# Effect of Temperature on Channel Compensation in Optical Camera Communication
## 1 Introduction  
Optical Camera Communication (OCC) is an Optical Wireless Communication (OWC) technology based on the use of general-purpose cameras for gathering data from optical sources. This technology was included in the last revision of the IEEE 802.15.7 standard on Visible Light Communication (VLC) [1], where several physical layer (PHY) transmission modes were defined. The most remarkable advantage of OCC with respect to traditional VLC is the ubiquity of cameras embedded into smartphones, tablets and laptops. Therefore, the likelihood of a massive adoption of OCC by the market is higher than in the case of other VLC technologies, which would require a costly adaptation of the device's interfaces. Furthermore, although OCC is intended to provide low-speed capabilities, the inherent spatial multiplexing capacity of cameras allows an easy integration of Multiple-Input Multiple-Output (MIMO) schemes [2]. Currently, OCC is being proposed as an enabling technology in Smart Cities [3], Intelligent Transportation Systems (ITS) [4], and e-Health [5]. Moreover, OCC has led to several theoretical and experimental works related to Visible Light Positioning (VLP) [6, 7], which may lead to a location-aware system feasible for marketing applications. Nevertheless, the use of OCC in the environments mentioned above is limited by the link geometry and the camera's optical system since the maximum achievable data rate in OCC is directly related to the projected size of the light source on the image sensor [8]. General-purpose Complementary Metal Oxide Semiconductor (CMOS) cameras usually present three color channels (red, green, and blue) comprising the typical RGB scheme. Each channel results from a band-pass wavelength filtering carried out typically using Foveon or Bayer-based image sensors [9]. These color-filter mosaics present a considerable overlap between their transmission spectra (Figure 1). Wavelength Division Multiplexing (WDM) or Color Shift Keying (CSK) communication schemes need to compensate the induced inter-channel interference in order to improve the Signal-to-Interference Ratio (SIR) and thus the Bit Error Rate (BER) performance [10]. This compensation is typically carried out by obtaining the Channel State Information (CSI) in the form of a deterministic channel matrix and performing a matrix multiplication by its inverse, constituting a Zero-Forcing (ZF) scheme. Many other approaches are currently being used in massive MIMO systems [11], but their higher complexity and computational cost are generally not justified in 3-channel OCC systems. On the other hand, Light-Emitting Diode (LED) devices increase their temperature with respect to their driving current due to the Joule effect. In addition, the p-n junctions' response is very sensitive to these temperature variations, producing significant modifications on the emitted spectrum and the energy efficiency of the light source. As a general rule of thumb, the band gap energy of the substrate is reduced as temperature increases [12], and therefore its peak wavelength red-shifts. Furthermore, an increment in the vibrational energy due to temperature leads to a reduction of the quantum efficiency (electron-to-photon conversion rate) [13]. The effects of temperature on both light sources and optical camera receivers are well documented in the literature separately. Nonetheless, the impact of the aforementioned temperature effects of LED emissions on the performance of the zero-forcing compensation scheme has not been analyzed in depth. This work provides a comprehensive methodology and experimental characterization of this impact using commercially available devices. It has been assumed that the CSI is acquired subject to an initial temperature condition, different from the stationary temperature regime of the LED. Therefore, the product between the obsolete inverted CSI matrix and the actual channel matrix will not be the identity, resulting in an SIR penalty.