# Repetition with Learning Approaches in Massive Machine Type Communications
## 3 Repetition with Learning Approaches  
Most repetition approaches involve determining the number of repetitions according to the one-dimensional channel quality measured in a data table generated through a simulation. This method is strongly reliant on specific channel models, and errors in the channel quality measurement can lead to the selection of an incorrect number of repetitions. Moreover, a large-dimension data table requires considerable memory space. With the future trend of repetition technology development, one-dimensional channel quality indicators can no longer comprehensively represent the conditions of the channels in complex systems. This is because the link efficacy is related to numerous system parameters, and this can lead to erroneous channel quality assessment and inhibited system efficiency. The accuracy of channel quality indicators can be improved through an increase in the dimension of the channel quality. Machine learning provides a system with high-dimensional channel quality indicators that take into account changes in the environment. The relationship between channel quality and link reliability can be identified through examining the historical records in data transmission, thereby attaining an accurate prediction of the number of repetitions required according to the channel quality measurement results. Conventional repetition approaches are based on inquired data tables and cannot be updated according to system environments; this reduces their flexibility. Machine learning enables a system to learn and adapt to changes in an environment and flexibly adjust its channel quality selection standards, thereby accurately predicting the number of repetitions required. Accordingly, research on the implementation of machine learning to predict the number of uplink repetitions in eMTC is paramount for system efficacy enhancement. \(K\)-nearest neighbor (KNN) is a supervised learning approach in which a particular sample is considered to belong to a specific class if most of the \(k\)-nearest neighbors to it in its eigenspace also belong to said class [30; 31; 32]. In particular, a non-classified sample is categorized to the class in which its nearest classified neighbors belong. When new samples enter a group of classified samples, their distances from the training data are calculated, and the \(k\)-nearest samples are determined. Subsequently, the class with the greatest number of neighbors among the \(k\)-selected data is determined, and the new sample is classified accordingly. In the training phase, according to the feature set acquired from the signal-to-interference-nce-plus-noise ratio (SINR) of each subcarrier, number \(i\), which corresponds to repetition number, is selected to optimize the data rate and categorize the training set. All of the elements in each feature set must satisfy the optimized class, which maximizes the number of data transmitted, subject to the limitations of the block error rate. \[\text{arg}\max_{i}\{RN_{i}:BLER_{i}<H\} \tag{1}\]  
RLA-KNN approach training requires a training set with SINR feature vectors. Each vector is assigned to a number \(i\) according to equation (1). In RLA-KNN, when the training sample set and the K value and distance are determined, the class of any new sample can be determined. \(U=\{u_{1},\ u_{2},\ldots,u_{n}\}\), representing the eigenvector training set, and \(\text{S}=\{s_{1},\ s_{2},\ldots,s_{n}\}\), representing the class to which each eigenvector corresponds. RLA-KNN approach training is performed to identify all the vectors in a feature set and the approximated repetition approach corresponding to them. Let the training sample set TSS in KNN be  
\[\text{TSS}=\{(s_{1},\ u_{1}),\ (s_{2},\ u_{2}),\ldots,(s_{n},\ u_{n})\} \tag{2}\]  
The sample to be classified, x, is imported. The distance between x and all other samples in the training set can be calculated as follows: \(\text{L}\big{(}\text{x},\ s_{j}\big{)}\), \(j=1,\ 2,\ \ldots,n\).