# 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
The adjustment direction is determined by the sign of the error, where a positive error increases the weight, thereby amplifying the corresponding signal component, while a negative error decreases the weight to reduce its influence. This signal-based update rule ensures that the system effectively mitigates ISI and channel distortions by dynamically compensating for variations in the received signal. Over time, the weights gradually converge to optimal values, allowing the equalizer to adapt to changing channel conditions with minimal computational complexity. Compared to conventional LMS algorithms, which rely on full error magnitude for weight updates, the SDLMS approach simplifies computation by only considering the error direction, making it more suitable for hardware-efficient implementations such as VLC and wireless communication systems. This balance between computational efficiency and real-time adaptability enables SDLMS to enhance signal integrity while maintaining low implementation complexity, making it an ideal choice for bandwidth-limited and noise-sensitive environments. Figure 6 illustrates the performance analysis of SDLMS equalization under different step sizes (\(\mu\)). Part (a) represents the original input signal, while part (b) shows the input signal corrupted by noise, demonstrating the impact of channel distortions and noise interference. As the step size \(\mu\) increases, the equalization process converges more rapidly, effectively mitigating noise and channel-induced distortions in fewer iterations. However, this accelerated convergence also introduces larger fluctuations in the step error, leading to increased variations in weight updates and potential instability in the steady-state solution. For a small step size (\(\mu=0.01\)), part (c) shows relatively small but stable step error fluctuations, part (d) presents the equalized output gradually recovering the sinusoidal waveform, and part (e) depicts the remaining difference between the equalized and original signals, showing minimal residual distortion. In contrast, for \(\mu=0.1\), part  
Figure 5: Block diagram of the adaptive SDLMS equalizer. (f) reveals a more noticeable increase in step error fluctuations, part (g) displays an equalized output that more closely aligns with the original signal, and part (h) further illustrates a reduction in the difference between the equalized and original signals, indicating improved performance. When \(\mu=0.5\); however, part (i) demonstrates significant fluctuations in step error, suggesting that the equalizer adapts much faster but at the expense of greater instability, part (j) shows that while the equalized output rapidly aligns with the original signal, transient deviations remain prominent, and part (k) indicates that the residual error between the equalized and original signals is still relatively high. These findings underscore the critical role of step size selection in SDLMS equalization, highlighting the trade-off between convergence speed and steady-state error. Achieving an optimal balance in \(\mu\) is essential to ensure robust performance in VLC systems, where dynamic channel conditions necessitate efficient and stable adaptive equalization. Among various adaptive equalization techniques, the LMS algorithm offers efficient ISI suppression with relatively fast convergence, making it suitable for high-speed VLC applications. However, the computational complexity of LMS, primarily due to the requirement of a large number of iterations, the LMS algorithm can be used to estimate the number of iterations needed to achieve the desired  
ment for multiplications in the weight update process, limits its feasibility in low-power and embedded VLC systems. To address this issue, the SDLMS algorithm provides a simplified alternative by replacing full-value multiplications with sign-based updates, significantly reducing computational overhead.