# Mobile User Connectivity in Relay-Assisted Visible Light Communications
## 1 Introduction  
With the enormous growth of data traffic over wireless infrastructures due to increased demands for video and audio streaming, file sharing, data and voice over Internet protocol (VoIP) [1], the lack of available radio-frequency (RF) spectrum is becoming the limiting factor for high-speed data transmission. One possible solution to address this problem, mostly in an indoor environment at the moment, is the visible light communications (VLC) offering attractive capabilities such as vast unregulated spectrum (\(\sim\)380-780 nm), inherent security and high energy efficiency [2, 3]. The rapid growth of VLC is due to the development in solid-state lighting (SSL) and highly efficient white light-emitting diodes (LEDs) [4]. White LEDs offer a longer life span and much higher power efficiency (\(\sim\)60-80 %) than the conventional fluorescent and incandescent lamps, as well as the possibility to be used in safe and secure applications (e.g., in hospitals, gas stations and airplanes) where RF-based technologies cannot be used [5]. Indoor VLC can be categorized into the line-of-sight (LOS) and diffuse systems. Data rates in the order of Gb/s over a very short transmission span can be achieved using LOS VLC links [6]. For instance, in [7] a 4.5 Gb/s VLC system employing carrier-less amplitude and phase (CAP) modulation and a recursive least square (RLS) based adaptive equalizer over a link span of 1.5 m was experimentally demonstrated. In [8] a data speed of 1.6 Gb/s over a 1 m link employing a combination of 16-quadrature amplitude modulation (QAM) and orthogonal frequency division multiplexing (OFDM) was reported. On the other hand, diffuse VLC systems are robust to blocking and shadowing. However, they suffer from higher losses and offer much lower data rates than LOS links due to multipath induced dispersion [9; 10]. In indoor environments, the LOS path cannot always be guaranteed due to objects, people's movement and the layout of the room [11]. To address this problem and offer seamless communications as well as to maintain an uninterrupted data access even in temporarily shadowed regions a number of solutions have been proposed [12; 13]. One of the most promising techniques is the relay-assisted VLC system. Note that, the current IEEE 802.15.7 standard does not cover the relay based VLC systems, but the standard supports device discovery mechanisms in homogeneous networks [14]. In order to improve the connectivity, a full-duplex relay based VLC employing an LED lighting triangular system topology was analytically investigated in [15]. In the case of the light from an LED source mounted on the ceiling not reaching the user directly, the information can be retransmitted via a relay node (RN). In [16], the connectivity performance of mobile users based on the optical mobile relays in cooperative multi-hop VLC was investigated. An improvement in the network performance was reported by using the multi-hop scenario, which was dependent on the users' density, coverage range ratio between hop regions, relay probabilities, and velocity of the mobile users. A number of existing works also analyzed the multi-hop VLC systems using a combination of RF and VLC links [17; 18]. In order to improve the quality of service, in [17] hybrid VLC and power line communications (PLC) with a backup parallel RF link were proposed. In [18] the authors investigated the scenario, where data is transmitted from the base station to the relay via the RF link and the signal is then amplified and re-transmitted to the user over the VLC channel. OFDM VLC over frequency-selective indoor channels was analyzed in [19] providing the first analytical statistics for pure VLC relaying using amplify-and-forward (AF) or decode-and-forward (DF) relaying schemes. In [20] a relay based DC-biased optical OFDM (DCO-OFDM) VLC was investigated for two test cases using a desk lamp and a ceiling light lamp to provide optimal power allocation and improved bit error rate (BER) performance when employing relays compared to the direct transmission.