## 2 Materials and Methods
### Genetic Programming Based Symbolic Regression
After passing the dataset through the Symbolic Regressor, the symbolic expression obtained for the dataset is as follows. \[\text{next\_e}= \sin(0.0667X_{0})\] \[-\sin\left(\frac{30.332}{X_{0}}+\frac{1}{X_{0}^{2}}\cdot\{135.039 \cdot\max(0,-0.077X_{0}\] \[+\sin(0.077X_{0}+\sin(0.077X_{0}+0.2009))\] \[\qquad+\frac{14.385}{X_{0}})\}\right)\] \[+\sin(0.0667X_{0}+1)\] \[+\sin(0.077X_{0}-0.563+\frac{14.385}{X_{0}})\] \[+\sin(0.077X_{0}+\sin(0.077X_{0}-0.579)-0.338)\] \[-\sin(\sin(0.0667X_{0}+\sin(0.077X_{0}-0.579)\] \[-\ \max(0,-0.077X_{0})-15.408+\frac{10.418}{X_{0}})\right)\] \[-14.595\]  
Also, the above expression can be depicted as a tree diagram using the graphviz python package as shown in \[-\sin\left(\frac{30.332}{X_{0}}+\frac{1}{X_{0}^{2}}\cdot\{135.039 \cdot\max(0,-0.077X_{0}\]0 Graphviz helps visualize the complex math expressions discovered by Symbolic Regression as tree diagrams, making them easier to understand and analyze. The leaves of the math parse tree [36] are numeric constants and variables from the symbolic expression. The internal nodes of the tree are arithmetic operations such as addition, subtraction, multiplication, division, and sine. Traversing the tree to its root will generate the entire symbolic expression. The tree diagram is a visual indication of the complexity of the regression. Now, when the trained model is evaluated for Symbolic Regression, the fit of the model to the data is determined by R2 score. R2 score is also called as the coefficient of determination. It is a statistical measure that tells how well a regression model, in this case the mathematical expression, fits the available data. It quantifies the proportion of variance in the dependent variable, the SNR values in this case, that is explained by the model. It ranges from 0 to 1, with 0 being the worst fit and 1 being the perfect fit. A higher R2 score means that the model is better at predicting the dependent variable. The evaluation of the model is illustrated in a scatter plot shown in \[-\sin\left(\frac{30.332}{X_{0}}+\frac{1}{X_{0}^{2}}\cdot\{135.039 \cdot\max(0,-0.077X_{0}\]1 The x-axis is the timeline indexed by the observation count. The y-axis refers to the Signal-to-Noise Ratio (SNR). The blue dotted line represents the observed SNR values. The red dotted line represents the symbolic function, which is the mathematical formula discovered by the Symbolic Regression algorithm to approximate the true function. The closer the red line is to the blue line, the better the fit. \[-\sin\left(\frac{30.332}{X_{0}}+\frac{1}{X_{0}^{2}}\cdot\{135.039 \cdot\max(0,-0.077X_{0}\]2 The mathematical expression from the Symbolic Regression. Modeling the SNR values is depicted as a tree diagram for better visualization. \[-\sin\left(\frac{30.332}{X_{0}}+\frac{1}{X_{0}^{2}}\cdot\{135.039 \cdot\max(0,-0.077X_{0}\]3 The scatter plot from the Symbolic Regression shows how well the mathematical expression fits the data. As can be seen, the fit is reasonably satisfactory. The R2 score for this fit is 0.82497861499. The symbolic function captures the general trend of the true function reasonably well. However, there are some deviations between the two lines, particularly at higher and lower SNR values. The deviation increases when the SNR is below -18 dB and above -10 dB. The deviation at lower SNR values may be because of the noise floor, which sets a minimum limit on how low the SNR can go [37]. In mmWave systems, this noise floor can be caused by thermal noise in the components, atmospheric noise, and interference from other sources. The short plateaus of the signal at the bottom may be caused by the noise floor. On the other hand, the deviation at higher SNR values can be related to non-linear effects in amplifiers and other components that can distort the signal, reducing the effective SNR even if the raw signal power is high. The fit method of the SymbolicRegressor class uses genetic programming to evolve a population of mathematical expressions that best fit the training data.