Eroğlu, I. Güvenç, A. Şahin, Y. Yapıcı, N. Pala, an M. Yüksel, Multi-element VLC networks: LED assignment, power control, an optimum combining, IEEE J. Select. Areas Commun. JSAC), vol. 3, no. 1, pp , Jan. 01. [] T. Komine an M. Nakagawa, Funamental analysis for visible-light communication system using LED lights, IEEE Trans. Consumer Electronics, vol. 50, no. 1, pp. 0 7, 00. [3] A. Şahin, Y. S. Eroğlu, I. Güvenç, N. Pala, an M. Yüksel, Hybri 3-D localization for visible light communication systems, J. Lightwave Technol., vol. 33, no., pp , Nov [] M. B. Rahaim, J. Morrison, an T. D. C. 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