Visible Light Communication Receiver Research Articles

Driving toward Connectivity: Vehicular Visible Light Communications Receiver with Adaptive Field of View for Enhanced Noise Resilience and Mobility.

Wireless communication represents the basis for the next generation of vehicle safety systems, whereas visible light communication (VLC) is one of the most suitable technologies for this purpose. In this context, this work introduces a novel VLC receiver architecture that integrates a field-of-view (FoV) adaptation mechanism in accordance with the optical noise generated by the sun. In order to demonstrate the benefits of this concept, a VLC prototype was experimentally tested in an infrastructure-to-vehicle (I2V) VLC configuration, which uses an LED traffic light as the transmitter. At the receiver side, an automatic FoV adaptation mechanism was designed based on a mechanical iris placed in front of a photodetector. Adjustments were made based on the values recorded by a multi-angle light sensor, built with an array of IR photodiodes covering an elevation from 0° to 30° and an azimuth from -30° to 30°. Depending on the incidence of solar light, the mechanical iris can adjust the FoV from ±1° to ±22°, taking into account both the light irradiance and the sun's position relative to the VLC receiver. For experimental testing, two identical VLC receivers were used: one with an automatic FoV adjustment, and the other with a ±22° fixed FoV. The test results performed at a distance of 50 m, in the presence of solar irradiance reaching up to 67,000 µW/cm2, showed that the receiver with a fixed FoV saturated and lost the communication link most of the time, whereas the receiver with an adjustable FoV maintained an active link throughout the entire period, with a bit error rate (BER) of less than 10-7.

Photodetector with a metalens packaging module for visible light communication based on RGBY illumination LED light source

A novel, to the best of our knowledge, photodetector with a metalens packaging module used as the visible light communication (VLC) receiver is proposed and designed. An LED consisting of red, green, blue, and yellow chips (RGBY-LED) is adopted as the transmitter for intensity modulation direct detection VLC systems. A metalens array with a numerical aperture (NA) of 0.707 used as a polarization-insensitive planar lens of the VLC system receiver is designed at wavelengths of 457, 523, 592, and 623 nm corresponding to blue, green, yellow, and red for high efficiency. Compared with a traditional Fresnel lens positive-intrinsic-negative (PIN) photodetector module as the VLC receiver, the introduction of a metalens module can decrease the form factor of the VLC receiver module and, in particular, it is much thinner. The combination of the multi-color LED transmitter and photodetector metalens packaging module receiver can increase the modulation bandwidth due to four different wavelengths used for the VLC system. Finite-difference time domain (FDTD) simulations are performed to validate the performance of the photodetector with a metalens module. It is revealed that the corresponding efficiencies of 57.5%, 55.4%, 57%, and 56.3% were achieved at wavelengths of 623, 592, 523, and 457 nm, respectively, based on a metalens array with a 0.707 NA and 2.5 µm radius of the active area of the photodetector. It is a promising technology for indoor VLC systems such as those for smart phones and other Internet of Things devices due to the need for compact packaging for the receiver.

Certification Grade Quantum Dot Luminescent Solar Concentrator Glazing with Optical Wireless Communication Capability for Connected Sustainable Architecture

AbstractEnergy sustainability and interconnectivity are the two main pillars on which cutting‐edge architecture is based and require the realization of energy and intelligent devices that can be fully integrated into buildings, capable of meeting stringent regulatory requirements and operating in real‐world conditions. Luminescent solar concentrators, particularly those based on near‐infrared emitting reabsorption‐free quantum dots, are considered good candidates for the realization of semi‐transparent photovoltaic glazing, but despite important advances in optical property engineering strategies, studies of finished devices suitable for real‐world operation are still lacking. In this paper, the first example of a fully assembled quantum dot luminescent solar concentrator‐based photovoltaic glazing is demonstrated that meets all international standards for photovoltaic and building elements. It is also shown that these devices are capable of functioning as efficient Visible Light Communication (VLC) receivers even under full sunlight, thus combining energy and wireless connectivity functions in a realistic solution for smart, sustainable buildings.

Side-emitting fiber-based distributed receiver for visible light communication uplink.

We present a distributed receiver for visible light communication based on a side-emitting optical fiber. We show that 500 kbps data rate can be captured with a bit-error rate below the forward-error correction limit of 3.8·10-3 with a light-emitting diode (LED) transmitter 25 cm away from the fiber, whereas by increasing the photodetector gain and reducing the data rate down to 50 kbps, we improve the LED-fiber distance significantly up to 4 m. Our results lead to a low-cost distributed visible-light receiver with a 360° field of view for indoor low-data rate, Internet of Things, and sensory networks.

RIS-aided dynamically adaptive wide field-of-view receiver for visible light communication in industrial internet of things.

In the current visible light communication (VLC) system, a condenser lens is generally used in the front of receiver to achieve a higher data rate, making an extremely narrow field-of-view for the receiver. With the spread of Industrial Internet of Things (IIoT), the communication between mobile terminals is urgently required. A wide-range detecting method for VLC system in IIoT scenario is asked. In this paper, a novel self-adaptive wide-FoV receiver involving reconfigurable intelligent surfaces (RIS) is proposed. The effective detecting range of the receiver can be expanded by dynamically adjusting the incident light directions with the assistance of RIS. Based on the maximum arrived flux criterion, the mathematical model is established and the optimized RIS parameter tuning algorithm is presented. The feasibility and validity of the method are verified by simulation. The results show that the tolerable transceiver offset can be increased to 2∼4 times as the conventional receiver.

Energy-Efficient Resource Allocation for Aggregated RF/VLC Systems

Visible light communication (VLC) is envisioned as a core component of future wireless communication networks due to, among others, the huge unlicensed bandwidth it offers and the fact that it does not cause any interference to existing radio frequency (RF) communication systems. In order to take advantage of both RF and VLC, most research on their coexistence has focused on hybrid designs where data transmission to any user could originate from either an RF or a VLC access point (AP). However, hybrid RF/VLC systems fail to exploit the distinct transmission characteristics (e.g., susceptibility of VLC transmissions to blockages, limited field-of-view of VLC APs and receivers, more coverage and better reliability of RF systems, etc.) of RF and VLC systems to fully reap the benefits they can offer. Aggregated RF/VLC systems, in which any user can be served simultaneously by both RF and VLC APs, have recently emerged as a more promising and robust design for the coexistence of RF and VLC systems. To this end, this paper, for the first time, investigates AP assignment, subchannel allocation (SA), and transmit power allocation (PA) to optimize the energy efficiency (EE) of aggregated RF/VLC systems while considering the effects of interference and VLC line-of-sight link blockages. A novel and challenging EE optimization problem is formulated for which an efficient joint solution based on alternating optimization is developed. More particularly, an energy-efficient AP assignment algorithm based on matching theory is proposed. Then, a low-complexity SA scheme that allocates subchannels to users based on their channel conditions is developed. Finally, an effective PA algorithm is presented by utilizing the quadratic transform approach and a multi-objective optimization framework. Extensive simulation results reveal that: 1) the proposed joint AP assignment, SA, and PA solution obtains significant EE, sum-rate, and outage performance gains with low complexity, and 2) the aggregated RF/VLC system provides considerable performance improvement compared to hybrid RF/VLC systems.

BiGRU-Based Adaptive Receiver for Indoor DCO-OFDM Visible Light Communication

Nonlinear devices and channel interference can significantly impact the received signal in visible light communication (VLC). While recent research has explored receiver recovery using deep learning, existing approaches often involve replacing traditional channel estimation and equalization modules with neural network models. However, these models introduce additional data processing steps after fast Fourier transform (FFT), leading to increased complexity. To address these challenges, this study introduces a novel direct time-domain waveform equalization approach using a bidirectional gated recurrent unit (BiGRU) neural network for indoor VLC employing direct current (DC)-biased orthogonal frequency division multiplexing (DCO-OFDM). Unlike previous methods, our proposed scheme utilizes time-domain waveform data from photodiode outputs for direct balancing, harnessing the potent nonlinear processing capabilities of the BiGRU model. We first analyze the nonlinear processing capacity of the BiGRU model and subsequently compare the performance of different receiving methods on a constructed indoor visible-light communication platform. Experimental results demonstrate that the BiGRU-based approach exhibits low complexity and exceptional nonlinear channel learning capabilities. Notably, the proposed method outperforms other strategies in terms of bit error rate without the need for pilot signals. These findings validate the potential of the BiGRU-based DCO-OFDM receiving scheme as a promising solution for future VLC systems.

A Comparison of VLC Receivers That Incorporate Two Different SiPMs

Previously, when selecting silicon photomultipliers (SiPMs) for use in visible light communications (VLC) systems the bandwidth of the SiPM has been a high priority. However, results of experiments on VLC receivers containing two different sizes of commercially available SiPMs show that, if equalization is used and the OOK bit time is less than one third of the duration of its output pulses, the SiPMs bandwidth doesn't significantly impact the receiver's performance. Consequently, for these data rates the criteria used to select which SiPM to incorporate in VLC receivers should put a higher priority on their area and photon detection efficiency than on their bandwidth. In addition, for these data rates, unless the SiPM becomes non-linear, the performance of a receiver containing a SiPM can be predicted based upon Poisson statistics.

Increasing Vehicular Visible Light Communications Range Based on LED Current Overdriving and Variable Pulse Position Modulation: Concept and Experimental Validation

Due to its unique advantages, the integration of Visible Light Communications (VLC) in vehicle safety applications has become a major research topic. Nevertheless, as this is an emergent technology, several challenges must be addressed. One of the most important of these challenges is oriented toward increasing vehicular VLC systems' communication range. In this context, this article proposes a novel approach that provides a significant communication distance enhancement. Different from most existing works on this topic, which are based on refining the VLC receiver, this new article is focused on improving the VLC system based on the benefits that can be achieved through the VLC transmitter. The concept is based on Light-Emitting Diode (LED) current overdriving and a modified Variable Pulse Position Modulation (VPPM). Therefore, LED current overdriving provides the VLC receiver higher instantaneous received optical power and improved Signal-to-Noise Ratio (SNR), whereas the use of the VPPM ensures that the VLC transmitter respects eye regulation norms and offers LED protection against overheating. The concept has been experimentally tested in laboratory conditions. The experimental results confirmed the viability of the concept, showing an increase of the communication range by up to 370%, while maintaining the same overall optical irradiance at the VLC transmitter level. Therefore, this new approach has the potential to enable vehicular VLC ranges that cover the requirements of communication-based vehicle safety applications. To the best of our knowledge, this concept has not been previously exploited in vehicular VLC applications.

Strong Noise Rejection in VLC Links under Realistic Conditions through a Real-Time SDR Front-End.

One of the main challenges in the deployment of visible light communication (VLC) in realistic application fields, such as intelligent transportation systems (ITSs), is represented by the presence of large background noise levels on top of the optical signal carrying the digital information. A versatile and effective digital filtering technique is, hence, crucial to face such an issue in an effective way. In this paper, we present an extensive experimental evaluation of a complete VLC system, embedding a software-defined-radio (SDR)-based digital signal processing (DSP) filter stage, which is tested either indoors, in the presence of strong artificial 100-Hz stray illumination, and outdoors, under direct sunlight. The system employs low-power automotive LED lamps, and it is tested for baud rates up to 1 Mbaud. We experimentally demonstrate that the use of the DSP technique improves 10× the performance of the VLC receiver over the original system without the filtering stage, reporting a very effective rejection of both 100-Hz and solar noise background. Indoors, the noise margin in the presence of strong 100-Hz noise is increased by up to 40 dB, whilst in the outdoor configuration, the system is capable of maintaining error-free communication in direct sunlight conditions, up to 7.5 m, improving the distance by a factor of 1.6 compared to the case without filtering. We believe that the proposed system is a very effective solution for the suppression of various types of noise effects in a large set of VLC applications.

Asymptotic Capacity Maximization for MISO Visible Light Communication Systems with a Liquid Crystal RIS-Based Receiver

Combined with reconfigurable intelligent surfaces (RISs), visible light communications (VLCs) can increase the communication performance to a great degree. However, the research into RIS-aided VLC systems has mainly focused on mirror array-based RISs deployed on the wall while neglecting liquid crystal (LC)-based RISs in VLC receivers. With the development of advanced materials, the LC RIS has been gradually attracting attention from researchers. Inspired by the current research into the LC RIS, the applications of the LC RIS in multiple-input single-output (MISO) VLC systems are investigated in this paper. We formulate an optimization problem with asymptotic capacity maximization as the objective function and the refractive index of the LC RIS as the independent variable. As for this nonconvex optimization problem, we propose the particle swarm optimization (PSO) algorithm to determine the configuration of parameters for the LC RIS. The simulation results indicate that the employment of the LC RIS in VLC receivers can raise the communication performance of the MISO-VLC systems; meanwhile, the proposed algorithm is an effective way to deal with the optimization problems for LC RIS-based MISO-VLC systems when compared with the exhaustive search method and a baseline scheme. The LC RIS is also expected to solve the dead zone problem in traditional VLC systems.

Intelligent MRI Room Design Using Visible Light Communication with Range Augmentation

Radio waves and strong magnetic fields are used by Magnetic Resonance Imaging (MRI) scanners to detect tumours, wounds and visualize detailed images of the human body. Wi-Fi and other medical devices placed in the MRI procedure room produces RF noise in MRI Images. The RF noise is the result of electromagnetic emissions produced by Wi-Fi and other medical devices that interfere with the operation of the MRI scanner. Existing techniques for RF noise mitigation involve RF shielding techniques which induce eddy currents that affect the MRI image quality. RF shielding techniques are complex and lead to RF leakage. VLC (Visible light Communication) is an emerging and efficient technology to avoid RF interference near MRI scanners. Range augmentation with power conservation of the LED is a big challenge in existing VLC systems. The major objective of the proposed work is to develop an intelligent-MRI room design without RF interference using visible light communication and enhance the distance between VLC transmitter and VLC receiver. In this paper, it is proposed to implement VLC using On-Off keying modulation and enhance distance using large active area photodiodes with Automatic Gain Control Circuit (AGC) using software and hardware. The performance of the proposed intelligent MRI-VLC system is analyzed by calculating Bit Error Rate at an inclined distance of 50 cm away from line of sight of the LED. The Experimental results showed that the maximum distance achieved was 400 cm at Bit Error Rate (BER) of 1.5 × 10−5.

Full-duplex visible light communication system based on single blue mini-LED acting as transmitter and photodetector simultaneously

GaN-based light emitting diodes (LEDs) have potential as photodetectors (PDs) for visible light communication (VLC). In current studies on LED-based PDs, devices are operated in a reverse-biased or zero-biased state. In this work, the performance of an 80 × 120 μm <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> blue mini-LED as both a PD and light source was studied. An aluminum oxide passivation was deposited on the sidewalls of the active region using atomic-layer deposition. In addition to improving the external quantum efficiency of mini-LEDs and reducing leakage current, sidewall passivation can also increase the responsivity of mini-LED PD. At the injection current used for display, the mini-LED device still worked as a PD with a good response to illumination. At a bias of 3 V (corresponding to injection current of 11.5 mA), the mini-LED PD had a response of 0.243 A/W and a high on-off ratio of 1.33 × 10 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">7</sup> . A cascaded bridged-T amplitude equalizer was used to extend the OE −3 dB bandwidth of mini-LED PD from 16 MHz to 116 MHz at 3V bias. Based on the system above, a VLC link over 1 m with a data rate of 528 Mbps is achieved using 16-ary quadrature amplitude modulation orthogonal frequency division multiplexing. Moreover, the mini-LED PD could simultaneously act as an uplink detector and a downlink transmitter in the same full-duplex VLC system. With transmission distance of 1m/ 1m, a transmission rate of 350 Mbps in the uplink and downlink was achieved. With transmission distance increasing to 1.2 m/1.2 m and 1.5 m/1.5 m, full-duplex VLC systems are also capable of achieving transmission rates of 300 Mbps and 225 Mbps, respectively. The proposed method allows the same mini-LED to be used simultaneously as a display and VLC transmitter and receiver, which not only simplifies the structure of the full-duplex communication system and reduces system power consumption, but also facilitates the integration of multifunctional small LED devices.

Design and Optimization of Liquid Crystal RIS-Based Visible Light Communication Receivers

In the design of reconfigurable intelligent surfaces (RISs)-aided visible light communication (VLC) systems, most studies have focused on the deployment of mirror arrays and metasurfaces on walls to influence signal propagation and enhance communication performance. This paper provides a new research direction in the design and performance optimization of RIS-aided VLC systems whereby voltage-controlled tunable liquid crystals (LCs) are deployed as part of the VLC receiver. The purpose of the LC RIS is to provide incident light steering and intensity amplification in order to improve the received signal strength and the corresponding achievable data rate. More specifically, an LC RIS-based VLC receiver design is proposed and its operating principles and the channel model for a VLC system with such a receiver are provided. Since the refractive index of the LC RIS plays a critical role in the wave-guiding and light amplification capabilities of this novel receiver, a rate maximization problem is considered to achieve the optimal refractive index and the required voltage to obtain the best light amplification and data rate performances. This communication design problem is a non-convex optimization problem for which a metaheuristic approach is developed based on the sine-cosine algorithm. Simulation results are used to confirm the considerable data rate improvement by the proposed LC RIS-based VLC receiver and optimization algorithm when compared to a VLC receiver without the LC RIS and a baseline scheme, respectively.

Joint Light Planning and Error-Rate Prediction for Dual-Use Lighting/Visible Light Communication

We consider error-rate prediction for dual-use lighting systems with visible light communication (VLC) functionality. Since <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">light planning</i> rather than communications engineering is usually the driving discipline for practical dual-use settings, we extract VLC channel parameters as a by-product from advanced 3-dimensional (3D) light-planning models. By this means, we attain realistic signal-to-noise ratios for exemplary positions of a VLC receiver, which allows us to predict corresponding end-to-end bit error rates (BERs). Specifically, our procedure accounts for important aspects of state-of-art lighting systems, such as realistic light distribution curves of employed luminaires, possible presence unmodulated light sources, and, particularly, adaptive dimming operations in response to prevalent sunlight. In this paper, we (i) devise a methodology for VLC systems with optical receive filtering to convert photometric quantities into radiometric quantities, (ii) present examples of BER predictions for selected modulation schemes within some basic office environments, and (iii) conduct an analysis of the resulting simulation accuracy for a particular 3D light-planning tool. Simulation results show that our approach is indeed suited to predict realistic end-to-end BERs for dual-use lighting/VLC systems. Moreover, our procedure is fairly general and may be tailored to specific practical office settings and particular light plans of interest.

Object recognition in optical camera communication enabled by image restoration.

As an important branch of visible light communication (VLC), optical camera communication (OCC) has received increasing attention recently, owing to its availability and low cost of deployment by re-using cameras as VLC receivers. However, cameras on popular smartphones and/or closed-circuit television systems have their primary function for taking pictures and recognizing objects, where the recorded images with objects are inevitable to be distorted by the coded light under OCC. To this end, we propose and experimentally demonstrate an improved OCC system which is able to achieve data communication and object recognition simultaneously. Basically, we devise an image restoration (IR) scheme to repair the pixels damaged by modulated light during data transmission, and it hence provides better image input to realize object recognition. Moreover, to maintain a reasonable data rate of OCC, we also engineer an object avoidance (OA) scheme to remove the negative effect caused by the object background in OCC frame. Finally, we implement a prototype of the proposed system to verify its performance on object recognition and communication, and experimental results show that the proposed IR can bring an improvement over 37% in terms of object recognition accuracy comparing to the baseline under a data rate of 5 kbps.

Indoor Positioning System Infrastructure Based on Triangulation Method through Visible Light Communication

Autonomous mobile robots are widely used in industry to help human’s work, but the concept has a weakness, that is robot still does not know its position in a room so it can not detect whether the robot has been at destination point. The technology commonly used to determine the position of objects is the Global Positioning System (GPS). However, GPS does not detect objects that are indoors. Previous research used Wi-Fi as a reference for designing an indoor positioning system, but the system could not determine the position in detail because Wi-Fi could only detect object zones. Based on these problems, this research will propose the infrastructure prototype design of an indoor positioning system based on Visible Light Communication (VLC). The main focus of this research is designing a VLC transmitter and receiver system, estimating the distance between the receiver and transmitter based on the received signal strength, and estimating the receiver's position using the triangulation method based on a minimum of 3 distance estimates. The estimating distance system get average accuracy is 76.47%. The estimated accuracy of the x-coordinate position has the best accuracy is 77.05% and the y-coordinate estimate has the best accuracy is 86.54%.

A 130 nm CMOS Receiver for Visible Light Communication

Visible light communication (VLC) is an emerging technology that has been gaining attention over the last few years. Transmission of data at higher rates in a VLC system is mainly limited by the modulation bandwidth of the employed LED. To alleviate this limitation, equalization is frequently employed. This is usually achieved by either using discrete circuit elements or in digital form. In this paper, we present a power-efficient VLC receiver as a system-on-chip, implemented in 130 nm CMOS technology. The proposed receiver supports LEDs with different bandwidths thanks to the switchable equalizer. We tested the proposed receiver using phosphorescent white LEDs with different bandwidths on an experimental VLC link. For each tested LED, around 20 fold improvement in data rate was achieved compared to the original bandwidth of the LED. For the LED with a modulation bandwidth of 1.6 MHz, data rates of 32 Mbps and 50 Mbps at a BER of <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$10^{-2}$</tex-math></inline-formula> were obtained at a distance of 2 meters without and with a blue filter, respectively.

A Full-Digital M-CAP Receiver With Synchronisation and Adaptive Blind Equalisation for Visible Light Communications

With an emphasis on the real-time implementation of a practical carrier-less amplitude and phase (CAP) receiver for visible light communication (VLC), this paper proposes a full-digital architecture for the <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$M$</tex-math></inline-formula> -CAP receiver with synchronisation and adaptive blind equalisation. The architecture is mainly based on the observation that a CAP signal can be demodulated using a quadrature and amplitude (QAM) receiver with an added counterclockwise rotation operation. The proposed CAP receiver employs two digital phase-locked loops (DPLL) to realise the symbol timing and carrier synchronisation, which are the most critical issues in practical systems. With the constant-modulus algorithm (CMA) offering the benefit of decoupling carrier and symbol timing synchronisation, the receiver can blindly equalise the distorted signal at the output of symbol timing synchronisation. Finally, the performance of 4/16/64-CAP receivers, which are designed using this architecture and operates at 80/160/240 Mbit/s through a low-pass light-emitting diode (LED) with a 3-dB bandwidth of 7 MHz cascaded with three measured optical wireless channels, is evaluated by Monte Carlo simulations. Results show that the receiver architecture can successfully solve the symbol timing and carrier synchronisation problems and mitigate inter-symbol interference caused by LED and/or wireless channels. The design framework for a full-digital CAP receiver has been laid out in this paper.

Neural Network Detection for Bandwidth-Limited Non-Orthogonal Multiband CAP UVLC System

In this paper, we propose a novel sparse data-to-symbol neural network (SDSNN) receiver for bandwidth-limited underwater visible light communication (UVLC) based on non-orthogonal multi-band carrierless amplitude and phase modulation (NM-CAP). Bandwidth limited NM-CAP signals usually carry severe inter-symbol interference (ISI) and inter-band interference (IBI). The SDSNN receiver directly converts the received NM-CAP data with ISI and IBI into quadrature amplitude modulation symbols without distortion for each sub-band. In contrast, the conventional receiver requires the least mean square (LMS) equalizer to cancel ISI, and the subcarrier component extraction with complex independent component analysis (SCE-ICA) to cancel IBI, respectively. SDSNN provides a novel receiving structure to replace post-equalization, matched filtering, and SCE-ICA. A blue-LED based UVLC system has been demonstrated utilizing NM-CAP16 with 3 sub-bands. The experimental results show that NM-CAP with the SDSNN receiver case reaches the highest spectral efficiency, where an enhancement of 43%, 20%, 6% has been measured over the orthogonal multi-band CAP case, NM-CAP with LMS equalizer case, and NM-CAP with joint LMS equalizer and SCE-ICA case, respectively. Compared with joint LMS equalizer and SCE-ICA case, the proposed SDSNN receiver can achieve 98% reduction of computational complexity.