# Software-Defined Visible Light Communication for Internet of Things: A Low-Complexity Approach
## 3 Modeling of BBP Unit in SD-VLC System
### Performance Analysis of SDLMS Equalization  
One of the key challenges in VLC systems is mitigating ISI and channel distortions caused by LED bandwidth limitations, multipath effects, and signal impairments introduced by IM/DD transmission. Traditional analog pre-distortion techniques are often used to compensate for LED nonlinearity by applying an inverse response function to the input signal, thereby improving linearity and extending the effective modulation bandwidth [24; 25; 26; 27; 28]. However, these analog solutions suffer from implementation complexity, including the need for precision analog circuit design, manual tuning of resistive and capacitive components, sensitivity to temperature and process variations, and limited reconfigurability. Such characteristics hinder scalability and adaptability, especially in IoT environments requiring frequent reconfiguration. To overcome these limitations, SD-VLC leverages digital signal processing techniques, particularly LMS-based adaptive equalization, which provides real-time adaptability, low computational complexity, and robustness against hardware-induced distortions [29]. Unlike analog pre-distortion, digital equalization dynamically adjusts filter coefficients based on the received signal, allowing it to effectively mitigate residual ISI and signal degradation without requiring precise LED characterization [30]. Figure 5 illustrates a schematic of an SDLMS equalizer, which is a variation of the LMS algorithm. For an SDLMS equalizer, only the signs of the input data are used for weight updates, reducing computational complexity. The input signal \(x\) (at a rate of symbol-spaced \(1/T\)) enters a tapped delay line, which consists of a series of delay elements, producing delayed versions of the signal \(u_{1},u_{2},\ldots,u_{L}\). These delayed samples are then multiplied by a set of adaptive weights (\(w_{1},w_{2},\ldots,w_{L}\)) and summed to generate the equalized output signal \(y\). \begin{table}
\begin{tabular}{l l l} \hline \hline  & **QAM** & **CAP** \\ \hline Carrier Generation & Digital NCO & No carrier needed \\ Computational Complexity & High (IQ mixing + phase tracking) & Lower (FIR-based filtering) \\ Hardware Complexity & Moderate (NCO + multipliers) & Low (FIR filters only) \\ IQ Imbalance & Present (sensitive to errors) & None (no IQ separation) \\ Phase Noise Sensitivity & Moderate (requires phase tracking) & None (no explicit carrier) \\ Spectral Efficiency & Comparable to CAP & Comparable to QAM \\ Suitability for IoT VLC & Flexible & Simple \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Comparison of QAM and CAP in VLC systems. If the training mode is enabled, a reference signal \(d\) is used for supervised learning. The error calculation block computes the difference \(e\) between \(y\) and \(d\), and this error signal is fed into an adaptive algorithm that dynamically updates the weights to minimize ISI and channel distortions. The LMS equalizer operates by iteratively adjusting its filter coefficients using a gradient descent approach, ensuring that the equalized output closely approximates the desired signal. The equalizer weight vector of the LMS algorithm is given by  
\[w^{(n)}=\alpha w^{(n-1)}+\mu e^{(n)}\text{sign}[u^{(n)}],(0\leq\alpha\leq 1) \tag{3}\]  
where \(\mu\) is the step size controlling the adaptation speed. The given formula is designed for dynamically updating the adaptive equalizer weights in order to minimize the error \(e\) and optimize equalization performance. This process relies on an adaptive learning mechanism that continuously adjusts the equalizer coefficients based on the observed error between the desired signal \(d\) and the actual output \(y\). When the equalized output deviates significantly from the desired value, the adaptive algorithm modifies the weight coefficients to reduce this discrepancy.