# Learning-Assisted Rain Attenuation Prediction Models
## 4 Insights of LARA Models
### LARA Model with One Factor  
[PERSON] et al. (2014) used three sites' attenuation data about the 11 GHz frequency to predict the short-term rain attenuation prediction for the standard fade mitigation technique (FMT) application. The technique is composed of AANN that enables predicting short-term rain attenuation while the ILA technique helps in case any rain event behavior is non-stationary (Figure 5). They performed calculated attenuation based on an ideal clear sky-based threshold value to mark the attenuation. They observed that at a low-frequency component (near 10 GHz and below), spectral density variations is low, while at higher frequency components, spectral density variations are comparatively higher. Using a window function, they eliminated the fluctuations encountered by higher frequency elements. Additionally, a linear curve is fitted using the least-square fit methodology for all samples within this window range of 10 min length. The weights of non-linear portions are modified by \(\Delta w_{k}(\tau)\), where \(\tau\) is the sample time. The weights of a non-linear portion of the error at the end of the non-linear portion is minimized through optimization at every sample time at \(\tau\):  
\[\Delta w_{1}(t)\ =\ 2\lambda^{0}\mu e_{1}(t)f_{1}{}^{\prime}I_{1}(t-1) \tag{1}\]  
\[\Delta w_{2}(t)\ =\ 2\lambda^{1}\mu e_{2}(t)f_{2}{}^{\prime}I_{2}(t-1)+2 \lambda^{0}\mu e_{1}(t)f_{1}{}^{\prime}f_{2}{}^{\prime}I_{2}(t-1) \tag{2}\]  
\[w_{k}(t)\ =\ w_{k}(t-1)+\Delta w_{k}(t) \tag{3}\]  
where \(\lambda\) is a forgetting factor (\(0<\lambda<1\)), \(\mu\) is the learning factor, \(f_{k}{}^{\prime}\) is the derivative of the activation function of the \(k\) module, and \(e_{1},e_{2}\) are errors. The error next to the linear block is minimized through modifying the weights of the least mean square technique. If there is a change during a sample time, the new weight will be:  
\[w(t)\ =\ w(t-1)+\Delta w(t) \tag{4}\]  
**Advantages:** The technique can predict attenuation for in situ application at about 11 GHz frequency components effectively. The model can be applied concerning the short-term prediction of rain attenuation for FMT operation. **Disadvantages:** The technique cannot determine or predict attenuation for scintillation that experiences fast fluctuations. Figure 5: Adaptive Artificial neural network (AANN) to predict short-term rain attenuation. **Future improvement:** To deploy measures to predict attenuation at higher frequency components. They had added a variable margin to the expected value in an efficient fashion to increase the excess over bound, resulting in recourse drainage. [PERSON] et al. [13] suggested two methods: the least square-support vector machine (LS-SVM) and the synaptic back-propagation (BP) technique. All strategies can forecast attenuation by taking the strength of the rainfall as the reference. For the BP-based model, they used 78 samples of the rainfall date to feed in a BP network that consisted of unregulated synaptic weights. However, after feeding a sample to the network, the network can calculate the attenuation based on the current synaptic weight. At this point, the mean-square error is measured. This error is propagated in the backward direction to measure and change the model's synaptic weights, recognizing that there might be a threshold error value. They repeated this process for the rest of the 77 samples as well. Based on this experiment, they chose a BP network that consists of single input and output node and a single hidden layer that consists of 13 nodes and optimized synaptic weights. For the LS-SVM case, they used the training data set \(S=\{(x_{1},y_{1}),(x_{2},y_{2}),\ldots,(x_{n},y_{n})\}\in R_{n}\times A_{n}\), where \(R_{n}\) is the rainfall intensity and \(A_{n}\) is the rain attenuation. From higher-dimension feature space, optimal linear regression function can be obtained. **Advantages:** The method can accurately forecast attenuation for 60 GHz, and the experimental findings demonstrate that both models outperform the ITU-R model.