> REPLACE THIS LINE WITH YOUR PAPER IDENTIFICATION NUMBER (DOUBLE-CLICK HERE TO EDIT) < 1 Abstract—The limited bandwidth of white light emitting diode (LED) limits the achievable data rate in a visible light communication (VLC) system. A number of techniques including multiple-input-multiple-output (MIMO) system are investigated to improvements the data rate. The high-speed optical MIMO system suffers from both spatial and temporal cross-talks. Spatial cross-talk is often compensated by MIMO decoding algorithm while temporal cross-talk is mitigated using an equalizer. However, the LEDs has a non-linear transfer function and the performance of linear equalizers are limited. In this paper, we propose a joint spatial and temporal equalization using an artificial neural network (ANN) for a MIMO-VLC system. We demonstrate using a practical imaging/non-imaging optical MIMO link that the ANN-based joint equalization outperforms the joint equalization using a traditional decision feedback as ANN is able to compensate the non-linear transfer function as well as cross-talk. Index Terms— Visible light communications, multiple input multiple output, joint equalization, artificial neural network, non- linear transfer function I. INTRODUCTION he solid-state lighting (SSL) devices are not only energy efficient in comparison to traditional illumination devices, but also have potential to play an enormous role in overcoming bandwidth congestion in the future wireless communication system [1]. SSL devices can be modulated at a very high speed, enabling these devices for high-speed data communications. Besides dual functionality of illumination and data communication, the visible light communication (VLC) system using SSL devices has additional benefits including license-free operation, free from electromagnetic interference and inherent security. A number of Gigabit/s VLC systems were demonstrated using commercial white light emitting diodes (LEDs) while multi-gigabit systems were demonstrated using multi-colored LEDs (see [1] and references therein for a detailed review of recent demonstrations of high-speed VLC systems). Recently, Manuscript received Jan 2019; S. Rajbhandari is with School of Computing, Electronics and Mathematics, Coventry University, Coventry, UK. E-mail: ac1378@coventry.ac.uk. H. Chun is with the Department of Information and Telecommunication, Incheon National University, Incheon, Korea. e-mail: hyunchae.chun@inu.ac.kr G. E. Faulkner, and D. C. O’Brien are with the Department of Engineering Science, University of Oxford, Oxford, UK. e-mail: {grahame.faulkner, dominic.obrien}@eng.ox.ac.uk. light bulbs have become available that comprise a large number of LEDs are packaged together in a single bulb using chips-on-board (COB) technology. These LEDs can be independently modulated, making high-density multiple-input- multiple-output (MIMO) system attractive for high-speed data communication. The spatial MIMO system has the potential to linearly increase the system capacity with the number of transmitter/receiver elements. The performance of the high-speed MIMO-VLC systems suffers from spatial cross-talk and temporal cross-talk (intersymbol interference (ISI)). The bandwidth commercial white LEDs are limited to a few MHz to 10’s of MHz due to slow yellow phosphor coating [1]. This leads to ISI when these LEDs are operated at a significantly higher data rate. Both the imaging and non-imaging optical MIMO system also have inter-channel interference. A commonly adopted approach in the MIMO-VLC system to overcome these shortcomings is to first compensate the spatial cross-talk by using a MIMO decoding algorithm, followed by ISI compensation, often by using decision feedback equalizer (DFE). The non-linear MIMO decoding algorithm like vertical Bell labs layered space- time (V-BLAST) offer improved performance in comparison to the zero-forcing (ZF) algorithm. V-BLAST can be considered as a matrix decision feedback equalizer (DFE) [2]. Hence, joint spatial and temporal equalization using a single DFE is feasible for a MIMO system [3]. The comparative studies of the transversal, Volterra and artificial neural network (ANN) based DFE to compensation ISI and non-linear effect for pulse amplitude modulation (PAM) demonstrates that ANN offers the optimum performance with less computational complexity then Volterra equalizer [4]. Though traditional DFE requires the least computational complexity, the performance is often unacceptable with a high bit error rate (BER) [4]. Furthermore, the theoretical and simulation studies in [5]–[7] indicates that PAM with DFE outperforms carrierless amplitude phase (CAP) modulation with DFE and discrete multitone (DMT)/optical orthogonal frequency division multiplexing (O-OFDM) with H. Haas are with the Institute for Digital Communications, Li-FI R&D Centre, The University of Edinburgh, Edinburgh EH9 3JL, U.K. E. Xie, J. J. D. McKendry, J. Herrnsdorf, E. Gu, and M. D. Dawson are with the Institute of Photonics, University of Strathclyde, Glassgow, U.K. e-mail: {enyuan.xie, jonathan.mckendry, johannes.herrnsdorf, erdan.gu, m.dawson}@strath.ac.uk. Color versions of one or more of the figures in this paper are available online at http://ieeexplore.ieee.org. Neural Network Based Joint Spatial and Temporal Equalization for MIMO-VLC System Sujan Rajbhandari, SMIEEE, Hyunchae Chun, Grahame Faulkner, Harald Haas, Member IEEE, Enyuan Xie, Jonathan J. D. McKendry, Johannes Herrnsdorf, Member IEEE, Erdan Gu, Martin D. Dawson, Fellow IEEE, Dominic O’Brien, Member IEEE T