Networked Indoor Lighting Controls with Visible Light Communication

Delft University of Technology Master’s Thesis in Embedded Systems

Kevin Warmerdam

Networked Indoor Lighting Controls with Visible Light Communication

Master’s Thesis in Embedded Systems

Embedded Software Section Faculty of Electrical Engineering, Mathematics and Computer Science Delft University of Technology Mekelweg 4, 2628 CD Delft, The Netherlands

Kevin Warmerdam 1505343 [email protected]

September 10, 2015 Author Kevin Warmerdam ([email protected]) Title Networked Indoor Lighting Controls with Visible Light Communication MSc presentation September 23, 2015

Graduation Committee Prof. Dr. Koen Langendoen (chair) Delft University of Technology Dr. Zaid Al-Ars Delft University of Technology Dr. Ashish Pandharipande Philips Research Dr. Marco Zuniga Delft University of Technology Abstract

Intelligent lighting systems employ dimmable luminaires, photosensors, and occupancy sensors to adapt to daylight and user presence conditions in indoor environments. By providing the illumination required for users and no more, significant energy savings can be made. The state of the art in these lighting systems currently relies on dedicated communication hardware such as radio networking modules. Additionally, the state of the art relies on parameters specific for the environment to be known called the optical channel gains. Although these may be measured in a calibration step while the system is offline, occupants interacting with the environment affect the optical channel gains. Currently, such environment changes can compromise the desired control behavior of intelligent lighting systems. Visible light communication (VLC) presents an alternative to radio communication in networked lighting control systems. It reuses the system’s luminaires as transmitters and its photosensors as receivers. This way, dedicated communication hardware is no longer required. Furthermore, the reception of signals on the optical channel between luminaires and photosensors allows for the estimation of the optical channel gains. By estimating these during communication, the system becomes adaptable to changes in the environment. The proposed system is evaluated against the state of the art in radio- networked lighting control using simulations as well as an experimental testbed. The VLC-networked lighting control system is shown to be resilient against changes to the environment which the state of the art systems are compromised by. iv Preface

In the field of indoor lighting, energy efficiency and user comfort are the two conflicting goals. An optimum between the two exists where the desired light is present, composed of both daylight and just the right amount of artificial light. Since it is not expected of the user to employ a dimming switch and constantly minimize the artificial light, depending on the amount of sunlight entering his or her room, indoor environments are to this day often either fully lit with the maximum power output provided by its overhead lamps or these are entirely turned off. One speculates to what degree users are even willing to switch off lights when leaving such rooms for any period of time. The desired optimum calls for the automation of lighting systems, where luminaires are dimmed based on daylight and occupancy conditions. This thesis proposes that user comfort may be guaranteed while energy costs may be minimized.

The work of this thesis was done at a company, namely Philips Research in Eindhoven. The history of Philips can be traced back to the 19th century, when it began the production of incandescent lamps which would eventually give Eindhoven the identity of ‘Lichtstad’ (City of Light). Where better to explore intelligent lighting systems for a master’s thesis than here?

Before the underlying challenges and novel solutions within intelligent lighting systems are revealed, allow me to express my earnest gratitude to several parties: to Ashish Pandharipande and Marco Zuniga for their supervision from near and far, respectively; to my parents for their prolonged support which has culminated into this conclusion of my studies; and to my girl- friend Lotte, who shared the move to Eindhoven with me as well as every day since.

Kevin Warmerdam

Eindhoven, The Netherlands September 10, 2015

v vi Contents

Preface v

1 Introduction 1 1.1 Motivation ...... 1 1.2 System considerations ...... 1 1.2.1 Sensor placement ...... 1 1.2.2 Lighting control algorithms ...... 3 1.2.3 Optical channel gain ...... 4 1.2.4 Visible light communication ...... 4 1.3 Problem statement ...... 5 1.4 Structure and organization ...... 5 1.4.1 Note on generality ...... 5 1.4.2 Thesis structure ...... 5

2 State of the art 7 2.1 Optical wireless communications ...... 7 2.2 Intelligent lighting ...... 8 2.2.1 Daylight adaptation ...... 8 2.2.2 Occupancy adaptation ...... 9 2.2.3 Networking ...... 9 2.2.4 Environment changes ...... 10 2.3 Contribution ...... 11

3 System model 13 3.1 Networked lighting control ...... 13 3.2 Visible light communication ...... 14 3.2.1 Modulated signal ...... 14 3.2.2 Message interpretation ...... 15 3.3 Scheduling ...... 17

4 Method 19 4.1 VLC link performance ...... 19 4.2 Estimation of control variables ...... 20 4.2.1 Optical channel gain extraction ...... 20

vii 4.2.2 Daylight estimation ...... 22 4.3 Control algorithm ...... 23

5 Results 27 5.1 Performance of VLC ...... 27 5.1.1 Simulation ...... 28 5.1.2 Experimental ...... 31 5.2 Performance of networked lighting control ...... 35 5.2.1 Simulation ...... 35 5.2.2 Experimental ...... 38

6 Conclusions and future work 45 6.1 Conclusions ...... 45 6.2 Future work ...... 46 6.2.1 Internet of Things application ...... 47

A Convex objective function derivation 55

viii Chapter 1

Introduction

1.1 Motivation

In the commercial sector, lighting is responsible for 19% of the total energy consumption [1]. Consider the multitude of buildings in existence and how their indoor lighting is regulated. On average 23% of the total electrical energy consumption in buildings has been shown to go to waste on poor management of occupancy conditions [2], where environments are illuminated while no one is present. The amount of energy that is spent on environments which are already illuminated by daylight is even greater [3]. Signiﬁcant costs may be saved in indoor oﬃce environments with a lighting solution which minimizes its expended energy while satisfying users’ illumination requirements. Intelligent lighting systems address these issues. Lamps, hereafter called luminaires, may be connected with sensors to detect both occupancy and illumination conditions. A system may be designed which, based on the input of these sensors, adapts and dims the luminaires to a desired level of output illuminance and no more.

1.2 System considerations

In the following sections, several key aspects of the proposed intelligent lighting system are introduced. They serve to illustrate concepts and challenges which are revisited in the chapters that follow.

1.2.1 Sensor placement Desired conditions of illumination within workplaces have been addressed in European standards [4]. Minimum levels of illuminance (measured in lux) on the workplane level, for instance on desks, are deﬁned in these standards based on whether the region is occupied or unoccupied. Note that for the purposes of an intelligent lighting system, it is impractical to mount

1 photosensor luminaire

1 2 3

workplane level

Figure 1.1: Example intelligent lighting system conﬁguration, showing the contributions of daylight and a neighboring luminaire to a photosensor.

2 photosensors on workplanes such as desks to measure this local illumination. These could easily become obstructed in daily activities, for example through shadows cast by moved equipment or by the occupants themselves. The photosensors may be placed elsewhere, for example adjacent to the luminaires at the ceiling, containing the workplane in their ﬁeld of view. See Fig. 1.1 for an illustration of this method of mounting. This way, the system becomes less obtrusive and practical. Note however that the distribution of light that has reached the workplane is not identical to what has reached the ceiling-mounted sensor. Hence, a translation will be required between the sensor reading and the illumination of interest at the workplane.

1.2.2 Lighting control algorithms Constrained optimization Two types of control algorithms may be distinguished for the intelligent lighting system. In a classical proportional integral diﬀerential (PID) approach, only the illuminance measured with a photosensor is used [5]. In such case of standalone control the error with respect to a reference illuminance is computed and it is corrected for by the luminaire corresponding to that photosensor. This aims to achieve a decreasing error over consecutive control cycles. Alternatively, a constrained optimization problem may be solved to de- termine an optimal control action. In this case, the desired control behavior is expressed in a cost function which is to be minimized under a set of constraints. For example, the power consumption expressed in terms of the dimming level is minimized under the constraint that the minimum illuminance is achieved. The dimming level which minimizes the cost function without violating the constraints then gives the optimal control action. This approach requires a mathematical model of the lighting behavior and its variables must be known in order to solve the optimization problem. Knowing only the illuminance sensed with a photosensor is insuﬃcient. Es- timations will need to be provided for the variables used in the optimization problem formulation such as the component of daylight contribution at a photosensor.

Networked control Most environments will require multiple luminaires to provide lighting to its entire surface area. In this case, the output light from one luminaire will contribute to the total illuminance in multiple photosensors’ ﬁeld of view, as illustrated in Fig. 1.1. Furthermore, based on occupancy conditions, the reference illuminance may diﬀer across neighboring luminaires. A situation could present itself where a luminaire is unable to reach its reference without the aid of neighboring luminaires.

3 In a networked control algorithm, these eﬀects may be taken into account. Radio communication is an established method of networking in intelligent lighting control systems [6]. The luminaires may be made to communicate their dimming levels and detected occupancy state, for example. If all the luminaires communicate their information to a central point, it is possible to formulate a single optimization problem which takes into account the whole environment.

1.2.3 Optical channel gain

Consider the contribution of artificial light luminaire 1 has on photosensor 2 in Fig. 1.1. This component of the total sensed illuminance depends on the environment. In this case, it depends largely on the color and size of the desk surface. A dimensionless variable called the optical channel gain is used to describe these factors between the luminaire and the photosensor. The optical channel gain may be used in the formulation of an optimization problem. Taking into account the effect of all luminaires on all photosensors makes it possible to consider the total illuminance due to distributions of dimming levels across the luminaires. These optical channel gains may be measured with a manual calibration while the control system is offline. This calibration may be performed by turning on luminaires one by one while there is no daylight and noting the contribution at every sensor. Using these stored values makes the system vulnerable to environment changes, however. By shifting furniture around, by placing or moving an object on a desk, or even by clearing or cleaning it, the calibrated values used in the control algorithm may no longer be correct. In this thesis, robustness is desired against environment changes.

1.2.4 Visible light communication

Visible light communication (VLC) is a method of wireless communication using modulated light from the visible spectrum. The light intensity from an artiﬁcial light source may be varied to encode a message. This modulated light may be detected with a photosensor. If the rate of communication is fast enough, the human eye will not be able to perceive the transmitter as a ﬂuctuating light source [7]. VLC may be used within networked lighting control systems to provide the communication links between luminaires. In this case, the modulated light undergoes the optical channel gain as well. This implies that if the originally transmitted signal is compared with the received signal, the optical channel gain may be estimated from it. These estimations may allow the system to become adaptable to environment changes.

4 1.3 Problem statement

Both networking and continuous estimations of environment parameters are required to attain the best performance in intelligent lighting systems. This thesis proposes a novel lighting control system which uses VLC to address both these issues. Networking is established by reusing luminaires as transmitters and photosensors as receivers. Additionally, VLC allows for the estimation of optical channel gains based on received messages. In order to realize the system, several challenges are overcome:

• A reliable communication scheme is established between luminaires.

• The extraction of optical channel gains from VLC messages is accurately performed.

• An optimization problem which takes constraints for VLC communication into account is formulated to serve as a control algorithm.

• The eﬀect of detected environment changes is translated into an adaptation of the reference illuminance at the luminaires.

By addressing these problems, the lighting system is made adaptable not only to daylight and occupancy conditions, but also to environment changes. Robustness against environment changes through VLC is a novel approach to the state of the art.

1.4 Structure and organization

1.4.1 Note on generality It is important to note that different application environments may require different parameters from the lighting control system proposed in this thesis. Based on the desired duration of a control cycle, the topology and number of luminaires in the environment, or the minimum required signal strength for communication, trade-offs must be made. Because of this, the proposed VLC-networked lighting control system is presented with a level of generality in this thesis. The trade-offs are shown by measures of system performance detailed in terms of these parameters. One example of parameter choices suitable for a wide range of environments is introduced later for evaluations.

1.4.2 Thesis structure The rest of this thesis is organized as follows. In Chapter 2, previous work on both intelligent lighting systems and optical wireless communication are discussed. The state of the art is reviewed and the key contributions of this thesis are noted. Chapter 3 presents a model of the considered system. This

5 includes a description of the proposed networked lighting control system as well as how visible light communication is accomplished. Next, Chapter 4 presents an in-depth look at the algorithms and methods used in the proposed system. The reliability of the proposed communication method is an- alyzed, the estimations of key control variables used in the control algorithm are explored, and the optimization problem for the lighting control law itself is detailed. Results obtained both in simulation and with an experimental testbed are discussed in Chapter 5. The quality of VLC networking and the accuracy of control variable estimation are evaluated. The proposed control algorithm is implemented and its robustness against environment changes is demonstrated. Lastly, conclusions are drawn from the work in Chapter 6 and possibilities for future work are listed.

6 Chapter 2

State of the art

This chapter presents the state of the art in the two ﬁelds on which this thesis builds, namely optical wireless communication and intelligent lighting systems. The previous work in optical wireless communication, of which visible light communication is a subset, is detailed in Section 2.1. Section 2.2 describes the previous work on intelligent lighting and shows how visible light communication may improve upon it. Lastly, the contributions of this thesis are listed in the context of this state of the art in Section 2.3.

2.1 Optical wireless communications

As a technology, optical wireless communications (OWC) can be traced back to the photophone invented by Alexander Graham Bell [8]. Here, speech was modulated over a beam of light by sound waves acting upon a mirror. A century later, optical communication gained renewed interest, where the ﬁrst LED-based OWC was introduced in 1979 by Gfeller and Bapst [9]. Here, diﬀusely scattered infrared light was used in an indoor environment as a broadcast channel which did not require a line of sight between transmitter and receiver. Besides infrared, OWC may also encompass the ultraviolet or the visible wavelengths of light. Its applications include indoor area networking as well as outdoor free space communication, where its advantages argue for an alternative to radio communication or a hybridization of the two methods [10]. In the application environment of indoor lighting systems, the visible light spectrum may be used. LED luminaires used for lighting may be reused as transmitters. This subset of interest of OWC is called visible light communication (VLC). The term applies to short range communication using the light spectrum from 380 nm to 780 nm [11]. VLC has been considered for internet networking hybridization because of the high luminous intensity already required in indoor environments [12]. By reusing sources of indoor lighting, high signal-to-noise ratios may be

7 achieved while installing dedicated high-power transmitters would not be necessary. The implementations of VLC with the highest data rates rely on the use of multiple independent LEDs within a single transmitter. For example, data rates of Gbit/s in VLC announced by Zeng et al. [13] used an array of LEDs in line of sight communication. When common LED luminaires are used for VLC, relatively low data rates may be expected. When VLC is applied with sources which must also act as luminaires for the purposes of lighting, trade-oﬀs arise. Communication signal strength and bandwidth are constrained by the requirements of light quality and the properties of commercial LEDs [14]. For example, it may be desired for the average illuminance perceived by users to remain constant throughout communication. Ntogari et al. [15] demonstrated a way to accomplish this by consolidating advanced modulation schemes in VLC with pulse-width modulation dimming support. An IEEE standard has since been developed to describe a PHY and MAC layer protocol for VLC communication, deeming it suitable for short-range support of multimedia services [16]. Manchester coding is suggested in this protocol to accomplish constant average illumination in simpler amplitude modulation schemes. In Manchester coding, one bit is represented by two symbols in either the order ‘10’ for a ‘1’ bit or ‘01’ for a ‘0’ bit [17]. This way, the average output power is made equal for either bit representation. This thesis explores whether the luminaires and photosensors used in lighting control may be reused as transmitters and receivers for VLC. This way, costs are saved on dedicated communication hardware. Messages may be expected to consist of a limited number of variables measured locally. Since control cycle durations need not be subsecond in order to satisfy lighting behavior, communication for the purpose of lighting control will then require relatively low data rates. Therefore, a simple amplitude modulation scheme using Manchester coding is considered. Note however that there is no line of sight between luminaires and photosensors in the ceiling-mounted conﬁguration shown previously in Fig. 1.1. Despite this, communication between luminaires must be reliable.

2.2 Intelligent lighting

2.2.1 Daylight adaptation Even before the widespread adoption of LED lamps, demonstrations showed significant energy savings were possible by implementing lighting control strategies. With fluorescent lights, energy savings of over 50% were accomplished in a commercial office building by Rubinstein et al. [18] with dimming schemes based on adaptation to daylight conditions. Photosensors were used here to perform standalone closed-loop control on ceiling-mounted

8 lighting ﬁxtures. In later years, the so-called “lighting revolution” introduced solid-state lighting. Without the implementation of intelligent dimming schemes, energy consumption was reduced by 50% as well [19]. Since this time, the state of the art in lighting control has been furthered using LED luminaires and various control strategies.

2.2.2 Occupancy adaptation Aside from daylight conditions, occupancy conditions can also be taken into account in control strategies. In this case, energy spent to illuminate empty environments can be saved. Miki et al. [20] have considered seat sensors for the automated detection of occupancy conditions. Here, an additional 30% increase in energy eﬃciency by accurately detecting user presence conditions is reported. The measurement of occupancy conditions has further been considered using ultrasound [21], passive infrared sensors [22], or wireless user-held devices [23].

2.2.3 Networking Control strategies may implement cooperation between networked luminaires as opposed to a standalone algorithm for independent luminaires. Without networking, problems arising from a standalone controller have been shown [22]. Here, local underillumination follows from situations where two neighboring zones have different illuminance goals because of different occupancy conditions. The occupied zone requires stronger contributions from its neighboring luminaires but these output less power because they detect no occupancy. Wen and Agogino [24] [25] have considered a wireless sensor network to collect information about workplane illuminance and user preference. A centralized approach was used. In this case, a central controller receives all information about the system through communication. It computes a new configuration of dimming levels based on all the available information. These dimming levels are then communicated to actuators. A networked distributed approach was presented by Pandharipande and Caicedo [26] where information is shared across asynchronous luminaires. Here, each luminaire solves for an optimization independently while taking neighbors’ contributions and detected occupancy into account. The same authors have presented similar systems where control is instead centralized by solving for an optimization which takes all sensors and luminaires into account [22, 27, 28]. In these works, the power consumption of the distributed approach is shown to be sub-optimal. Assuming a feasible solution to the problem exists, the centralized optimization is able to find the optimum solution [26]. This thesis therefore builds on the centralized approach and will

9 require networking capabilities. Networking may be achieved in different ways. Work by Miki et al. [29] has shown the complexity of wiring networks between all luminaires. In- stead, wireless communication is attractive for this application. Wen and Agogino further argue for ease in retrofitting older lighting systems by em- ploying small sensors and actuators, each of which uses a radio communication module [24] [25]. Pandharipande and Caicedo [26, 22, 27, 28] considered systems with photosensors as well as occupancy sensors co-located with ceiling-mounted LED luminaires. The impracticality and cost of mounting sensors on the workplane level is thereby taken into account and only one radio communication module is required per sensor-luminaire pair. As discussed previously, VLC may replace radio networking in intelligent lighting systems. By reusing luminaires and photosensors as transmitters and receivers, the costs of dedicated communication hardware are saved in the system proposed by this thesis. The effects of wireless networking in an intelligent lighting system have been investigated. A ZigBee wireless network was implemented and shown to cause delays in the settling time of luminaires’ dimming levels due to packet losses [27]. The quality of the VLC link will therefore be investigated in this thesis and probability of packet errors quantified. Miki et al. have previously considered using VLC in an intelligent lighting system [30, 31]. Here, VLC is used to identify and locate remote sensors placed on the workplane. These sensing devices can be moved by users and may emit LED light to communicate desired local illumination to a luminaire above it. Instead, this thesis proposes the use of VLC while re- taining a practical configuration of luminaires and sensors mounted at the ceiling. No additional devices or user input will be required. Furthermore, communication will not affect the perceived illumination in the room.

2.2.4 Environment changes State of the art methods used in the above works introduce a cost function to be minimized within the lighting system [22, 26, 27, 28]. Solving for these optimization problems forms the control actions in these systems. In this formulation, a parameter of the environment is considered to be explicitly known, namely the optical channel gains between all luminaires and photosensors. These systems rely on a calibration step while the system is oﬄine to obtain these parameters and assume the environment remains unchanged. A method has been suggested by Caicedo et al. [32] for estimating changing optical channel gains during control operations of a distributed lighting system, under the assumption that daylight does not change across control cycles. This method requires changes in dimmming levels to occur before an estimation can be made. By using VLC, this thesis explores the possibility of directly measuring

10 the optical channel gains instead. The same optical channel relevant for control is here used for communication. A method is devised for extracting the optical channel gains from every message received at every luminaire. This way, the values used in an optimization problem may be updated based on changes to the environment at every control cycle.

2.3 Contribution

This thesis proposes a networked lighting control system which implements visible light communication. Powerful potential VLC transmitters are already present in the form of the system’s LED luminaires. By using modulated light emitted from the luminaires themselves at a rate faster than the human eye can perceive, messages may be transmitted which can be interpreted with the photosensors. This method fulfills the required communication for the system without any additional hardware. A centralized control algorithm is proposed because this method has the potential to find an optimal distribution of dimming levels for the whole environment. Furthermore, the unobtrusive, practical and cost efficient configuration with ceiling-mounted sensors is considered. This implies no direct line of sight is available between any source and destination in VLC. This thesis verifies that communication is reliable despite this. Additionally, this thesis explores whether it is possible to use the received signal in communication to extract the optical channel gains in the network. State of the art lighting control algorithms rely on accurate estimations of these values. This thesis shows that the state of the art control behavior is compromised when environment changes occur. By being able to measure the optical channel gains during control operations, the system proposed in this thesis can detect environment changes. The reference illuminance attained at the ceiling level may be adapted based on changes observed. This way, the system may adapt not only to occupancy and daylight conditions, but also to changes in the environment.

11 12 Chapter 3

System model

In this chapter, the proposed system is introduced. The characteristics and setup of the networked lighting control are detailed in Section 3.1. Sec- tion 3.2 describes how messages are modulated and demodulated using luminaires and photosensors. Lastly, Section 3.3 brieﬂy describes how the network may be scheduled.

3.1 Networked lighting control

Consider an indoor office space with N ceiling-mounted luminaires whose dimming levels may be independently adapted through a local embedded computer. Jointly placed at each luminaire is a photosensor with a downward- facing field of view. Under fluctuating daylight conditions, the desired control behavior guarantees a constant minimum illuminance at the workplane level below the luminaires while minimizing their power consumption. This behavior may be approximated by adapting the dimming levels based on information from the photosensors at the ceiling. A centralized control algorithm is considered. In this setup, a central controller receives messages from each luminaire before computing the optimal dimming levels for the next cycle. This controller then communicates back to all the luminaires these dimming levels to be used. The desired level of illumination at the workplane level may vary based on occupancy conditions. European norms recommend an average illuminance of 500 lux for occupied zones in office environment, and 300 lux for unoccupied zones [4]. To incorporate this, passive infrared (PIR) occupancy sensors are used in the lighting control system to detect local occupancy conditions. One PIR sensor is mounted at each luminaire with a field of view similar to the co-located photosensor. For the two individual levels of desired average workplane illuminance, a step of manual calibration is required to translate this requirement to a reference illuminance measured at each sensor.

13 3.2 Visible light communication

Visible light communication is implemented as the means of communication between luminaires. By modulating its own emitted light intensity, a luminaire can encode messages which may be interpreted with the photosensors located at other luminaires. Note that during transmission, the average luminous power output of a luminaire must remain constant, corresponding to the current desired dimming level. Amplitude modulation is then considered with Manchester coding to retain the average power output [11]. Furthermore, guidelines to avoid harmful ﬂickering of the light sources for the human eye are followed by determining a minimum communication speed of 140 baud [7]. In the following sections, a mathematical model is presented to describe visible light communication in the lighting control system. All the steps to recover a transmitted bit sequence based on the sensed signal at a photosensor are explained. These derivations will be used in Chapter 4 to evaluate the performance of the VLC link, to formulate a method of extracting optical channel gains from a received message, and to estimate daylight contributions at photosensors.

3.2.1 Modulated signal The signal received at a photosensor may be described in terms of the underlying contributions. In an environment with N luminaires capable of VLC, the sensed signal at receiving luminaire m within the scope of one received packet is N X ym(t) = dm(t) + vm(t) + (αm,nβm,n(un + ∆nbn(t))) ∗ hm,n(t), (3.1) n=1 where n = 1, ..., N, m = 1, ..., N, dm(t) is the daylight contribution at destination m over time, and vm(t) is the modeled additive white Gaussian noise 2 (AWGN) contribution with vm(t) ∼ N (0, σm). Furthermore, hm,n(t) is the normalized impulse response of the channel between source n and destination m, αm,n is the optical channel gain from source n to destination m, and βm,n is the maximum illuminance contribution from source n to destination m deﬁned by β = Pn , where P is the maximum luminous power output m,n Am n of source n and Am is the sensing surface area of the sensor at destination m. ∆min ∆min The dimming level un at source n takes values in the range [ 2 , 1− 2 ], and ∆n is the modulation depth used ranging [∆min, 1], with ∆min being the minimum modulation depth for reliable communication. The message contribution is bn(t), deﬁned by  2L  P t 1 MjΠ( T − j + 2 ) if n is the transmitting luminaire bn(t) = j=1  0 otherwise,

14 1 1 where L is the message length in bits, Mj is the jth symbol ranging {− 2 },{ 2 } in the Manchester coding of the bit sequence corresponding to the message, T is the symbol period, and Π(t) is the rectangular function

1 1 if |t| ≤ 2 Π(t) = 1 0 if |t| > 2 .

3.2.2 Message interpretation For the following theoretical analysis of how a bit sequence is recovered from the modulated signal, the assumption is made that hm,n(t) = δ(t), where δ(t) is the Dirac delta function. In this case, (3.1) may be rewritten as

N X ym(t) = dm(t) + vm(t) + αm,nβm,n(un + ∆nbn(t)). (3.2) n=1

At receiving luminaire m, the signal ym(t) is sampled at a frequency fs and processed using a matched ﬁlter which computes for each sample s

2T fs−1 1 X s + k k ρm[s] = ym g , (3.3) 2T fs fs fs k=0 where g(t) is the template signal deﬁned by

1 if t ≤ T g(t) = −1 if t > T,

corresponding to the Manchester coding of a ‘1’ bit. For simplicity, it is assumed that 2T fs ∈ N here and in the rest of this work. In the noiseless case, assuming un and dm are constant in the scope of a bit period, the average sensed illuminance in (3.2) during a ‘1’ Manchester symbol from transmitting luminaire p is

N 1 X y+ = d + α β ∆ ( ) + α β u (3.4) m m,p m,p p 2 m,n m,n n n=1 and the average value during a ‘0’ Manchester symbol is

N 1 X y− = d + α β ∆ (− ) + α β u . (3.5) m m,p m,p p 2 m,n m,n n n=1 Using (3.4) and (3.5), in the case of a transmission of a ‘1’ bit at matching sample s? from transmitting luminaire p, the output of the matched ﬁlter is 1 1 ρ [s?] = (y+ − y−) +v ˜ = α β ∆ +v ˜ , (3.6) m 2 m 2 m,p m,p p m

15 40

35 ) t ( 30 m y

20 0 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.1 t (a) Received signal with sensor.

0.5 ) t

( 0 g

−0.5

−1 −0.01 0 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 t (b) Template signal for matched ﬁlter.

1.5

0.5 ] s [

m 0 ρ −0.5

−1

−1.5 ? 0 s 500 1000 1500 2000 2500 3000 s

1.5

0.5 ] i [

m 0 µ −0.5

−1

−1.5 1 2 3 4 5 6 7 8 9 10 11 i

(d) Matched ﬁlter output sampled down to bit rate.

Figure 3.1: Example of signals in noisy message interpretation for T = 5 ms, fs = 32 kHz, and L = 8 bits.

16 wherev ˜m represents the reduced noise due to the matched ﬁlter:v ˜m ∼ N (0, 1 σ2 ). Equivalently, a ‘0’ bit would result in the value −ρ [s?]. 2T fs m m 1 The matched ﬁlter output is sampled down to the bit rate 2T to obtain

µm[i] = ρm[2T fs(i − 1)] for i = 1, ..., L. (3.7)

Fig. 3.1 illustrates how the sequence µm[i] is obtained from ym(t), in- cluding the intermediate steps described above. Note that it is necessary to employ the correct sampling phase on a received signal. This is called timing recovery. A method such as the Gardner algorithm accomplishes this [33]. The values of µm[i] are compared with a zero-level threshold in the slicer. Thus, all positive values are interpreted as ‘1’ bits and all negative values are interpreted as ‘0’ bits. These values will also be used to make an estimation of the optical channel gains αm,n. The knowledge of all optical channel gains in the environment will be used to make an estimation of the daylight contributions dm at the sensors. The details of how this is achieved are discussed in Chapter 4.

3.3 Scheduling

Assuming one luminaire is capable of reliable communication with all other luminaires in the environment, a time division multiple access (TDMA) schedule may be regulated from this luminaire. Call this luminaire the master luminaire. The same luminaire may also act as the central controller for the lighting control system. In TDMA, each luminaire in the environment is assigned a unique time slot within one control cycle by the master luminaire. In its time slot, a luminaire may transmit its VLC message. This way collisions in messages are avoided. It is important to note that the proposed VLC-networked lighting system is presented in this thesis with a level of generality. Environments with diﬀerent luminaire topologies may require diﬀerent scheduling methods however. This is discussed further in Chapter 6. For completeness, one possible implementation is provided below. For luminaires to adhere to their time slot, clock synchronization is required between them. To achieve this, a method such as the Berkeley algorithm may be integrated with the existing message structure. The Berkeley algorithm synchronizes distributed devices by communicating timestamps to a master device [34]. The master device then computes an average clock time and communicates back the adjustment each device must make to its internal clock. Accordingly, luminaires can be made to include a timestamp in the VLC message transmitted every control cycle. The master luminaire compares the transmitted timestamps with its own, taking into account the known duration of communication, and stores them. After each luminaire has transmitted in a control cycle, the master luminaire

17 One control cycle

Each luminaire transmits Master luminaire transmits Sense its own measurements all control actions

1 ......

2 ......

...... luminaire

N ......

0 1 2 ... N N+1 ... 2N−1 scheduling slot

Figure 3.2: TDMA scheduling for N luminaires in centralized control. computes the control actions for the next cycle as well as an average clock time. Each following message from the master luminaire then contains both the control action to be used by the destination luminaire as well as an adjustment to be applied to its internal clock. Fig. 3.2 illustrates one control cycle of the proposed TDMA scheduling. Here, luminaire 1 is the designated master luminaire. In the case of a centralized control algorithm, the information contained in the VLC message transmitted by each luminaire now includes its iden- tiﬁer m, a timestamp, the most recent estimations of αm,n for all n, the modulation depth used ∆m, and a measurement of the average ym(t) for the current control cycle.

18 Chapter 4

Method

This chapter provides a detailed analysis of the proposed system’s func- tionalities. The control behavior relies on the accuracy of the information provided for the constrained optimization problem. Both optical channel gains between all luminaires and photosensors and daylight contributions at all photosensors are used in the formulation of its cost function and constraints, as is shown below. Section 4.1 ﬁrst describes the performance of VLC communication. Next, Section 4.2 details the method used to extract optical channel gains from received VLC signals and the method used to estimate daylight contributions at sensors. Lastly, Section 4.3 formulates the optimization problem which may be solved to obtain optimal control actions across all luminaires in the system.

4.1 VLC link performance

The performance of VLC networking may be expressed in the probability of a packet error. This probability depends on the parameters introduced in Chapter 3 such as the modulation depth used and the amount of noise. In (3.6), noise conditions captured withv ˜m may result in a bit error when ? a negative value occurs for ρm[s ] while a ‘1’ bit was present, or when a positive value occurs while a ‘0’ bit was present. The bit error ratio (BER) in a message from source p to destination m may be expressed in terms of 2 the AWGN power σm by [35]

1 2 αm,pβm,p∆p BERm,p = 1 − Φ( q ) 1 σ2 2T fs m √ T f α β ∆ = 1 − Φ( s√m,p m,p p ), (4.1) 2σm

19 where Φ(x) is the cumulative distribution function of the normal Gaussian distribution. Assuming constant message lengths L and assuming that no error correcting technique is used, the packet error ratio (PER) between source p and destination m in the VLC setup may be characterized by

L PERm,p = 1 − (1 − BERm,p) √ T f α β ∆ = 1 − Φ( s√m,p m,p p )L. (4.2) 2σm

This expression for the probability of a packet error relates the performance of communication in the proposed system. The system’s parameters may be chosen in such a way that the PER is minimized. Trade-oﬀs arise here. For example, increasing T lowers the communication speed and can improve reliability. However, this will lead to longer control cycle durations and longer periods of waiting before dimming levels are updated.

4.2 Estimation of control variables

By using VLC, the optical channel gain αm,n may be estimated at destination m based on a message received from n. The maximum illuminance contribution βm,n is a known constant of the system and the original modulation depth ∆n used is communicated in the message itself. This means (3.6) may be used to recover the optical channel gains αm,n based on the ? matched ﬁlter output ρm[s ] as shown below. Furthermore, if all the optical channel gains and all the current dimming levels used are known, an estimation may be made of the contribution of daylight dm at every sensor, given its total measured illuminance. If both these estimations are made, an optimization problem may be formulated to obtain a control action um, as will be shown in Section 4.3. Fig. 4.1 shows a ﬂowchart combining the message interpretation methods from Section 3.2.2 with the methods described here.

4.2.1 Optical channel gain extraction

Consider a VLC message sent from source p. The message contents include ∆p used at the source. Any luminaire m in range may make an interpretation of the transmission. The system’s βm,p is considered known. Assuming that un for all luminaires n and dm are constant in the scope of this message and that no bit errors occur in detection, an estimationα ˆm,p can be made from the matched ﬁlter output at matching sample s? in (3.6) as

? 2ρm[s ] αˆm,p = . (4.3) βm,p∆p

20 Daylight Interpreter estimation

Slicer

C co e Matched filter Gain extraction n nt tr ra ol l ler L si um de i na Photosensor ire si de

Artificial light & Daylight

Figure 4.1: Flowchart of control variable estimations.

The error in the optical channel gain extraction with (4.3) is

2˜vm 2 2 αˆm,p − αm,p = ∼ N (0, 2 2 σm). (4.4) βm,p∆p T fsβm,p∆p

In the above method, the optical channel gain extraction occurs based on a single bit. One extraction may also be performed over the scope of the entire packet to reduce the error. In this case the estimation is made by

L 2 X αˆ0 = bit[i]µ [i], (4.5) m,p β ∆ L m m,p p i=1 where 1 if bit i is ‘1’ bit[i] = −1 otherwise. The error in the optical channel gain extraction with (4.5) is

0 2 2 αˆm,p − αm,p ∼ N (0, 2 2 σm). (4.6) T Lfsβm,p∆p

Expressed as an expected absolute proportional error, the error correspond-

21 ing to (4.6) is

0 0 αˆ αm,p − αˆ E 1 − m,p = E m,p αm,p αm,p 1 0 = E |αm,p − αˆm,p| αm,p r s 1 2 2 2 = 2 2 σm αm,p π T Lfsβm,p∆p 2 = √ σm. (4.7) αm,pβm,p∆p πT Lfs

This expression shows the performance of optical channel gain extractions in terms of the system parameters. Similar design trade-oﬀs are seen here as in the VLC link performance of Section 4.1.

4.2.2 Daylight estimation

In the case of a centralized control algorithm, the central controller obtains 0 estimates of the optical channel gainsα ˆm,n for all destinations m and all sources n after each luminaire has transmitted its VLC message. The messages also containy ¯m, the sample average of ym(t) obtained in a time slot in the beginning of the control cycle, where no VLC messages were transmitted. Also, all dimming levels un used in the current control cycle are stored at the central controller. Lastly, the system’s maximum illuminance contributions βm,n are again considered known. At a luminaire m, the average daylight contribution d¯m during the measurement ofy ¯m of duration 2TL is given by

N X d¯m =y ¯m − v¯m − αm,nβm,nun, (4.8) n=1 where 2T Lfs−1 1 X k y¯m = ym 2T Lfs fs k=0 is the sample average of ym(t) at sampling frequency fs andv ¯m represents the remaining noise contribution:v ¯ ∼ N (0, 1 σ2 ). m 2T Lfs m An estimation of the daylight contribution dˆm can be made by

N ˆ X 0 dm =y ¯m − αˆm,nβm,nun. (4.9) n=1

22 The error in daylight estimation in (4.9) is given by

N ˆ ¯ X 0 dm − dm =v ¯m + (ˆαm,n − αm,n)βm,nun n=1 N 1 X 2un 1 ∼ N (0, σ2 + ( )2 σ2 ) 2T Lf m ∆ 2T Lf m s n=1 n s N 1 1 X 2un ∼ N (0, σ2 + ( )2σ2 ) 2T Lf m 2T Lf ∆ m s s n=1 n N 1 X 4u2 ∼ N (0, (1 + n )σ2 ). (4.10) 2T Lf ∆2 m s n=1 n The expected absolute error in daylight estimation corresponding to 4.10 is v √ u N 2 u 1 X 4u2 E|dˆ − d¯ | = √ t (1 + n )σ2 m m π 2T Lf ∆2 m s n=1 n v u N u 1 X 4u2 = t (1 + n )σ . (4.11) πT Lf ∆2 m s n=1 n

These estimated daylight contributions dˆm are computed by the central controller for all luminaires m. With these, and the optical channel gains, all the information has been provided to compute optimal dimming levels to be used in the next control cycle.

4.3 Control algorithm

Consider A the N × N matrix containing the products of the extracted 0 optical channel gainsα ˆm,n and maximum luminous received power βm,n from source luminaire n to receiving luminaire m, as

 0 0  αˆ1,1β1,1 ... αˆ1,N β1,N  . .. .  A =  . . .  . 0 0 αˆN,1βN,1 ... αˆN,N βN,N

Also let u be the vector containing all luminaires’ dimming levels um, d be the vector containing all estimated daylight contributions dˆm, and l be the vector containing the reference illuminance at each sensor lm, as       u1 dˆ1 l1  .   .   .  u =  .  , d =  .  , l =  .  . ˆ uN dN lN

23 Lastly denote 0 and 1 the N × 1 vectors 0 1 . . 0 = . , 1 = . . 0 1 Note once more that although the photosensors are mounted at the ceiling due to practicalities, the constant level of illuminance is desired at the workplane below it. Two different levels of average workplane illumination are needed: 300 lux for unoccupied zones and 500 lux for occupied zones [4]. To account for this, the system is calibrated once after installation with tem- porary workplane sensors while there is no contribution of daylight in the environment. During this calibration, two configurations of dimming levels are manually chosen which match these levels of workplane illumination, u300 and u500, and these are stored. A mapping of workplane illuminance is approximated with these stored dimming levels. To handle environment changes affecting the average workplane illumination, the reference illuminance l is updated each control cycle by computing for each element

( PN 0 300 n=1 αˆm,nβm,nun if the zone under m is unoccupied lm = PN 0 500 (4.12) n=1 αˆm,nβm,nun if the zone under m is occupied. The desired control behavior results from the least possible error with respect to the reference illuminance. By minimizing the Euclidean norm of the error ||Au + d − l|| for some optimal u? this is achieved and the power consumption is minimized as well. The solution to the minimization of ||Au + d − l|| is equivalent to the solution of the minimization of ||Au + d − l||2 = (Au + d − l)T (Au + d − l).

Solving for this minimization alone does not guarantee dimming levels un ∆min ∆min within the permitted range [ 2 , 1 − 2 ]. Also, the system must guarantee the minimum illumination is met, i.e. overillumination errors may occur while underillumination errors may not. The optimization problem may then be expressed as: u? = arg min(Au + d − l)T (Au + d − l) u Au + d > l (4.13) subject to ∆min ∆min 2 1 ≤ u ≤ (1 − 2 )1. The formulation in (4.13) may be rewritten in standard form [36]. The optimization problem then becomes u? = arg min(Au + d − l)T (Au + d − l) u  −Au − d + l ≤ 0  (4.14) ∆min subject to 2 1 − u ≤ 0  ∆min u − (1 − 2 )1 ≤ 0.

24 This is a convex quadratic minimization problem with linear inequality constraints. A derivation for the objective function’s convexity is provided in Appendix A. It is attractive to use a method of quadratic programming to solve the optimization problem, such as the interior point or barrier method [36]. This solution for u gives the control action at every control cycle.

25 26 Chapter 5

Results

This chapter features evaluations of the proposed system. Both simulations and an experimental testbed are employed. Section 5.1 details several results concerning the VLC aspect of the system and discusses them. This includes evaluations on packet errors, optical channel gain extractions, and daylight estimation. Section 5.2 explores the control behavior of the proposed system and compares its performance to that of a non-VLC state of the art approach. The eﬀect of environment changes are shown to compromise the control behavior of the state of the art systems, while the proposed system is robust against them.

5.1 Performance of VLC

The communication link performance detailed in Section 4.1 is evaluated as well as the estimation methods for optical channel gain and daylight contribution detailed in Section 4.2. Simulations are employed to evaluate the mathematical models established to describe the system. An experimental testbed is also used to evaluate the proposed VLC networking under real-world conditions. In both cases, the same system parameters are used:

• The bit rate is set at 1000 bits/second, thus T = 500 µs.

• The sampling rate of the sensors is fs = 32 kHz. • The message length is L = 512 bits.

These parameters are suitable to most indoor environments. The relatively low-rate communication still allows for regular updates of dimming levels. For instance, with N = 8 luminaires communicating back and forth with the central controller, control cycle durations can be kept under 10 seconds. Further denote

1 2 ( 2 αm,pβm,p∆p) Channel SNRm,p = 2 (5.1) σm

27 as the ratio of signal power to noise power at the input of the matched ﬁlter at destination m when source p is transmitting.

5.1.1 Simulation

In Chapter 4, the mathematical expressions (4.2) and (4.7) were presented which described trade-offs between system parameters and the quality of VLC communication. These expressions to aid in the design for specific environment topologies are evaluated here. In simulation, (3.2) is used to model a received VLC signal. One source and one destination are considered under different channel noise conditions. Messages consist of random bits following a uniform distribution. Because the performance in terms of system parameters are of interest, the timing recovery of the detected signal is assumed to be ideal.

Packet error ratio

Ten distinct Channel SNRs are chosen and 10 000 packets are simulated for each one. Message interpretation occurs as described in Section 3.2.2. A packet is considered erroneous when at least one of its bit is incorrectly interpreted. The PERs found for these messages are compared with the theoretical description in (4.2). Fig. 5.1 shows the simulated detection method matches well with what was described in theory. Electrical noise conditions, the modulation depth used, and the distance between source and destination contribute to the Channel SNR shown in Fig. 5.1. The performance of the system’s VLC link has been characterized with this result. A further experimental result is required to conﬁrm whether the shown Channel SNRs are below the expected conditions in communication between luminaires without line of sight. To have the impact of packet losses on control be acceptable, consider the PER must be less than 1%.

Optical channel gain extraction

Again, ten distinct Channel SNRs are chosen and 10 000 packets are simulated for each one. The method for optical channel gain extraction described in Section 4.2.1 is applied to each packet. The absolute proportional errors αˆ0 in these gains |1 − m,p | are calculated and compared with the expected αm,p theoretical value in (4.7). Fig. 5.2 shows that the mean error found per distinct SNR matches the expected value well. This result shows that the error in optical channel gain extraction is relatively small. Comparing with Fig. 5.1, it is reasonable to say that so long as communication is reliable (PER < 1%), the optical channel gain extraction αˆ0 are accurate as well (|1 − m,p | < 1%). αm,p

28 0 10 Theoretical Simulated

−1 10 PER

−2 10

−3 10 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 Channel SNR

Figure 5.1: Theoretical and simulated PER by SNR for T = 500 µs, fs = 32 kHz, and L = 512 bits.

29 0.1 Theoretical 0.09 Simulated

0.08

0.07 6 - - - 0.06 0 m,p m,p ˆ α α 0.05 − 1 - - -

5 0.04 E

0.03

0.02

0.01

0 0 0.2 0.4 0.6 0.8 1 Channel SNR

Figure 5.2: Theoretically expected and simulated absolute proportional error in gain extraction by SNR for T = 500 µs, fs = 32 kHz, and L = 512 bits.

30 windows 5

4 1 3 5 7

3 y [m]

2 4 6 8 1

0 0 1 2 3 4 5 6 7 x [m]

Figure 5.3: Overview of experimental testbed and room layout with desks, ceiling-mounted LED luminaires, and photosensors indicated.

5.1.2 Experimental To further evaluate the proposed VLC system, it is implemented on an experimental testbed to introduce realistic conditions found in practice. The testbed consists of N = 8 LED luminaires mounted on the ceiling as a 2- by-4 grid within an in-use oﬃce room. The distance between the centers of any two neighboring luminaires on the grid is 2.1 meters. The oﬃce is furnished with desks, monitors, chairs, and cabinets, which result in a variety of optical channel gains in the environment. The north side of the room features windows all along its length which can be occluded with blinds. An overview is shown in Fig. 5.3. Co-located sensors at each of the luminaires are read out with a data ac- quisition (DAQ) device which is connected to a central computer. Dimming levels for each of the luminaires are described from the same computer in a signal with an equal number of samples to what is sensed.

Packet error ratio The effect of realistic components used in the system is investigated with the testbed. The effect of other factors on communication performance are minimized. The blinds are closed to remove fluctuating daylight conditions.

31 Also, the timing recovery during detection is made ideal through the central computer by applying a synchronized sampling phase. One combination of source (luminaire 1) and destination (luminaire 4) is selected and a range of 11 unique SNRs are used. To obtain different SNRs, the signal strength is varied by changing the modulation depth ∆n used in transmission. For each distinct modulation depth, 400 packets are communicated. The erroneous packets are counted to conclude a PER. To measure the SNR, a period of no communication precedes each message. During this time, noise power PÑ is measured. Then, during the message, the combined power P˜S+N is measured. The Channel SNR is then estimated ˜ ˜ by PS+N −PN . Per unique modulation depth used, the measured SNRs for PÑ the packets are averaged. Note that the PER result shown in Fig. 5.1 was obtained by simulation with the VLC received signal model in (3.2), which assumed a Dirac delta function for the channel impulse response, or h(t) = δ(t). In practice, the PER is affected by a realistic channel impulse response. Factors such as the response time of the photosensor shape the signal, causing intersymbol interference. Such a photosensor may be modeled as a low-pass filter with a decaying exponential as an impulse response [37]. A simulation where this modeled component is included is then also considered and compared with the result obtained through the testbed. In this case, the channel −t 1 τ −4 impulse response is modeled as h(t) = τ e with τ = 10 and (3.1) is used as a received signal model. Other than this, the setup for this additional simulation is identical to the PER by SNR simulation found in Section 5.1.1. Now consider Fig. 5.4, where the earlier theoretical model, the additional simulation with a low-pass response, and the result obtained with the testbed are shown. The PER found with the testbed shows a clear loss in performance. The additional simulated case shows that the cause of this is characterized by the properties of realistic components. The shown quality of communication performance with the testbed indicates desired channel conditions for reliable communication. It is now possible to evaluate the VLC link between luminaires. Recall a minimum modulation depth ∆min was defined in Section 3.2. The modulation depths used to achieve the shown PERs in the experimental case are all below the expected operating conditions for the office room. Using for example ∆min = 0.1 in the experimental testbed results in reliable communication for this set of parameters even though there is no line of sight between luminaires and photosensors.

Daylight estimation In this experiment, the daylight estimation functionality is illustrated using the testbed. By doing so, the underlying optical channel gain extractions on which the daylight estimation depends are also tested. For this result, all

32 0 10 Theoretical, delta response Simulated, low−pass response Experimental

−1 10 PER

−2 10

−3 10 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 Channel SNR

Figure 5.4: Comparison of PER by SNR for T = 500 µs, fs = 32 kHz, and L = 512 bits, with diﬀerent channel responses.

33 1070 Sensor input Daylight estimation 1060 Daylight ground truth

1050

1040 ) [lux] t ( m y 1030

1020

1010 0 50 100 150 t [s]

Figure 5.5: Experimental daylight estimation at luminaire 7 over 10 scheduling cycles.

luminaires in the testbed are made to communicate. TDMA scheduling is applied so that each luminaire communicates once in a cycle of 12 seconds in the order of their identiﬁers. Realistic timing recovery is now performed during detection and the blinds of the room are opened to allow daylight into the oﬃce.

In Fig. 5.5 the daylight estimation behavior is shown. For around the first 15 seconds of the experiment, the sensed illuminance at luminaire 7 equals the ground truth of daylight. All luminaires in the room are then turned on to a dimming level of 0.5 (half the maximum power output) for ten cycles of scheduling. For each cycle, after all eight luminaires’ optical channel gains are extracted from the transmitted messages, a daylight estimation is performed. The occurrence of these messages can be seen in the received signal of each cycle. After the ten cycles, the luminaires are switched off again. In the figure, the daylight estimations were found to be close to the ground truth.

34 5.2 Performance of networked lighting control

The proposed control algorithm is evaluated by comparing its behavior to a state of the art algorithm. The robustness of either system against environment changes is observed. To investigate the system’s dimming behavior over a sequence of control cycles, the optimization problem detailed in Section 4.3 is solved using quadratic programming to obtain a control action u based on the available information. Changes are introduced to the environment during these operations. The eﬀect of this is investigated for two distinct system setups. The ﬁrst setup implements the proposed method of this work. By using 0 VLC for networking, extractions of optical channel gainsα ˆm,n and estimations of daylight contributions dˆm occur as described in Section 4.2. The other setup employs a non-VLC method of communication and thus while sharing information across luminaires cannot provide continuous estimation of the optical channel gains. Instead, the stored result of a manual 00 measurement of these gainsα ˆm,n is used. This non-VLC setup is repre- sentative of state of the art intelligent lighting systems using centralized control [27, 28]. Daylight estimation using these values as in the proposed method may lead to negative values for dˆm under changes to the environment. This can render (4.14) infeasible when the constraints −Au − d + l ≤ 0 and ∆min u−(1− 2 )1 ≤ 0 become mutually exclusive. Because of this, the insight is added that negative values for daylight contribution estimation at a sensor could not be a correct representation of daylight behavior. Thus, instead of (4.9), this method uses

( PN 00 ˆ 0 ify ¯m − n=1 αˆm,nβm,nun < 0 dm = PN 00 (5.2) y¯m − n=1 αˆm,nβm,nun otherwise. A constant minimum level of illuminance at the workplane level is the desired control behavior. Therefore the average levels of illuminancew ¯z(t) for workplane zone z resulting from both methods are compared. Further denote pz(t) the daylight contribution of illuminance at a workplane zone z. The evaluations are performed both in simulation and with the experimental testbed described in Section 5.1.2.

5.2.1 Simulation The proposed controller is first compared with the state of the art using simulations. This way, it is possible to isolate and observe the effectiveness of the proposed environment change adaptation. Several situations are modeled in simulation to highlight different aspects of the underlying behavior. An indoor open-plan office environment model is considered. It consist of N = 80 ceiling-mounted luminaires in an 8-by-10 grid. The workplane

35 zone 20 luminaire 58

Figure 5.6: Environment model used in simulation. level below consists of a configuration of desks where each desk defines one zone of interest. One luminaire-zone combination, as indicated in Fig. 5.6, is observed while all luminaires in the environment are controlled. Values for A and d in this environment are obtained using DIALux [38]. In this model, daylight may enter through one side of the room, where windows are situated. The daylight conditions used here may be replicated in DIALux using the settings: mixed sky conditions for March 3rd, 2015, from 8:00 a.m. onward. Environment changes are introduced by changing desk reflectance in the underlying DIALux model. The reflectance parameter is a value between 0% and 100%. Low values represent a surface with a dark color and high values represent one with a light color. Changing it results in different values for A and d. Different environment changes are explored in the simulations below. For the following simulations, (3.2) is used to model the input of a photosensor. Since the effect of environment changes is of interest, the noiseless case is considered, i.e. vm(t) = 0. All zones are considered occupied, making the desired workplane illuminance 500 lux [4]. Both the proposed system and the non-VLC system are considered for each simulation. The non-VLC system setup uses the same initial values for A for its entire run while the system using VLC obtains a new A every control cycle. For each simulation, the daylight contributions d58 and p20 are observed, as well as the average ceiling illuminance per control cycley ¯58, the dimming level u58, and the average workplane illuminance per control cyclew ¯20. The performance of both systems is judged by how wellw ¯20 corresponds to the

36 desired constant level of light.

Local underillumination and overillumination In the first simulation, three consecutive environment situations are considered. Originally, all desks have a reflectance of 60% as their natural color. After 12 control cycles, only the desk corresponding to zone 20 has its reflectance changed to 90%. This may represent white-colored paper placed on it. Lastly after 24 control cycles, this same desk has its reflectance changed again to 30%. This may represent a dark object has been placed on the desk, such as a bag or a laptop. Consider Fig. 5.7 for the resulting control behaviors. Note firstly in Fig. 5.7a how the environment changes affect ceiling illuminance differently than workplane illuminance. Further, the behavior marked in red in Fig. 5.7d shows that using the non-VLC setup which cannot update A during control leads to undesired behavior. Underillumination occurs after the reflectance is increased, compromising user satisfaction, and slight overillumination occurs after the reflectance is decreased, wasting energy in increased dimming levels. However, the proposed method implementing VLC can update A and thus obtains new references l using (4.12). The result is a constant satisfactoryw ¯20 across environment changes for the behavior marked green in Fig. 5.7d.

Local oscillation In the second simulation, three consecutive environment situations are again used. Now, all desks are modeled as having a darker natural color by using a reflectance of 30%. After 12 control cycles, only the desk corresponding to zone 20 has its reflectance changed to 90%, again representing a light- colored object placed on the desk. After 24 control cycles, this same desk has its reflectance changed again to 60%. This may represent an object of neutral color is placed on the desk, such as brown cardboard. The control behavior resulting from these changes is shown in Fig. 5.8. Note that the stored values for A in the non-VLC setup correspond to desk reflectances of 30% in this simulation. The increased reflectances compared with this in environment changes that follow result in irregular behavior for the non-VLC state of the art system as shown in Fig. 5.8c. The larger discrepancy with the ground truth of the optical channel gains causes slowly converging oscillations in the output dimming level. This means that after placing a light-colored object on a dark desk surface, a user would observe a flashing overhead luminaire. Furthermore, the positive reflectance change results in constant underillumination as seen in Fig. 5.7d. Contrarily, the setup implementing VLC can adapt to these changes, resulting in desired workplane illumination.

37 Global oscillation

So far, only local changes to one desk have been considered in the above simulations. With an occupied office space, such changes may be expected to occur on all desks. The third simulation applies the same environment changes as the previous simulation, only they are applied to all desks. First, all desks have a reflectance of 30%, then all desks have their reflectance changed to 90%, lastly all desk have their reflectance changed again to 60%. Also, dm and pz are scaled by a factor of 1.5 from the previous two simulations, as an example of stronger daylight conditions. Consider Fig. 5.9 for the behavior resulting from this last simulation. Because more than a single zone is altered in the environment change, the oscillating behavior in the state of the art approach is now much stronger. Note how for the red behavior in Fig. 5.9b, the dimming level oscillations in Fig. 5.9c do not correspond. This is because now that environment changes have occurred at all zones, the neighboring luminaires are oscillating as well. The sum of all oscillating artificial light results in the non-decreasing fluctuations seen in Fig. 5.9b and 5.9d. The proposed implementation using VLC shown in green in Fig. 5.9d is still able to capture the larger environment changes and adapts to them. The desired control behavior is exhibited despite large changes all throughout the environment.

5.2.2 Experimental

In order expose the proposed control algorithm to real-world conditions, it is evaluated in practice. Physical environment changes are now applied. Both the proposed system and the non-VLC state of the art system are implemented on the experimental testbed of N = 8 luminaires described in Section 5.1.2. Again, all zones are considered occupied. In order to compare the two behaviors, similar external light contributions must be present for both measurements. Because of this, daylight adaptation cannot be taken into account here. The blinds in the testbed are therefore closed. In this real-world application, the sensed signals are subject to realistic conditions such as noise. This introduces errors in both calibrations and estimations of A to which the system must remain robust. Luminaire 3 is observed as well as the workplane surface below it, denoted as zone 3, using an external light meter. Environment changes consist of different objects which are common in office environments to be placed on the desk under the luminaire. Again three environment situations are defined. During the first, plain brown cardboard is placed on the desk. After 3 control cycles, it is overlaid with white paper of similar size. Lastly, after 6 control cycles, the black fabric of a common overcoat is placed over the paper.

38 The resulting control behaviors are shown in Fig. 5.10. Again, the behavior shown in red corresponds to the non-VLC state of the art setup and the behavior shown in green corresponds to the proposed VLC setup. In the control cycle following either environment change, the diﬀerence in sensed ceiling illuminance is evident from Fig. 5.10a. The proposed VLC setup is shown to be able to adapt to these changes in practice, providing the desired constant workplane illuminance shown in Fig. 5.10c. As can be seen in the same plot, using the setup without ongoing estimations of the optical channel gains leads to irregular workplane illuminance. Clear underillumination presents after the ﬁrst environment change and clear overillumination presents after the second environment change. The experimental result re- sembles the simulated behavior shown in Fig. 5.7 and shows that unlike the state of the art, the proposed VLC system adapts to environment changes.

39 10

6 [lux] 20 p

, 4 58 d

2 Daylight at ceiling Daylight at workplane 0 0 5 10 15 20 25 30 35 control cycle (a) Daylight contribution, both at the ceiling and at the workplane.

[lux] 40 58 ¯ y

20 Precalibrated A Estimations of A with VLC 0 0 5 10 15 20 25 30 35 control cycle (b) Total illuminance sensed with the ceiling-mounted photosensor.

0.8

0.6 58 u 0.4

0.2 Precalibrated A Estimations of A with VLC 0 0 5 10 15 20 25 30 35 control cycle (c) Dimming level used by the luminaire.

600

500

400

[lux] 300 20 ¯ w 200

100 Precalibrated A Estimations of A with VLC 0 0 5 10 15 20 25 30 35 control cycle (d) Total illuminance at the workplane.

Figure 5.7: Simulated control behavior through localized changes in desk re- ﬂectance (60%, 90%, then 30%) under changing daylight conditions, showing underillumination and slight overillumination are prevented in the proposed VLC method. 40 10

6 [lux] 20 p

, 4 58 d

2 Daylight at ceiling Daylight at workplane 0 0 5 10 15 20 25 30 35 control cycle (a) Daylight contribution, both at the ceiling and at the workplane.

[lux] 40 58 ¯ y

20 Precalibrated A Estimations of A with VLC 0 0 5 10 15 20 25 30 35 control cycle (b) Total illuminance sensed with the ceiling-mounted photosensor.

0.8

0.6 58 u 0.4

0.2 Precalibrated A Estimations of A with VLC 0 0 5 10 15 20 25 30 35 control cycle (c) Dimming level used by the luminaire.

600

500

400

[lux] 300 20 ¯ w 200

100 Precalibrated A Estimations of A with VLC 0 0 5 10 15 20 25 30 35 control cycle (d) Total illuminance at the workplane.

Figure 5.8: Simulated control behavior through localized changes in desk re- ﬂectance (30%, 90%, then 60%) under changing daylight conditions, showing oscillation is prevented in the proposed VLC method.

41 14 12 10

[lux] 8 20 p

, 6 58 d 4 2 Daylight at ceiling Daylight at workplane 0 0 5 10 15 20 25 30 35 control cycle (a) Daylight contribution, both at the ceiling and at the workplane.

[lux] 40 58 ¯ y

20 Precalibrated A Estimations of A with VLC 0 0 5 10 15 20 25 30 35 control cycle (b) Total illuminance sensed with the ceiling-mounted photosensor.

0.8

0.6 58 u 0.4

0.2 Precalibrated A Estimations of A with VLC 0 0 5 10 15 20 25 30 35 control cycle (c) Dimming level used by the luminaire.

600

500

400

[lux] 300 20 ¯ w 200

100 Precalibrated A Estimations of A with VLC 0 0 5 10 15 20 25 30 35 control cycle (d) Total illuminance at the workplane.

Figure 5.9: Simulated control behavior through changes in all desks’ re- ﬂectances (30%, 90%, then 60%) under changing daylight conditions, showing oscillation is prevented in the proposed VLC method. 42 70

40 [lux] 3 ¯ y 30

10 Precalibrated A Estimations of A with VLC 0 0 1 2 3 4 5 6 7 8 9 control cycle (a) Total illuminance sensed with the ceiling-mounted photosensor.

0.8

0.6 [lux] 3 u 0.4

0.2 Precalibrated A Estimations of A with VLC 0 0 1 2 3 4 5 6 7 8 9 control cycle (b) Dimming level used by the luminaire.

600

500

400

[lux] 300 3 ¯ w 200

100 Precalibrated A Estimations of A with VLC 0 0 1 2 3 4 5 6 7 8 9 control cycle (c) Total illuminance at the workplane.

Figure 5.10: Control behavior in experimental testbed through changes in objects placed on desk (plain cardboard, white paper, then black fabric), showing both underillumination and overillumination are prevented in the proposed VLC method.

43 44 Chapter 6

Conclusions and future work

6.1 Conclusions

This thesis presented a novel intelligent lighting system. It makes use of a centralized control algorithm by networking between luminaires with visible light communication. By doing so, no dedicated hardware for communication is required. Moreover, the use of VLC has been shown to allow for the optical channel gains between luminaires and sensors to be extracted successfully from received signals. This allows the proposed lighting control system to adapt to changes in the environment, something state of the art lighting control systems using radio communication have not taken into account. The VLC communication method was evaluated in theory, in simulation, and with an experimental testbed, to reveal the limitations of its performance in terms of channel noise conditions. In an experimental testbed used, the normal operating conditions were found to be nowhere near these limitations. Environment changes were represented by changing surface reflectance values in simulation. In an experimental testbed, different objects common in an office environment were placed on the workplane level, producing an equivalent effect to the changes applied in simulation. These realistic environment changes were shown to compromise the desired lighting behavior in non-VLC lighting control systems, while the proposed system was able to correct for them. The proposed system was presented with a level of generality. The system’s performance was described in terms of its parameters. Different luminaire topologies, environment sizes, and application fields will lead to different trade-offs between system parameter choices, like the communication speed, the number of luminaires, or the desired duration of a control cycle.

45 6.2 Future work

The implementation of VLC in this thesis is a sufficient one for its purpose. The performance may however be further improved. Amplitude modulated communication with Manchester coding in TDMA scheduling has been considered here for simplicity. Filtering the sensed signal at the symbol rate for the purposes of bit detection may increase the SNR further. Furthermore, error correcting codes may yet be applied just as more advanced modulation schemes may be considered, so long as a notion of received signal strength (received modulation depth, here) remains in order to perform optical gain extractions. Also, the system may benefit from photosensors whose response is more suited to high communication speeds. With an impulse response closer to a Direc delta function the effect seen in Fig. 5.4 is minimized. In spacious environments with large numbers of luminaires, the proposed approach may be met with additional challenges. The requirement that one master luminaire is capable of communication with all other luminaires may become infeasible. The implementation of message forwarding between luminaires may overcome this issue. However, another issue that arises with such large networks is the extended duration of communication itself, which determines the minimum time before a control cycle update may be achieved. Further research is thus required into possibilities of distributed control networks or a seamless integration of several smaller centralized networks within the same environment. Note once more that it is impractical to mount photosensors on the workplane level due to the ease with which they might become obstructed. The proposed system translates desired workplane illumination to illumination sensed at the ceiling with (4.12). This translation is an approximation and still relies on a calibration step to obtain u300 and u500. With environment changes significant enough to constitute for example a renovation of the office, this step will have to be repeated. While this is not an unreasonable task, intelligent lighting system may still benefit from a method of more accurately mapping ceiling-mounted photosensors to workplane illumination. The presented control algorithm updates all optical channel gains based on the most recently extracted value. While this allows for immediate cor- rections for environment changes, user comfort may be increased by using a method of filtering to smooth out changes in provided illumination. Also, only desired levels of illuminance have been taken into account as a factor of user satisfaction in this thesis. Future work may incorporate quality metrics such as color temperature as well. Lastly, concerning user comfort, while the proposed intelligent lighting system provides the required amount of illumination in the absence of daylight, overillumination caused by daylight is not taken into account. Future lighting systems may be integrated with an intelligent system of blinds to protect against glare.

46 6.2.1 Internet of Things application The proposed intelligent lighting system provides opportunities for networking beyond inter-luminaire communication for the purposes of lighting control. In the context of the Internet of Things (IoT), external devices in the environment may also be enabled for VLC networking. One example of such a device which may even be integrated with the proposed intelligent lighting system is a seat occupancy sensor which determines the presence of a user based on a pressure sensor. Other sensors which provide helpful information for building management or even actuators such as a controllable system of blinds may benefit from connectivity through VLC. An aspect of this exten- sion to an intelligent lighting sytem with IoT connectivity has been explored over the course of this thesis’ work and is presented here. Consider an indoor office space where ceiling-mounted luminaires act as a point of global access with an IP address. Through VLC, data from external devices is collected at the luminaires and there made available to the outside world through other networking means such as power over ethernet [39, 40]. In this manner, networking traffic is offloaded to the wireless optical channel. The applications suggested here have low demands on communication rate and are thus suited to VLC. Challenges with such an interconnected intelligent environment include the scheduling of its diverse devices, achieving synchronization between them, and in the case of external devices which may be moved by users, the tracking of them. One approach could employ the luminaires for the polling of the external devices. For an external device to be polled by one of the luminaires in order to receive its data, it must be known which luminaire is closest to it. The proximity of an external device may be derived from the optical chan- 0 nel gains extracted from messages it transmits. Letα ˆm,n for all luminaire destinations m be the optical channel gains extracted from a message orig- inating at source external device n. If no message was received between n 0 and m,α ˆm,n = 0. These values are collected and processed by the luminaires through their point of global access. For the transmitting device n, the luminaire q?(n) of greatest estimated proximity is

? 0 q (n) = arg max αˆm,n. (6.1) m This method of determining external device proximity is evaluated with the experimental testbed described in Chapter 5. A transmitting VLC device is placed at a workplane-appropriate height of 80 cm above the ground. The device is moved along the length of the oﬃce room under a row of luminaires while oriented towards the ceiling. At thirteen evenly-spaced locations between luminaire 2 and luminaire 8, the device transmits 512 bits at a communication speed of 1000 bits/s. The locations of these transmission are shown in Fig. 6.1.

47 5

4 1 3 5 7

3 y [m]

2 4 6 8 1

0 0 1 2 3 4 5 6 7 x [m]

Figure 6.1: Experimental testbed layout with locations of external device transmissions indicated.

6 ?

q 4

luminaire 2 luminaire 4 luminaire 6 luminaire 8 location location location location

0 1 2 3 4 5 6 7 distance [m]

Figure 6.2: Estimated luminaires of greatest proximity based on external device position.

48 The luminaires each perform an optical gain extraction on every message. Using (6.1), the resulting proximities shown in Fig. 6.2 were found. These determined proximities match the closest photosensor at any given location. Proximity determination as presented here is but one aspect of the VLC- interconnected environment. Further research is required to investigate the beneﬁts of IoT applications in indoor environments and their realization with VLC communication.

49 50 Bibliography

[1] Energy Information Administration, Commercial Buildings En- ergy Consumption Survey [Online]. Available: http://www.eia.gov/ consumption/commercial/ [Accessed: 2015, August 25]. [2] O. T. Masoso and L. J. Grobler, “The dark side of occupants behaviour on building energy use,” Energy & Buildings, vol. 42, no. 2, pp. 173–177, 2010. [3] F. T. L. Doulos, A. Tsangrassoulis, “Quantifying energy savings in daylight responsive systems: The role of dimming electronic ballasts,” Energy & Buildings, vol. 40, no. 1, pp. 36–50, 2008. [4] Light and Lighting - Lighting of Work Places - Part 1: Indoor Work Places, EN standard 12464-1, 2011. [5] A. Barghi, A. R. Kosari, M. Shokri, and S. Sheikhaei, “Intelligent lighting control with leds for smart home,” in Smart Grid Conference, 2014, pp. 1–5. [6] A. Schaeper, C. Palazuelos, D. Denteneer, and O. Garchia-Morchon, “Intelligent lighting control using sensor networks,” in IEEE Interna- tional Conference on Networking, Sensing and Control, 2013, pp. 170– 175. [7] A. Wilkins, J. Veitch, and B. Lehman, “LED lighting ﬂicker and potential health concerns: IEEE Standard PAR1789 update,” in IEEE Energy Conversion Congress and Exposition, 2010, pp. 171–178. [8] A. G. Bell, “Apparatus for Signaling and Communicating, called Pho- tophone,” U.S. Patent 235 199 A, Dec 7, 1880. [9] F. R. Gfeller and U. Bapst, “Wireless in-house data communication via diﬀuse infrared radiation,” Proceeding of the IEEE, vol. 67, no. 11, pp. 1474–1486, 1979. [10] M. A. Khalighi and M. Uysal, “Survey on free space optical communication: A communication theory perspective,” IEEE Communications Surveys & Tutorials, vol. 16, no. 4, pp. 2231–2258, 2014.

51 [11] S. Rajagopal, R. D. Roberts, and S. K. Lim, “IEEE 802.15.7 visible light communication: modulation schemes and dimming support,” IEEE Communications Magazine, vol. 50, no. 3, pp. 72–82, 2012.

[12] O. Bouchet, M. El Tabach, M. Wolf, D. C. O’Brien, G. E. Faulkner, J. W. Walewski, S. Randel, M. Franke, S. Nerreter, K.-D. Langer, J. Grubor, and T. Kamalakis, “Hybrid wireless optics (HWO): Build- ing the next-generation home network,” in International Symposium on Communication Systems, Networks and Digital Signal Processing, 2008, pp. 283–287.

[13] L. Zeng, D. C. O’Brien, H. L. Minh, G. E. Faulkner, K. Lee, D. Jung, Y. Oh, and E. T. Won, “High data rate multiple input multiple output (MIMO) optical wireless communications using white LED lighting,” IEEE Journal on Selected Areas in Communications, vol. 27, no. 9, pp. 1654–1662, 2009.

[14] A. Tsiatmas, C. P. M. J. Baggen, F. M. J. Willems, J.-P. M. G. Lin- nartz, and J. W. M. Bergmans, “An illumination perspective on visible light communications,” IEEE Communications Magazine, vol. 52, no. 7, pp. 64–71, 2014.

[15] G. Ntogari, T. Kamalakis, J. Walewski, and T. Sphicopoulos, “Com- bining illumination dimming based on pulse-width modulation with visible-light communications based on discrete multitone,” IEEE/OSA Journal of Optical Communications and Networking, vol. 3, no. 1, pp. 56–65, 2010.

[16] IEEE Standard for Local and Metropolitan Area Networks - Part 15.7: Short-Range Wireless Optical Communication Using Visible Light, IEEE standard 802.15.7-2011, 2011.

[17] R. Foster, “Manchester encoding: opposing deﬁnitions resolved,” En- gineering Science and Education Journal, vol. 9, no. 6, pp. 278–280, 2000.

[18] F. Rubinstein, M. Siminovitch, and R. Verderber, “Fifty percent energy savings with automatic lighting controls,” IEEE Transactions on Industry Applications, vol. 29, no. 4, pp. 768–773, 1993.

[19] S. T. Tan, X. W. Sun, H. V. Demir, and S. P. DenBaars, “Advances in the LED materials and architectures for energy-saving solid-state lighting toward “lighting revolution”,” IEEE Photonics Journal, vol. 4, no. 2, pp. 613–619, 2012.

[20] M. Miki, R. Okunishi, K. Matsutani, H. Ikegami, and S. Fujimoto, “An intelligent lighting system with a seat management mechanism,”

52 in IEEE International Conference on Systems, Man, and Cybernetics, 2013, pp. 4571–4576.

[21] A. Pandharipande and D. Caicedo, “Daylight integrated illumination control of led systems based on enhanced presence sensing,” Energy & Buildings, vol. 43, no. 4, pp. 944–950, 2011.

[22] N. van de Meugheuvel, A. Pandharipande, D. Caicedo, and P. M. J. van den Hof, “Distributed lighting control with daylight and occupancy adaptation,” Energy & Buildings, vol. 75, pp. 321–329, 2014.

[23] L. Yeh, C. Lu, C. Kou, Y. Tseng, and C. Yi, “Autonomous light control by wireless sensor and actuator networks,” IEEE Sensors Journal, vol. 10, no. 6, pp. 1029–1041, 2010.

[24] Y. Wen, J. Granderson, and A. M. Agogino, “Towards embedded wireless-networked intelligent daylighting systems for commercial buildings,” in IEEE International Conference on Sensor Networks, Ubiqui- tous, and Trustworthy Computing, 2006.

[25] Y. Wen and A. M. Agogino, “Wireless networked lighting systems for optimizing energy savings and user satisfaction,” in IEEE Wireless Hive Networks Conference, 2008, pp. 1–7.

[26] H. Wang, A. Pandharipande, D. Caicedo, and P. P. J. van den Bosch, “Distributed lighting control of locally intelligent luminaire systems,” in IEEE International Conference on Systems, Man, and Cybernetics, 2012, pp. 3167–3172.

[27] A. Peruﬀo, A. Pandharipande, D. Caicedo, and L. Schenato, “Lighting control with distributed wireless sensing and actuation for daylight and occupancy adaptation,” Energy & Buildings, vol. 97, pp. 13–20, 2015.

[28] M. Rossi, A. Pandharipande, D. Caicedo, L. Schenato, and A. Cenedese, “Personal lighting control with occupancy and daylight adaptation,” Energy & Buildings, vol. 97, pp. 13–20, 2015.

[29] Y. Kasahara, M. Miki, and M. Yoshimi, “Preliminary evaluation of the intelligent lighting system with distributed control modules,” in Inter- national Conference on Intelligent Systems Design and Applications, 2011, pp. 283–288.

[30] M. Miki, E. Asayama, and T. Hiroyasu, “Intelligent lighting system using visible-light communication technology,” in IEEE International Conference on Cybernetics and Intelligent Systems, 2006, pp. 1–6.

[31] M. Miki, K. Yoshida, M. Yoshimi, H. Ito, and M. Nagano, “Faster illuminance convergence for the intelligent lighting system using visible

53 light communication,” in IEEE International Conference on Systems, Man, and Cybernetics, 2012, pp. 3179–3184.

[32] D. Caicedo, A. Pandharipande, and F. M. J. Willems, “Illumination gain estimation and tracking in a distributed lighting control system,” in IEEE Conference on Control Applications, 2014, pp. 1650–1655.

[33] F. M. Gardner, “A BPSK/QPSK timing-error detector for sampled receivers,” IEEE Transactions of Communications, vol. 34, no. 5, pp. 423–429, 1986.

[34] R. Gusella and S. Zatti, “The accuracy of the clock synchronization achieved by TEMPO in Berkeley UNIX 4.3BSD,” IEEE Transactions on Software Engineering, vol. 15, no. 7, pp. 847–853, 1989.

[35] J. Proakis and M. Salehi, Digital Communications. McGraw-Hill Ed- ucation, 2007.

[36] S. Boyd and L. Vandenberghe, Convex Optimization. Cambridge Uni- versity Press, 2004.

[37] S. B. Alexander, Optical Communication Receiver Design. SPIE Op- tical Engineering Press, 1997, pp. 54–55.

[38] DIALux [Online]. Available: http://www.dial.de/DIAL/en/dialux/ download.html [Accessed: 2015, August 25].

[39] L. Yseboodt and M. Wendt, “Lighting over ethernet,” IEEE 802 4- Pair Power over Ethernet (PoE) meeting presentation, May 2013 [On- line]. Available: http://www.ieee802.org/3/4PPOE/public/may13/ yseboodt 1 0513.pdf [Accessed: 2015, August 25].

[40] K. Ahmed, O. Orabi, E. Hasaneen, and M. Youssef, “Design of high performance powered device for power over ethernet systems,” in IEEE International Telecommunications Energy Conference, 2014, pp. 1–6.

[41] R. Bhatia, Positive Deﬁnite Matrices. Princeton University Press, 2007.

54 Appendix A

Convex objective function derivation

In order to apply quadratic programming methods, the objective function of the optimization problem must be a convex function. A function f(x) is convex for all x if the second derivative ∇2f(x) 0 for all x [36]. Here, the relation indicates the generalized inequality for positive semidefinite matrices. A symmetric matrix M is positive semidefinite when vT Mv ≥ 0 for any column vector v [41]. In the proposed optimization problem, the N objective function f : R → R is f(u) = (Au + d − l)T (Au + d − l). The first derivative is shown by ∂ ∇f(u) = (Au + d − l)T (Au + d − l) ∂u ∂ ∂ = (Au + d − l)T (Au + d − l) + (Au + d − l)T (Au + d − l) ∂u ∂u = 2AT (Au + d − l). The second derivative is then shown by ∂ ∇2f(u) = 2AT (Au + d − l) ∂u = 2AT A. Therefore, the object function (Au + d − l)T (Au + d − l) is convex if 2AT A 0. The matrix 2AT A is symmetric since 2AT A = (2AT A)T . Furthermore, for any N × 1 vector v it holds that vT 2AT Av = 2(Av)T (Av) = 2(Av) · (Av) ≥ 0.

55 Therefore, the proposed objective function is convex for all inputs to the control algorithm.