# Adaptive Software Defined Equalization Techniques for Indoor Visible Light Communication
## 1 Introduction  
In wireless and visible light communications (VLC), data are susceptible to interference caused by variations in the transmission channel. In the ideal communication channel model, the signal propagates directly from the transmitter to the receiver. However, the ideal model is practically unreachable as a number of reflected signals caused by various obstacles influence the whole platform. As their time of arrival (ToA) at the receiver varies in comparison to the direct wave, they cause a phenomenon called multipath propagation. In addition, various atmospheric effects, such as rain, fog, or even temperature turbulence can cause additional noise; see [1; 2; 3; 4] (Figure 1). Figure 1 represents various scenarios of visible light communication systems. The left side represents various transmitting sources (represented by physical solutions), which are often explored by scientists. The center column represents examples of various channel impairments, which influence the transmitted signal. The right column presents examples of receiving solutions, spanning from conventional PIN photodetectors [5; 6; 7; 8; 9] to pricier avalanche photo diodes (APDs) [10; 11; 12], advanced CMOS cameras [13; 14; 15; 16; 17], and inexpensive alternatives in solar panels [18; 19; 20; 21; 22]. As a result of signals being delayed differently (due to multipath propagation), so-called intersymbol interference (ISI) occurs on the receiving side. ISI is a major concern in visible light communication, as the medium (light) can be reflected by various surfaces [23]. It can be also causedby the position of LEDs or the bit interval [24]. Intersymbol interference is a situation when one symbol (or state) interferes with other symbols, thus increasing the error rate and leading to the lower reliability of the whole platform. Adaptive equalization is one of the ways to overcome intersymbol interference; see [25; 26; 27; 28; 29]. Error correction codes can be also used to alleviate ISI [24]. Currently, the requirements for quality of RF and VLC systems are slowly increasing, and even higher data rates are desired. However, by increasing the number of symbols transmitted during a period of time, the length of said symbols is shortened; therefore, any delayed pulse that arrives outside the set interval causes significant distortion of the transmitted data. Modern microwave links can use up to 4096-QAM [30]; however, the signal quality requirements increase significantly for modulation formats with a large number of states. [PERSON] et al. in 2015 [31] used RLS based adaptive equalization for RGB-LED based wavelength division multiplexing (WDM) VLC system. They compared RLS algorithm with the modified cascaded multi-modulus algorithm (M-CMMA) and concluded that the RLS algorithm can outperform it by a Q factor of 1 dB. Their results showed that an adaptive equalization scheme for indoor high-speed VLC systems provides benefits and is feasible. [PERSON] et al. in 2014 [32] proposed a hybrid time-frequency adaptive equalization algorithm, which combines frequency domain equalization (FDE) and decision-directed least mean squares (DD-LMS). By using this hybrid system, they reached improvements in performance. They concluded that their system reached the highest data rate ever (until 2014) by using a single commercially available RGB-LED in a VLC system. [PERSON] and [PERSON] in 2016 [33] tested NLMS equalization. They concluded that the bit error ratio (BER) was vastly improved by employing NLMS based equalization. [PERSON] et al. in 2017 [34] tested a linear adaptive least mean squares fractionally spaced equalizer to mitigate ISI and jitter. In their work, LMS managed to outperform the conventional symbol spaced equalizer (SSE) with three times better results. Moreover, LMS was insensitive to timing jitter. [PERSON] et al. in 2016 [35] tested an LMS algorithm against a novel scalar modified cascaded multi-modulus algorithm (S-MCMMA). Based on their work, both  
Figure 1: Examples of various impairments in visible light communication systems.