# Design and Implementation of DSLMS Algorithm Based Photoelectric Detection of Weak Signals
## 5 Experimental Verification
### DSLMS Simulation Parameter Selection and Experimental Analysis  
The simulation experiments in this paper set the filter order to 8 orders and the number of sampling points to 3000 points. Three sets of simulations are conducted to compare the noise reduction effect of the fixed-step LMS algorithm, the variable-step LMS algorithm based on the Sigmoid function, and the DSLMS algorithm proposed in this paper. Before the comparison experiment, each algorithm's optimal parameter selection values are determined. The value of \(\mu\) of the fixed-step-size LMS algorithm is related to the maximum eigenvalue of the input signal correlation matrix, and based on the literature [35; 36], the \(\mu\) value of the fixed-step-size LMS algorithm is randomly adjusted within the theoretical range for 100 simulation experiments, and the effect of the step size on the error is observed. Analyzing the experimental results, it can be found that the \(\mu\) value is too large or too small and can not converge stably or keep a small steady-state mean square error. The results of the simulation experiments are synthesized. Under the experimental conditions of this paper, the \(\mu\) value of the fixed-step-size LMS algorithm should be around 0.15 for the best effect. For the \(\alpha\) and \(\beta\) values of the variable-step-size LMS algorithm based on the Sigmoid function, based on the literature research [37], 100 simulation experiments are carried out, respectively, with randomly selected values within the theoretical range, and the results are statistically analyzed to determine the appropriate parameter values. According to the comprehensive simulation experiment results, under the experimental conditions of this paper, the Sigmoid function-based variable-step-size LMS algorithm with an \(\alpha\) value of 6 and a \(\beta\) value of 3 has the best effect. Figure 15 shows the comparison of the mean square error (MSE) curves of the three algorithms, and Table 1 shows the comparison of the number of iterations of the algorithms under different signal-to-noise ratios, from which it can be seen that the traditional fixed-step LMS algorithm converges the slowest under four noise backgrounds (signal-to-noise ratios of 5, 10, 20 and 30, respectively). The DSLMS algorithm in this paper has the fastest convergence speed. The algorithm in this paper maintains a small mean square error and good stability in the convergence completion stage. Figure 15: Comparison of MSE of the three algorithms in different SNR contexts. (**a**) SNR = 5 dB; (**b**) SNR = 10 dB; (**c**) SNR = 20 dB; (**d**) SNR = 30 dB. Analyzing the above results, it can be found that the signal-to-noise ratios of the filtered signals are 8\(\sim\)16 dB higher than those of the pre-filtered signals, and the signal portion of the filtered signals that converge stably is 18\(\sim\)37 dB higher than that of the pre-filtered signals. The DSLMS algorithm proposed in this paper can maintain good convergence and stability under high and low signal-to-noise ratios and has a strong anti-noise interference capability when combined with the pair of eliminator systems. To demonstrate further that the algorithm proposed in this paper performs better, we compared it with the traditional fixed-step LMS algorithm and the variable-step LMS algorithm with the Sigmoid function. We optimized the function equation and parameters that were set. Figure 17a,b shows the comparison between the ideal output signal and the filtered results of each algorithm under the conditions of a signal-to-noise ratio (SNR) of 1, 15, and 30, respectively. The figure shows that the SNR has a more significant effect on the traditional fixed-step LMS algorithm and the variable-step LMS algorithm with the Sigmoid function. In contrast, it has a lesser impact on this paper's DSLMS algorithm. Overall, the curves obtained by this paper's algorithm are closer to the ideal values, and the stability of the curves is reached more quickly.