Vicente Matus
email: vmatus@idetic.eu

Victor Guerra
email: vguerra@idetic.eu

Cristo Jurado-Verdu

Rajendra Shivani

Teli

Stanislav Zvanovec
email: xzvanove@fel.cvut.cz

Jose Rabadan
email: jrabadan@idetic.eu

Rafael Perez-Jimenez

Experimental Evaluation of an Analog Gain Optimization Algorithm in Optical Camera Communications

Keywords: Optical Camera Communications, analog gain, Pearson's correlation coefficient, signal-to-noise ratio

The operation of Optical Camera Communication systems in outdoor conditions is challenged by interfering sources of light and optical attenuation induced by the atmosphere. The low signal power at the receiver is prone to be affected by the quantization noise at the analog-to-digital converter. In this paper, an algorithm for optimizing the camera's analog gain has been experimentally evaluated under laboratory conditions. The image quality improvement is estimated by Pearson's correlation coefficient to a template signal, and it is shown to improve the signal-to-noise ratio up to 27.8 dB.

I. INTRODUCTION

Optical Camera Communication (OCC) is a group of schemes within the Visible Light Communication (VLC) field to be included in the IEEE 802.15.7r1 [START_REF] Cahyadi | Mobile phone camera-based indoor visible light with rotation compensation[END_REF], and where the main principle is to use a digital camera as a receiver (R x ), taking advantage of the low price of these devices. In OCC, the extensive use of Rolling Shutter (RS) cameras is based on their ability to scan lines of pixels delayed between each other by orders of tens of µs [START_REF] Nguyen | Highspeed asynchronous optical camera communication using led and rolling shutter camera[END_REF]. These cameras are the most available in commercial devices using Complementary Metal-Oxide-Semiconductor (CMOS) sensors [START_REF] Boubezari | Smartphone camera based visible light communication[END_REF], [START_REF] Nguyen | Current status and performance analysis of optical camera communication technologies for 5g networks[END_REF]. The signal coming from a Light Emitting Diode (LED) transmitter (T x ) is captured by the lines of the sensor at different times, allowing the receivers to decode several symbols from each image frame.

Outdoor applications of OCC such as localization, Vehicular VLC, and Sensor Networks, face relevant challenges such as long link spans, optical degradation by atmospheric conditions [START_REF] Islam | Convolutional neural networkscheme-based optical camera communication system for intelligent internet of vehicles[END_REF], and require mobility support in most cases. Applications such as VLC positioning specifically rely on beacon signals, and This project has received funding from the European Union's Horizon 2020 research and innovation programme under the Marie Skłodowska-Curie grant agreement No 764461. most systems use packet structures with well-known patterns for the detection of Region of Interest (ROI) and synchronization. Correlators can be used for the recognition of such patterns [START_REF] Jurado-Verdu | Correlation-based receiver for optical camera communications[END_REF].

The signal-to-noise ratio (SNR) at the receiver is crucial for allowing any communication link to have longer spans. The SNR depends on the transmitted power, on the attenuation factor of the channel, and in the case of OCC, it also depends on the optical lens array of the camera. In addition, an OCC system can be exposed to various sources of noise and interference. The area of the transmitter projected over the imaging sensor is also relevant in OCC, the maximum link distance is then bounded by the amount of sensor rows covered by the transmitter, in the case of RS-OCC. Geometrical derivations can estimate the image projected area [START_REF] Chavez-Burbano | Experimental characterization of close-emitter interference in an optical camera communication system[END_REF]. The SNR can be estimated from the data-containing pixels In this work, the use of an analog gain control algorithm for optimizing the SNR through a cost function based on the correlation is proposed. The correlation is extensively used for spatial synchronization and channel estimation in OCC. Therefore, the inclusion of this control algorithm will have little or no impact on computation performance of the R x if the correlation is considered already a process of other algorithms. Several experiments involving different input powers, the algorithm's convergence iteration, and the SNR improvement are also provided.

The structure of this paper is the following. The OCC channel of an RS-based OCC system is modelled in II. The control algorithm for the optimization of the signal quality is derived in Section III. Both methodology and experimental design are described in Section IV. In Section V, the results obtained from the experiments are discussed. Finally, the conclusions of this work are drawn in Section VI.

II. OCC CHANNEL

The simplified diagram of an outdoor OCC scenario is shown in Fig. 1 in which a VLC transmitter using On-Off Keying (OOK) modulation sends pulses of each of the redgreen-blue (RGB) colors. The shape of the ROI or the pixels of the frame that are exposed to the transmitted signal is not necessarily known beforehand. The attenuation of some atmospheric conditions that might be present, e.g. in foggy weather, is modeled by A in dB/m. The link span d in m depends on the relative position of the source with respect to the camera and its orientation, which in most cases are constantly changing. The power signal at the receiver P Rx (t) under an attenuated channel, when the transmitter is modeled as an m-order Lambertian source with power P T x (t), can be expressed as

P Rx (t) = P T x (t)e -Ad • m + 1 2π • cos m θ A lens cos Ψ d 2 , ( 1
)
where θ is the emission angle, Ψ is the incident angle, and A lens is the area of the camera's external lens. From this expression, it can be seen that by varying either the transmitted power or the factor A•d, known as the optical density, the received power can be affected alternatively, allowing to emulate the effect of the other parameters. Note that the projected area of the source over the camera sensor is mostly only dependent on d. In Fig. 2, the block diagram of a regular CMOS camera subpixel is shown, as described in [8]. The photodiode (PD) at position x, y and channel c ∈ {R, G, B} receives light from a colored Bayer filter and generates a current i pd (x, y, c) which is turned into a voltage signal V 1 by the CMOS drive. Since the sequential reading by rows allows it, an analog amplifier and analog-to-digital converter (ADC) are shared by each column of sub-pixels of the sensor. The gain of the analog amplifiers G V is set globally by the software of the camera and the voltage signal that is sampled by the ADC is given by

V 2 = G V • V 1 .
The ADC induces a noise (σ 2 adc ), that can be modeled as a random Normal of mean zero with a variance that depends on the digitalization levels. The SNR of the signal that enters the digital signal processing (DSP) block can be modeled as

SN R ≈ G 2 V • i 2 pd (x, y, c) G 2 V (σ 2 th + σ 2 sh ) + σ 2 adc , (2)
where σ 2 th and σ 2 sh correspond to the thermal noise and shot noise of the process, respectively. Note that the noise induced by the ADC can be virtually reduced to zero by increasing G V as lim

G V →∞ SN R = i 2 pd (x, y, c) σ 2 th + σ 2 sh , (3)
nevertheless, the ADC has an upper bound for the input voltage, then G V can only be increased up to the point V 2 does not saturate the ADC. In previous work [START_REF] Matus | Experimentally derived feasibility of optical camera communications under turbulence and fog conditions[END_REF], it was shown that the SNR can be obtained empirically from image frames. Nevertheless, its computation can be substituted by the calculation of the Pearson's correlation coefficient r xy between the image frames and a well known template, which is used in some implementations of OCC for synchronization of the received signal in the images and also for ROI detection. The parameter r xy is defined as

r xy = N i=1 (x i -x)(y i -ȳ) N i=1 (x i -x) 2 N i=1 (y i -ȳ) 2 , (4)
where x i are the rows of the template of size N rows, y i are N consecutive rows of the image, and x, ȳ are the mean values. The computation is iterated for all possible subsets y j , y j+1 , ..., y j+N -1 , (j + N -1) < M of consecutive rows of the frame. When the template is matched in phase with the signal it emulates, the maximum value r max xy is achieved. This value is considered the overall correlation between the image frame and the template, which has been shown to be closely related to the SNR, giving high values of r max xy when the signal quality is high [START_REF] Matus | Experimentally derived feasibility of optical camera communications under turbulence and fog conditions[END_REF].

III. ANALOG GAIN CONTROL ALGORITHM

As it was aforementioned, r max xy is closely related to SNR, and may serve as a fast estimator of it. Therefore, optimizing the correlation using G V would implicitly maximize SNR. The following paragraphs describe each one of the development of the algorithm for controlling G V to maximize r max xy proposed in this work, which is based on the typical feedback-based design, as shown in Fig. 3. The set point r * xy is the desired value for r max xy to be achieved by the controller, which is set to 1 in order to force the system to get the highest signal quality.

+ Gain Control Camera G V Correlator
The camera block receives each updated value of G V and sets this parameter on the physical device. Generally, camera's do not have a continuum of analog gains, but a discrete range of possible values. In this work, since Sony IMX219 image sensor is considered, the possible gains in linear units is defined by

G V (X) = 256 256 -X , ( 5
)
where X is an integer between 0 and 232 (233 possible analog gains). Due to the hyperbolic nature of G V (X), there is higher resolution at lower gain values. Furthermore, this quantization could be considered as an extra noise term, since each iteration will probably not coincide with valid values.

Finally, this block also captures the image and passes it to the correlation calculation block, which carries out Pearson's correlation coefficient with a parametric template. The maximum value of this operation is then forwarded to the gain control algorithm.

Mathematically, it is straightforward to define a cost function

C(G V ) that optimizes r max xy as C(G V ) = 1 -r max xy 2 . ( 6
)
The performance of the control algorithm would significantly depend on the shape of the error curve. Nonetheless, in this work a simple squared difference scheme is proposed. C(G V ) can be easily optimized using an iterative approach via a gradient descent on G V , yielding

G (i+1) V = G (i) V -λ C G (i) V ∂C (G V ) /∂G V | G (i) V , ( 7
)
where λ is the learning rate or damping coefficient. It can be observed that the cost function's derivative can be reformulated as

∂C(G V ) ∂G V = -2(1 -r max xy ) ∂r max xy ∂G V . ( 8
)
Since there is no closed-form relationship between r max xy and G V , its derivative must be numerically estimated. In this work, a N-points linear regression was performed to obtain the curve's slope on the point of interest. However, the neighbourhood of the starting point must be explored during the algorithm's initialization by forcing a fixed analog gain change until an Nsize estimation buffer is full to begin with the linear regressions, where N = 4 has been chosen arbitrarily.

Finally, combining equations ( 7) and ( 8), it yields the final iterative scheme, expressed as

G (i+1) V = G (i) V + λ 2 1 -r max xy (i) ∂r max xy /∂G V G (i) V . (9)
The performance of the proposed algorithm would highly depend on the estimation of r max xy 's slope. As it was commented, this magnitude will be calculated using a linear regression of N points. Hence, the accuracy of the denominator in Equation ( 9) depends on the curve's shape, which will not be linear a priori, and the separation between samples.

IV. METHODOLOGY

It has been shown that the Pearson's correlation coefficient is a computationally quick estimator of the signal quality. Moreover, the camera analog gain can optimize the SNR by reducing quantization noise. The objective of this work is to propose a control algorithm for G V based on the r xy values obtained from each image capture. In order to demonstrate this hypothesis, a series of experiments were carried out using the experimental setup shown in Fig. 4. The scenario comprises a commercial RGB lamp controlled by a general purpose microcontroller [START_REF]ATmega328[END_REF] and a receiver built using an Element14 Raspberry Pi board with a camera based on Sony IMX sensor [START_REF]IMX219PQH5-C[END_REF]. The lamp transmits pulses of a period T chip and consecutively repeats a sequence of G-R-B-K pulses, where K stands for black, meaning it is an off state of the lamp. Different conditions can be emulated varying the LED power source voltage and using a Methacrylate sheet in order to emulate channel loss (optical density). The T x and R x parameters can be observed in Table I. The algorithm presented in Section III was evaluated for the three synthetic scenarios using different initial gain values (G (0) V ). Furthermore, the estimation of the correlation's slope was based on N = 4 samples. The analyzed performance metric of the algorithms was the convergence iteration, estimated using:

r th = r max xy (∞) (1 ± ε) , (10)
where r max xy (∞) is the final value after convergence, and ε is the threshold's parameter (which was set 0.05 arbitrarily for all experiments). The parameter r th is the final threshold value of the correlation.

V. RESULTS AND DISCUSSION

The first step of experimentation consisted on the acquisition of frames at all the available G V values, and under three conditions of received intensity of radiant energy (I), as it is shown in Table II. These conditions were implemented by varying transmitted power and the channel attenuation, which derived in three different values of I at the receiver position. In each of the three conditions, the camera acquired images using the 233 available G V values, repeating 50 times the acquisition, resulting in 11,650 frames under the same radiant energy conditions. These frames were processed to get the Pearson's correlation coefficient with respect to a template signal equal to the transmitted pulses of OOK. In order to illustrate the impact of the variation of G V in the image frames captured by the camera, Fig. 5 shows two signals obtained in the conditions of Experiment 3. The sub-optimal gain setting image was captured using G V = 15.3 dB and the optimized gain setting image was captured using G V = 2.0 dB. The images obtained r max xy = 0.76, and r max xy = 0.85, respectively, and the SNR obtained was 27.8 dB and 24.2 dB, respectively.

In Fig. 6, the average results of r max xy obtained from data acquisition and correlation processing are shown for the three experiments. The lowest received intensity of radiant energy at Experiment 1 shows more fluctuations of the correlation, and it shows that the contribution of G V is to improve the signal quality since it is weak. In the other two experiments, a similar behaviour is seen. The high intensity of the received signal makes the gain to deteriorate the signal with saturation, which builds up mostly smoothly. In Experiments 2 and 3, the gain control algorithm should converge to the minimum gain values, and in Experiment 1, it should converge to the maximum gain. It is also important to note that none of the experiments have resulted in a r max xy curve with a maximum point at an intermediate value of G V .

By setting arbitrary initial G V values, the correlation data sets evaluated from Experiments 1, 2 and 3 were used to run the gain control algorithm for a fixed number of 150 iterations. In Fig. 7, the results of the chosen G V at each iteration are shown. It can be seen that the Experiments 2 and 3 converge to the minimum gain, as expected, in which the correlation is the maximum. The convergence is obtained after about 25 iterations. For the case of Experiment 1, the algorithm takes longer to converge, after about 60 iterations.

The results obtained show that the gain control algorithm can successfully converge to the gain value that ensures maximum correlation available in each scenario. Considering a standard frame rate of 30 fps, and negligible delays at the DSP, the algorithm could converge in about 1 s.

VI. CONCLUSIONS

This work shows the development an algorithm for the automated control of analog gain in a CMOS sensor camera used in an experimental RS-based OCC under laboratory conditions that emulated an optical attenuation of the signal across the channel. It was shown that the camera analog amplifier stage before the ADC can reduce the quantization noise only if it does not saturate the ADC, thus, the optimal value of G V can vary depending on the transmitted power and the attenuation induced by the channel. In addition, the use of Pearson's correlation coefficient was shown to be an estimator of the signal quality at the R x , as an alternative to the calculation of SNR. The algorithm was developed for the use of r max xy as the feedback, allowing to estimate the next capture's G V to maximize the quality. It was found that in high received power cases, the algorithm converges to the optimal gain in about 25 iterations, whereas in low received power cases, it takes more than double the amount of iterations. With these values, and considering a standard 30 fps frame rate of the camera, the convergence time is between 1 and 2 s. In case of mobility or changing conditions, it would be necessary to repeatedly run the algorithm. For future work, the parameters of the control algorithm such as damping coefficient and gain seed need to be optimized in more realistic conditions. It is also necessary to demonstrate its convergence under conditions where the optimal G V is an intermediate value.

Fig. 1 .

 1 Fig. 1. Simplified diagram of the RS-OCC system considered.

Fig. 2 .

 2 Fig. 2. Typical configuration of Complementary Metal-Oxide-Semiconductor (CMOS) camera sub-pixels.

Fig. 3 .

 3 Fig. 3. Block diagram of the gain control algorithm.

Fig. 4 .

 4 Fig. 4. Pictures of the experimental setup. In the experiments, the radiant energy at the camera position is 3.39 µW/cm 2 in (a) , 11.79 µW/cm 2 in (b), and 45.11 µW/cm 2 in (c)

Fig. 5 .

 5 Fig. 5. Processing from two images obtained in the conditions of Experiment 3. The plot curves correspond to the Rx signal R-G-B channels, labeled as s R , s G , s B , respectively, and the dashed curves to the template pulses G-R-B-K labeled as t G , t R , t B , t K , respectively. The picture insets represent a portion of the actual images captured. The red dashed line highlights the detected ROI.

Fig. 6 .

 6 Fig. 6. Data acquisition average values of r max xy obtained varying G V over all the available values. Results from Experiment 1 are shown in (a), Experiment 2 in (b), and Experiment 3 in (c).

Fig. 7 .

 7 Fig. 7. Convergence of the algorithm in each of the experiments, where (a) corresponds to Experiment 1, (b) to Experiment 2, and (c) to Experiment 3.

TABLE I

 I Experiment key parameters.

	Parameter	Value
		Transmitter
	Device	12 V DC RGB LED strips
	Front-end device	Atmel ATMega328p controller [10]
	Power levels [W]	min = 1.8, max = 4.8
	Dominant wavelengths [nm] 630 (Red), 530 (Green), 475 (Blue)
	T chip [s]	1/3600
		Receiver
	Camera	Picamera V2 module (Sony IMX219) [11]
	Resolution	3280 × 2464 px
	texp [µs]	300
	Gain (G V ) [dB]	0, . . . , 20.6 (233 values)

TABLE II Experiments conditions .

 IIconditions I [µW/cm 2 ] Gains [dB] No. of Captures

	Experiment 1 3.39	0 -20.6	50 per each G V
	Experiment 2 11.79	0 -20.6	50 per each G V
	Experiment 3 45.11	0 -20.6	50 per each G V

12th International Symposium on Communication Systems, Networks and Digital Signal Processing (CSNDSP)


Edmundo Torres-Zapata

Victor Guerra
email: vguerra@idetic.eu

Jose Rabadan Borges

Jose Martin Luna-Rivera

Rafael Perez-Jimenez
email: rafael.perez@ulpgc.es

VLC network topology design for seamless communication in a urban tunnel 1 st

Keywords: MAC layer, handover, VLC, network topology, vehicular communication

Visible Light Communications networks are usually based on isolated access points which deals individually with the handover strategy. Basically when a node is detected by an access point the network's protocol upper layers redirect the traffic to the new access point. This strategy cannot be suitable for vehicle communications and different alternatives of handover should be developed. In this paper, a new network architecture is presented including a novel handover scheme based on distributed receivers. This system has been tested for vehicle to infrastructure applications in a tunnel scenario and results show that, in comparison with classical scheme, it demonstrates an upgrade in general performance.

I. INTRODUCTION

Autonomous vehicles are getting closer to becoming a reality. In previous years, the discussion about the reliability of these systems in real urban scenarios has been on the spot [START_REF] Perez-Jimenez | nhtsa opens av test autonomous vehicle tracking program to 'all stakeholders[END_REF]. One of the most important elements of this technology is the need of information gathering from external agents. This is a challenge to fulfill and Dedicated Short Range Communication (DSRC) has been adopted as the main option by the most important vehicle manufactures [START_REF] Kenney | Dedicated short-range communications (dsrc) standards in the united states[END_REF]. However, there are some scenarios where its performance can be severely impacted and alternative technologies are required. One viable option is Visible Light Communications (VLC), a technology that uses the spectrum of the visible light band, instead of traditional radio frequency. In a VLC system, data is transmitted by modifying the intensity of LED sources (street lamps, car's headlights), and using quick light changes to avoid undesirable effects for humans. For vehicular applications, VLC can take advantage of hardware built-in the car to decrease the implementation cost, such as the headlights and the rearlight mainly.

VLC presents some supplementary upsides in the vehicular scenario that becomes it a strong candidate. When the vehicle or Road Side Unit (RSU) has a VLC transmitter incorporated This project has received funding from the European Union's Horizon 2020 research and innovation programme under the Marie Skłodowska-Curie grant agreement No 764461. in the car lights, it can save energy consumption since the energy is employed at the same time to light up the streets and communicate. The VLC transmission spectrum is far from radio frequencies used by DSRC, so they cannot interfere each other. Both technologies can work together to increase redundancy and capacity. Additionally, the lamps' relative short range permits VLC system to have high reuse of spectrum in crowded spaces such as the main street during a rush hour.

VLC for vehicular applications has been studied for years by the scientific community and industry [START_REF] Cailean | Impact of ieee 802.15.7 standard on visible light communications usage in automotive applications[END_REF]- [START_REF] Yu | Smart automotive lighting for vehicle safety[END_REF]. Vehicle-to-Vehicle(V2V) channel was analized by [START_REF] Tseng | Characterizing link asymmetry in vehicle-to-vehicle visible light communications[END_REF], they considered that the channel has unusual characteristics due to its location and particular headlamp's radiation profile. The authors in [START_REF] Lee | A snr analysis of the visible light channel environment for visible light communication[END_REF] dealt with the Infrastructure-to-vehicle case (I2V), where the transmitter is incorporated in a traffic light. Other works such as [START_REF] Wu | Modeling vehicle-to-vehicle visible light communication link duration with empirical data[END_REF] have studied the channel using a time-varying approximation but assuming that it acts as a wide sense stationary (WSS) in these environments. They characterized the channel fading and link duration in urban scenarios using real information of vehicles position in these areas obtained by video recording and image processing. Nevertheless, works in vehicular VLC has not limited to theoretical models and channel analysis, and some research groups have done experimental validations. For example, the authors in [START_REF] Turan | Physical layer implementation of standard compliant vehicular vlc[END_REF] performed a practical validation of VLC standard IEEE 802.15.7 with Commercial Off-The-Shelf (COTS) hardware. They integrated a Universal Radio Peripheral (USRP) to the vehicle's fog lights using Software Define Radio (SDR) for the modulation and codification of light signals. Additionally to traditional VLC schemes based on the photodiode, Optical Camera Communications (OCC) has been recently thought of as a viable option [START_REF] Eso | Experimental demonstration of vehicle to road side infrastructure visible light communications[END_REF], [START_REF] Goto | A new automotive vlc system using optical communication image sensor[END_REF]. The main reason is that OCC can provide a longdistance link due to the camera's high sensibility.

As it can be seen, the use of VLC in vehicular applications has been widely studied in literature. However, a great part of these works have not considered the problems regarding network protocols' upper layers that the massive use of this technology can cause due to its particular properties and performances. One of these challenges is the limited communication range of VLC-RSU that makes necessary to define specific handover strategies to ensure the user hold the communication link. Current literature on handover mainly study indoor scenarios or vertical schemes [START_REF] Liu | Dynamic dwell timer for vertical handover in vlc-wlan heterogeneous networks[END_REF]. A vertical handover case is where a user loses the VLC link, and it has to be assisted by an additional technology. Nevertheless, the vehicular scenario differs from indoor, because the user stays briefly in the AP coverage area. So, the handover's latency has to be marginal. Neither, DSRC's handover strategies can be used without modifications, due to the strong contrast between both channels. Just a few studies have covered this topic, for example [START_REF] Jarchlo | A flexible transport layer protocol architecture for handover in a vehicular vlc network[END_REF]. Here, the user manages two or more simultaneous VLC links (one per AP). These are monitored continuously, when one of the links suffers from a failure, the user changes its packet route using the backup link. This solution requires the use of multiple transmitters and receivers working at different optical wavelengths.

In this paper, we present a system network topology which helps to improve the connectivity of a vehicular user increasing the reliability of the communication and improving the user mobility. This topology will be referred as 2.5 layer topology. Additionally, we propose a handover scheme implemented for these kind of scenarios. The proposed scheme is compatible with the MAC standard IEEE 802.15.7. and the topology and handover scheme are validated together by system-level simulation considering the vehicular tunnels as the use case scenario.

The paper organization is the following. First, we present the proposed topology in Section II. Then, Section III introduces the used handover scheme. In Section IV, we explain the used methodology and provide details about the implementation process. Section V shows the obtained result. And finally, we give our conclusion and future work.

II. SYSTEM TOPOLOGY

Commonly, a VLC network has a star topology where there are some VLC Access Points (VLC-AP) distributed on the scenario that provides service. They are connected by a wired medium to a network controller called Aggregation Agent (AA) [START_REF] Kim | Idmp-vlc: Iot device management protocol in visible light communication networks[END_REF]. VLC-AP consists on a receiver(Rx), a transmitter(Tx), and a control unit that carries on random access and backoff mechanism. The AA manages the traffic, and controls the access of the users when they change from one point to another. This common configuration in this work is referred as "traditional topology". Figure 1 shows an overview of this common system. In our study case, the VLC system will be deployed in vehicular tunnels where DSRC decreases its reliability. Thus, VLC-AP is integrated into the tunnel's luminaries including the control unit and the receiver is located separately to take advantage of its position getting a direct contribution from the car's headlights. It is placed 60 cm from the floor near the tunnel walls.

The introduced topology, referred to as the "2.5 layer" topology, proposes a different functionality for receivers. Instead of receivers exclusively associated with an AP, we propose to implement a receiver arrangement included to a sublayer controlled by a switch. Any of these receivers can get the information destined to any of the AP. Furthermore, the receiver at the same time senses the signal power and attaches this information to the frame. The switch collects these frames and removes redundant packets. It uses the logical address (OWPAN ID) to determine who is the addressee AP. At the same time, it compiles Signal-to-Noise Ratio (SNR) information from every Rx. This information is used by Handover Manage Entity (HME), to know when it is necessary to perform a mobility scheme. We can see this arrangement in Fig. 2. The main difference between both topologies is that in traditional topology, the Rx is connected to one AP, and it can only provide communication to this point. But, Rx location is the same in both. The changes in the topology are intended to increase redundancy in the mobile transmission and avoid abrupt interruptions in the uplink. In the test tunnel scenario configuration, the optical signal from the vehicle increases when the vehicle approach the receiver, but this suddenly goes down. In [START_REF] Torres-Zapata | Channel characterization of full-duplex vlc system for urban tunnels[END_REF], we studied time-varying optical channel for this system, where this problem is addressed.

III. HANDOVER SCHEME

Complementary to the topology design, this work presents a handover scheme specifically designed for dealing with the new receivers deployment. The protocol requires low latency because the user should change from an AP to another in less than a second. On the other hand, the tunnel scenario predetermines a linear movement of the user with a steady speed which makes predictable the moment for the cell exchange. In consequence, a simple logic in the decision can determine when the user is coming to the new station, and when to apply the handover function.

The proposed handover protocol uses Hierarchical Mobile IPv6 (HMIPv6) as a reference [START_REF] Aljeri | A dynamic map discovery and selection scheme for predictive hierarchical mipv6 in vehicular networks[END_REF]. In HMIPv6, the networks keep the IP address in Mobility Anchor Point (MAP) and manage the user localization with a short address. All updates are local with a layer 2 handshake, this action reduces the latency considerably. Figure 3 shows the handover process followed described. Before it starts, it is necessary that the mobile node be associated with any VLC-AP AP n previously. The association process is described in the standard IEEE 802.15.7. When the user transmits a data packet to the receiver cluster, each Rx gets the optical signal and estimates the transmission SNR. HME collects these values to determine if the user achieves the conditions to begin the mobility process. For our work, the handover decision is made by a simple method comparing the value with a fixed limit. Nonetheless, a more resilient criterion needs to be implemented in further steps of our research line. When the SNR over lapses a fixed threshold in a receiver referenced Rx for the AP n+1 the procedure starts. HME sends a handover request to the MAP. It verifies that there are enough resources in the next site (AP n+1 ) to proceed and communicates to it. The mobile node is notify about a handover request by AP n+1 . But only when it can respond it, the handover process is completed. Then, AP n+1 notifies MAP to divert the data traffic and also advertises the AP n that the user does not belong more to its network. The protocol design was done to avoid problems from asymmetrical links. A similar protocol was implemented in the traditional topology to make a fair comparison between them. Due to the hardware limitations in the traditional system, AP n+1 senses the optical signal and triggers the mobility process.

IV. METHODOLOGY

The study was performed using system-level simulations in the OMNET++ platform. These simulations recreate the interaction among network elements without a detailed model of the internal node's processes. Some libraries permit the inclusion of PHY and MAC layer of VLC standard IEEE 802.15.7, for example, [START_REF] Aldalbahi | Extending ns3 to simulate visible light communication at network-level[END_REF]. Nevertheless, we have built our own programmed modules to have the flexibility to include the modifications in the system design and the handover scheme.

As it was commented before, the solutions were done considering the context of a Vehicular tunnel. To represent this environment, we have made the following setup in the simulations. The scenario is composed of 32 VLC-AP, each one is in the typical placement of tunnel lamps. VLC-AP is at 4.5 m height pointing downwards near the tunnel wall. The receivers are mounted at a height of 0.6 m from the floor with an elevation angle of 90 o in the vehicle direction. The receiver is separated 13 m onwards on the road from its transmitter, this position was set experimentally. The VLC-AP are separated from 8 to 13 m, according to the tunnel specification [START_REF]Road tunnel ligthing. common nordic guideline. Standard, Comitte 61:Bridges and[END_REF] to avoid the flickering effects on the drivers. Fig. 4 illustrates the distribution of the elements for the tunnel simulation scenario.

The vehicle lamp's and its receiver are situated at 1 m height. As well, the headlamps have an elevation angle of 85 o . The receiver is placed on the vehicle's hood. Usually, the lateral distance between the vehicle right headlamp's and the wall is around 2.4 meters considering an error margin of ± 0.225 m. In the simulations, the uplink and downlink were evaluated considering the radiation profile of real light sources (vehicle and tunnel lamps). These profiles can be seen in Fig. 5.

During the simulation, the mobile node moves linearly at 80 km/h for 10 seconds. It receives a data rate of 450 kbps from the infrastructure which fulfill the minimum requirements for vehicular safety applications. When the vehicle is leaving the coverage area of AP n , the handover mechanism acts to ensure a soft transition. When this mechanism fails or does it untimely, the vehicle can eventually lose its connection. Consequently, it has to re-join the network which is a slower process than the handover itself. This means that for a period of at least 200 ms, the vehicle interrupts its service. While, AP n detects the link failure, it will lose some frames. The data traffic is re-established when a new connection has been set up.

For the simulations, we have considered the different delays in the core communication during the handover resolution. The network discovery, synchronization, and data transmission fulfill the protocols from standard IEEE 802.15.7.

Each experiment was repeated 100 times. The system was evaluated using the follow metrics, which reflects the status of the connection, how much reliable is the new communication link when a handover happens and how is the service.

• Normalize connected time: This is the ratio of time when the user is able in the network. shows the reliability to deliver correctly a frame in the system. It is calculated as successfully delivered frames divided by the total of frames received in AA from the Core Network. This metric takes into count the lost frame during the handover transition. As it was commented before, the evaluation of handover was performed using the protocols of the IEEE 802.17.5 standard. Table I shows the parameters corresponding to the network configuration.

V. RESULTS

Simulation experiments have been conducted to evaluate the proposed VLC network topology which includes a new handover scheme. The results of these simulations are compared to traditional network topology results, see Fig. 1. Some preliminary simulations were necessary for setting up the initial parameters of the networks' configuration. These initial results showed us that the traditional system's performance degrades drastically unless precise values for parameters are used, E.G. the handover threshold. Additionally, the system cannot accomplish an accurate detection when the vehicle is not perfectly aligned to the lane road. On the other hand, the proposed topology is more resilient to these variations in the system configuration and the scenario. In this work, we present the comparison of both system's performance using the described metrics. On each figure, the top part shows the result of the traditional system. While in the bottom part, there are the results of our proposal. The VLC-AP receiver is set at 13m from its transmitter in both configurations. Also, the handover initializes when AP n+1 collects the optical signal with an SNR over 21dB. Most of the time, VLC networks have to adapt to the illumination system configuration. Thus, we have estimated the performance considering multiple distances between adjacent VLC-AP, from 8 to 13 m. The distance is presented in the X-axis on the charts, while the Y-axis shows the metric value. The results are presented in boxplot format which shows the statistical information. The rectangular shape illustrates their distribution while the red cross represents their outlier values, and the red line is the mean value.

Figure 6 shows the connection percentage for the mobile user. In traditional topology, the median value of connection cannot be supported without more reliable handover criteria. Because of the narrow radiation profile of the headlamp, the low variations of its lateral placement cause a decrease of the received power and changes the uplink range. As consequence, the handover initialization has a delay, and the communication link breaks. Additionally, we can see that the results have high variability especially when the nodes are separated from 10 to 11.3 meters. On the other hand, 2.5-layer system can support communication until the system fulfills the handover conditions. But, the are some cases when the performance degrades. Moreover, for a longer distance than 12 meters, it is necessary to fix a new handover threshold. The two systems can improve their connection time if the handover logic uses a dynamic threshold and a more sturdy detection method. Another helpful metric is the number of re-transmission by each frame, they are shown in Figure 7. This value reflects the quality of the VLC link. Not always an inopportunely handover causes an interruption of the link, sometimes just flawed temporally the communication. In our proposal, the AP habitually does not need an extra transmission to deliver the frame successfully. Besides, the worst-case barely presents a difference. Furthermore, the traditional topology requires more resources to sustain communication. And, in some isolated cases the link is highly affected, causing that the backoff mechanism works continuously. This is a global picture of the transmission during the entire simulation. This behavior changes during different phases, when the mobile user is at the edges of the coverage area requires more transmissions. Contrarily, when it is closer to the AP center, this number decreases. This metric is related to channel occupancy, so limit the network capacity. Figure 8 display the datarate. According to it, our proposal can provide an average datarate close to our expected goal (450 kbps). However, some low-performance cases decrease our mean performance to 90 %. On the other hand, the service on traditional topology suffers from a lot of variation. It keeps a mean service between 250 to 200 kps.

Finally, figure 9 shows the link probability. A frame can be drop at several moments. Mainly, it can be lost during the transmission. But also when a user left the site, the AP scrub its queued message and losing some more during the handover resolution. Our proposal exceeds 98 % of the probability of successful packet delivery. Nevertheless, the traditional system has approximately 92 % probability. In both systems, the number of packets lost can be considered high for safety applications. This reflects that it is essential to implement a packet recovery protocol to avoid packet loss during the handover resolution. Even, when 2.5 layer system can support reliable communication, it needs to improve its vulnerabilities to stay connected almost all the time. Otherwise, a traditional system can have several problems to hold a session.

VI. CONCLUSSION

This paper introduces some modifications in the orthodox conception of network construction. In our scheme, the receivers are separated into an intermediate layer. This approach shows good results, increasing the redundancy and general stats in the network. Moreover, the 2.5 layer system demonstrates flexibility to adapt its hardware to the scenario necessities, it can be easily reshaped without a profound evaluation. In the real world, it is rarely possible to take control of network elements and the scenario, so this is a great advantage. The redundancy helps to avoid abrupt interruptions on the communication in most cases. However, the solution has not been finished yet, and some details have to be solved. Among others, it is necessary to implement a better handover strategy to improves its reliability. In future work, we are going to do a deeper analysis of this proposal. Furthermore, a robust handover logic needs to be developed and tested under irregular movement conditions. Finally, the system can take advantage of a packet recovery scheme after the handover has been completed.

Fig. 1 .

 1 Fig. 1. Traditional VLC network topology.

Fig. 2 .

 2 Fig. 2. The proposed topology.

Fig. 3 .

 3 Fig. 3. Handover scheme for vehicular tunnel.

Fig. 4 .Fig. 5 .

 45 Fig. 4. Diagram of the element distribution for the simulation for both system evaluation.

Fig. 6 .

 6 Fig.6. The percentage connected time by the mobile user using both topologies.

Fig. 7 .

 7 Fig. 7. Number of times that a packet need to be send to arrive successfully.

Fig. 9 .

 9 Fig. 9. Probability to deliver successfully a packet in both topologies.

TABLE I SIMULATION

 I PARAMETERS FOR THE PHY AND MAC LAYERS.

	Parameter	Value	Parameter	Value
	Simulation time	10 s	BO , SO	7, 5
	Simulations numbers	100	Data frame payload	1000 bits
	VLC-AP Tx power	50 w	Frame header	270 bits
	vehicle's Tx power	15 w	Biding update payload	448 bits
	vehicle's speed	80 km/h	number Backoff	5
	Distance between APs	8-13 m	Number of slots	16
	Photodiode area (Rx)	1 cm	Optical clock	60 MHz
	Photodiode FOV (Rx)	40º	Backoff unit	200
	aBaseSlotDuration	60	maxMaxBE	3
	Datarate per user	450 kbps	Handover trigger	SNR= 21 dB
	Code	10B8B	Handover L2 resolution	2 ms
	Modulation	OOK	Association Resolution time	200 ms

that a VLC frame is sent by backoff mechanism for successful packet delivery. When it increases the channel is busy for longer periods.

• Data rate: This is the mean of payload bits delivered correctly to the mobile user per time unit. • End-to-end Packet Delivery Probability (EPDP): This

  Authorized licensed use limited to: UNIV DE LAS PALMAS. Downloaded on April 07,2022 at 01:58:18 UTC from IEEE Xplore. Restrictions apply.Fig. 8. The average datarate during the simulation for the mobile user.

	0.5
	0.4
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	0.1
	0
		8.3 8.6	9	9.3 9.6	10 10.3 10.6 11 11.3 11.6 12 12.3 12.6 13
	0.5
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	0.1
	0
	8	8.3 8.6	9	9.3 9.6	10 10.3 10.6 11 11.3 11.6 12 12.3 12.6 13
	1.2
	1
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	8	8.3 8.6	9	9.3 9.6	10 10.3 10.6 11 11.3 11.6 12 12.3 12.6 13
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	8	8.3 8.6	9	9.3 9.6	10 10.3 10.6 11 11.3 11.6 12 12.3 12.6 13

Authorized licensed use limited to: UNIV DE LAS PALMAS. Downloaded on April 07,2022 at 01:58:18 UTC from IEEE Xplore. Restrictions apply.


Edmundo Torres-Zapata

Victor Guerra
email: vguerra@idetic.eu

Jose Rabadan
email: jrabadan@idetic.eu

Rafael Perez-Jimenez

Jose Martin Luna-Rivera

Channel characterization of full-duplex VLC system for urban tunnels

Shortly, many communication dependent processes will be deployed in cities. However, there are scenarios where traditionally RF solutions cannot provide communication. Visible Light Communication has recently emerged as a favorable complement to RF to cover this need. In particular, the vehicular tunnel are a major challenge, where the communication needs to be redundant. This paper presents a fullduplex VLC system for vehicular tunnels. The system allows communication between vehicle and infrastructure using the vehicle's lamps and tunnel lighting system. Simulations are conducted to analyze the performance of the communication system links. Them demonstrate that VLC full-filled the minimum requirements.

I. INTRODUCTION

In recent years, automatic processes are being developed in many areas of our everyday life. They aim to cover all possible tasks in urban scenarios and need to guarantee that their systems are permanently connected. However, there are certain situations or places where traditional Radio Frequency (RF) systems do not work well such as the urban vehicular tunnels. This raises the necessity of deploying alternative and complementary communication technologies for these type of environments. For instance, RF propagation inside tunnels at the Dedicated Short Range Communications (DSRC) band is highly affected by multipath propagation. Furthermore, the time behavior of the channel is influenced by the movement of vehicles. This means that propagation is affected by Doppler Spread [START_REF] Li | Radio channel measurements and analysis at 2.4/5ghz in subway tunnels[END_REF], reducing both effective coherence bandwidth and time along the road [START_REF] Hrovat | Traffic impact on radio wave propagation at millimeter-wave band in tunnels for 5g communications[END_REF].

Under these circumstances, there is a need to develop an adequate complementary communication system for ensuring connectivity. A feasible option for these harsh scenarios is the use of Visible Light Communication (VLC) as the aforementioned complementary technology. VLC uses the visible optical spectrum which ranges from 400 nm to 700 nm. This technology uses light sources This project has received funding from the European Union's Horizon 2020 research and innovation programme under the Marie Skłodowska-Curie grant agreement No 764461 such as LED lamps, LED screens or the vehicles' head and tail lamps to transmit information [START_REF] Cȃilean | Current challenges for visible light communications usage in vehicle applications: A survey[END_REF]. The light sources transmit data modifying their emitted optical power following the traditional Intensity Modulated with Direct Detection (IM/DD) paradigm. Moreover, light intensity changes at a frequency high enough to avoid flickering. Furthermore, this technology does not cause interference with RF communications.

The integration of VLC systems in vehicular scenarios has been studied for a decade. These studies include channel investigations for Vehicle-to-Vehicle (V2V) communication [START_REF] Uysal | Visible light communication for vehicular networking: Performance study of a v2v system using a measured headlamp beam pattern model[END_REF], [START_REF] Yu | Smart automotive lighting for vehicle safety[END_REF] and validations of the VLC standard in vehicular scenarios [START_REF] Turan | Physical layer implementation of standard compliant vehicular vlc[END_REF]. In addition, the inclusion of VLC in the Infrastructure-to-Vehicle (I2V) communication model has been studied in [START_REF] Lourenc ¸o | Visible light communication system for outdoor applications[END_REF], [START_REF] Cailean | Visible light communications cooperative architecture for the intelligent transportation system[END_REF]. This is essential to allow local authorities to provide vital information to the Intelligent Transport System (ITS). In these works, vehicular communication is deployed using Road Side Units (RSU), which are integrated into the streets and traffic lights. However, most of the literature in I2V communication is focused on using VLC only for performing downlink communications.

The advantages of VLC respect to DSRC have been also studied. On the one hand, the VLC channel is stationary for longer periods and presents less fading than RF communications [START_REF] Wu | Modeling vehicle-to-vehicle visible light communication link duration with empirical data[END_REF], [START_REF] Cui | Characterizing channel fading in vehicular visible light communications with video data[END_REF]. Furthermore, the negative effect of Doppler spread in RF systems decreases in VLC channels. This occurs because the used VLC transmitters are significantly directive, whilst DSRC RF signals are affected by the entire surrounding area. Moreover, the ray-based propagation nature of VLC clearly delimits the coverage area, allowing high scalability, less complex medium access schemes in consequence, and finally lower latencies [START_REF] Cheng | Comparison of radio frequency and visible light propagation channels for vehicular communications[END_REF]. VLC has been also considered to provide support and localization capabilities in mining tunnels where RF signals are restricted [START_REF] Iturralde | A new vlc system for localization in underground mining tunnels[END_REF]. Several studies have been carried out to characterize the channel of these types of applications [START_REF] Wang | A general channel model for visible light communications in underground mines[END_REF], [START_REF] Yusuf | Experimental investigation of v2i radio channel in an arched tunnel[END_REF]. However, VLC in tunnel environments has not been deeply studied nor implemented yet.

In this paper, an analysis of VLC as a vehicular communication technology in urban tunnels is presented. Both optical downlink and uplink were studied using a time-frequency approach in order to observe the effect of the relative movement of vehicles respect to the other endpoints. The time-varying impulse responses needed for the analysis were obtained using a Modified Monte Carlo Ray Tracing (MMCRT) [START_REF] Francisco | Ray-tracing algorithms for fast calculation of the channel impulse response on diffuse IR wireless indoor channels[END_REF] algorithm and the 3D model of the scenario under consideration.

This paper is structured as follows. Section II describes the implemented system under an urban tunnel scenario. Section III explains the method used in the evaluation. In Section IV, the results are discussed. Finally, Section V presents a set of conclusions. II. SYSTEM OVERVIEW This section describes the scenario conditions and the system's characteristics. The design and construction of urban road tunnels need to comply with very strict regulations and technical requirements, including the lighting system. Each European country has its own regulations. In order to ensure the implementation of a VLC system in the urban road tunnels, they need to adapt their designs to follow these rules. restriction deals with the illumination levels, which variate according to the vehicle's localization and speed limits. These levels are changed with the lamp's driver and adjusting the distance between lamps. The LED drivers are based on dimming techniques, which are considered in the VLC standard [START_REF]Ieee standard for local and metropolitan area networks-part 15.7: Short-range optical wireless communications -redline[END_REF].

The use of a dimmer modifies the average humanperceived power, but the channel response is not affected by them. However, depending on the dimming technique, this may require a minimum device bandwidth. Otherwise, the modification of the lamps' distance can impact the channel parameters. To avoid flickering, the guidelines give some recommended distances according to the speed [START_REF]Road tunnel ligthing. common nordic guideline. Standard, Comitte 61:Bridges and[END_REF]. For the current evaluation, the longest inter-lamp distance was taken into consideration (12 meters). This case would a priori represent a case with significant variations.

The simulated scenario considers a segment of a twolane tunnel with the maximum dimensions (a width of 14.2 m and a height of 4.9 m) [START_REF]Guia técnica de aplicación de eficiencia en iluminación de alumbrado exterior-anexo ii[END_REF]. The floor has been assumed to be made of asphalt, whilst the tunnel's walls have been modeled as concrete.

The system is composed of multiple Access Points (AP) distributed along the tunnel. Each AP provides communication services to an area. They are interconnected by an optical backbone and coordinated by a module called Aggregation Agent (AA). The ITS can access this network using the Mobile Unit (MU), a VLC module installed on the vehicle.

Typically, APs have their downlink and uplink endpoints in the same enclosure. Nonetheless, in this work downlink and uplink are disaggregated since both communication directions are VLC-based. The downlink comprises a tunnelmounted VLC transmitter (LED lamp) and a vehiclemounted VLC receiver. On the other hand, the uplink is formed by the vehicle's headlamp and a RSU close to the tunnel's wall.

The MU utilizes the vehicle's headlamps for the uplink and its receiver is placed at the vehicle's hood. A system diagram can be seen in figure 1. The MU's design has an analogous architecture. However, one of the most significant differences in respect to the AP is that the latter uses a tunnel lamp as part of its transmitter while MU uses a vehicle's headlamp. Furthermore, the control unit is linked with the ITS computer, instead of the core network. Figure 2 depicts the architecture of each module and their interaction. The last module is AA. In essence, it is a router that distributes data traffic. To perform a correct distribution, it is necessary that this module could be capable of tracing each user in the network. Another important task is keeping the network's security. Finally, it coordinates the mobility process in the network (usually handover).

This work has considered commercial lamps on both AP and MU looking for a realistic approach. The downlink uses an Ariana lamp installed in the Altel tunnel (Alicante, Spain) [START_REF]Guia técnica de aplicación de eficiencia en iluminación de alumbrado exterior-anexo ii[END_REF], whilst the uplink is carried out with a Toyota Corolla headlamp. However, the vehicular lamps have similar radiation patterns in most of the commercial vehicles [START_REF] Sivak | A market-weighted description of low-beam headlighting patterns in europe[END_REF]. For the simulations, the recreation of the radiation profiles of both light sources were done. The tunnel lamp's profile was based on its technical datasheet. However, due to the lack of information was necessary to obtain the vehicle's lamp radiation pattern. It was by a set of measures of its transmitted optical power on a referenced plane using a power-meter with a photodiode. Both radiation patterns can be observed in Figure 3.

III. METHODOLOGY

A set of simulations using a MMCRT software [START_REF] Lopez-Hernandez | Monte carlo calculation of impulse response on diffuse ir wireless indoor channels[END_REF], [START_REF] Guerra | Spatial interpolation of optical wireless impulse responses[END_REF] were carried out to obtain the Channel Impulse Response (CIR) at different positions h(d, τ ). Assuming rectilinear uniform motion, it is straightforward to transform h(d, τ ) into a time-varying impulse response h(t, τ ) knowing the mobile's speed v. With h(t, τ ) it is possible to estimate an upper bound system performance in terms of coherence time and bandwidth. In the evaluation description, a referenced Cartesian coordinate system is used to facilitate the comprehension of the distribution of the elements. The origin O = (0, 0, 0) is located at the beginning of the tunnel segment, in the right down corner. The width of the tunnel is aligned with the X-axis, the height with the Z-axis, and finally the tunnel route with the Y-axis. The system's uplink and downlink have independent channels. Thus, the simulations were done with 2 different simulation configurations.

The downlink was tested assuming two different transmitter configurations: the lamp on the tunnel's center pointing downwards (case 1) and on the sides with an elevation of 45 • (case 2). The CIR using a photodiodebased receiver of area 7.6 mm 2 and 68 • of Field Of View (FOV) pointing upwards was obtained in the XY plane at a height of 1 meter. The simulated scenario can be observed in Figure 4. Since the uplink implies the V2I part of the architecture, the vehicle's movement must be simulated. Taking advantage of the scenario's geometry, a line of receivers was placed close to the tunnel's walls. Using this approach, all the values of h(d, τ ) can be obtained in a single run of the MMCRT algorithm.

transmitter was placed pointing slightly tilted (85 • elevation and -5 • azimuth) respect to the tunnel's direction at 3 meters from the wall. The orientation of the lamp corresponded to a real vehicle's headlamp orientation. Regarding the receiver, it pointed to the traffic's opposite direction and was placed at 1.5 meters from the wall. Three different receiver heights were tested to explore the link's behavior with this parameter, which a priori will highly impact the channel availability due to the transmitter's orientation and radiation pattern. Figure 5 depicts the uplink scenario.

Regarding the simulation parameters, the MMCRT simulation engine was configured to launch 40,000 random rays from the optical source and to consider 3 rebounds. Moreover, both concrete and asphalt reflection patterns were assumed Lambertian with reflectivities 0.17 and 0.07 respectively.The reflection coefficients were taken from [START_REF] Adrian | Influence of pavement reflectance on lighting for parking lots[END_REF], and considering the spectral distribution of the light source.

In this work, both time-varying channel gain H(t, 0) (Equation 1) and delay spread τ rms (t) (Equation 2) are calculated and analyzed.

H(t, 0) = ∞ 0 h(t, τ ) dτ (1)
τ rms (t) = M 2 (t) -M 2 1 (t) 1/2
(2) These two parameters provide preliminary insight about the impact of the vehicle's speed on the communication capabilities of the presented V2X scenario.

M i (t) = 1 H(t, 0) ∞ 0 τ i h(t, τ ) dτ

IV. RESULTS

The simulation results show that the excess delay contributions on the CIR significantly vary with distance. Due to the link's geometry, the downlink receives only significant contributions from second order and above rays, whilst the uplink is also affected by the more energetic first order reflections. This can be easily observed comparing both figures, and implies an asymmetry between downlink and uplink bandwidths.Additionally, the headlights are designed to emit a uniform light on the road. As a consequence, the power contribution on the floor does not decreases so much with distance. After calculating the downlink's time-varying channel gain using Equation 1, strong differences between the two considered cases can be observed in Figure 8. In case 1, the highest values are concentrated in a narrow area, whilst case 2's spatial response is wider. In consequence, the received optical power would not be strongly affected in case 2 by lateral moves of the vehicle (X-axis). Furthermore, for the wall-mounted luminaires the channel gain fluctuation in the Y-axis (traffic flow direction) is less sharp than in the top-mounted case. This would probably imply a higher coherence time if a whole timefrequency analysis was carried out.

An approximation of the slow fading can be calculated using the normalized autocorrelation function of H(t, 0). This approximation is valid for Wide Sense Stationary with Uncorrelated Scattering (WSSUS) channels. In this work the stationarity of the channel has not been mathematically assessed and taking into account the scenario, it will probably be non-stationary. Nonetheless, the same metric can be calculated as a preliminary metric before carrying out the whole time-frequency analysis. When the autocorrelation falls below a threshold R th , the resulting lag can be interpreted as coherence time T c (Equation 3).

T c = arg t {E [H(t , 0)H * (t + t , 0)] < R th } (3)
In this work, the threshold has been set to 50% of the signal's peak (3 dB). To determine this threshold, it is necessary to know the vehicle speed v and carry out the change of variable of Equation 4, in which y corresponds to the tunnel's traffic flow axis.

t = y v (4)
As an example, a vehicle moving at 100 km/h has been assumed. Figure 9 shows the autocorrelation function of the downlink when the vehicle is located at different Xaxis locations.

The results from case 1 are less affected by the receiver's lateral position, but the obtained coherence time values are lower than in case 2. T c is below 150 ms for case 1 and around 200 ms for case 2. On the other hand, the uplink's transmitter (car headlamp) has a narrow radiation pattern. Therefore, channel gain is strongly affected by the receiver's height. For each evaluated height, both channel level and time variations are different. Concretely, the tallest location is associated with the shortest range and the strongest variations. The DC channel gain of these 3 configurations can be seen in Figure 10. The uplink's fading is stronger than the downlink's. Furthermore, the coherence time of around 160 ms is almost independent of the receiver's height. Nevertheless, as it was commented above, height affects coverage and must be taken into account. This result can be seen in Figure 11. Finally, the time-varying Delay Spread has been also analyzed. The downlink channel owns a Delay Spread below of 1 nanosecond in both cases, which provides a generous channel capacity beyond 100 MHz. And as a consequence, high available data rate. In spite of good value, the Case 2 channel capacity degrades fast when the vehicle leaves the AP. Figure 12 shows the delay spread depends on vehicle lateral position. However, the lowest value guarantees enough capacity to prove communication. The uplink channel is less affected by Delay Spread than the downlink. The obtained values vary significantly with the receiver's height. Nonetheless, the worst case (photodetector at 0.8 m height) presents values that evolve from 6 ps to less than 1 ps, suggesting that there is practically no bandwidth limitation due to the link's geometry.

V. CONCLUSIONS

In this work, the communication channel of a VLC system for the urban tunnel was evaluated. The results prove its use as a viable alternative. This technology fullfill the bandwidth requirements of ITS where in [START_REF] Kenney | Dedicated short-range communications (dsrc) standards in the united states[END_REF] suggest has at least 3 Mb/s datarate for safety applications. The system's channel has a longer coherence time and it is less affected by delay spread than DSRC channel in this environment. The channel is strongly affected by the lateral movement of the vehicle. Nevertheless, more channel features need to be considered as Doppler Spread of signal in the next step. Additionally, the influence of external agents also needs to be studied such as the scattering caused by car fumes.

As future work, deeper channel studies will be performed considering the channel as time-variant making a time-frequency analysis. Additionally, the result also will be used for further studies in the MAC layer of this system. Mainly focus on the mobility problems of a user in the network (handover).

Fig. 1 :

 1 Fig. 1: VLC tunnel system diagram representation.

Fig. 2 :

 2 Fig. 2: Diagram of the VLC communication between AP and MU.

Fig. 3 :

 3 Fig. 3: Radiation patterns of the vehicle's headlamp (top) and the tunnel lamp (bottom).

Fig. 4 :

 4 Fig. 4: Simulated downlink scenario.

Fig. 5 :

 5 Fig. 5: Receiver locations (top) and receiver's schematic orientation (down) .

  Figure 6 and 7 illustrate this point showing how h(d, τ ) changes at different point in the scenario. On Figure, the downlink 6 is shown at { 0, 3.75 , 7.5}, while uplink on Figure 7 at { 7.5, 11.2 , 15}. These points where selected because has the most notorious differences.

Fig. 6 :

 6 Fig. 6: Downlink h(d, τ ) at different Y-axis distances. d = {7.5, 3.75, 0.0} for both cases (top is case 1 and bottom case 2).

Fig. 7 :

 7 Fig. 7: Uplink h(d, τ ) at different Y-axis distances. d = {7.5, 11.2, 15}

Fig. 8 :

 8 Fig. 8: Channel gain for both cases. Receiver at x=4 m (top), x=5 m (middle) and x=6 m (bottom).

Fig. 9 :

 9 Fig. 9: Normalized downlink's autocorrelation function.

Fig. 10 :

 10 Fig. 10: DC channel gain of the uplink channel.

Fig. 11 :

 11 Fig. 11: Normalized uplink's autocorrelation function.

Fig. 12 :

 12 Fig. 12: Downlink's delay spread evolution. In both case 1 (top) and case 2 (bottom) three different lateral positions are evaluated.

Fig. 13 :

 13 Fig. 13: Evolution of the uplink's delay spread.

12th International Symposium on Communication Systems, Networks and Digital Signal Processing (CSNDSP) Authorized licensed use limited to: UNIV DE LAS PALMAS. Downloaded on April 07,2022 at 02:05:22 UTC from IEEE Xplore. Restrictions apply.

Authorized licensed use limited to: UNIV DE LAS PALMAS. Downloaded on April 07,2022 at 02:05:22 UTC from IEEE Xplore. Restrictions apply.