# Clustering-Based Nonstationary Massive MIMO Channel Modeling at 1.4725 GHz
## 3 Channel Model  
The following sections demonstrate the results of data measured on Massive MIMO radio channels. These investigations aim to unfold the critical correlation features from the experimental data. According to the measured results, the correlation fading characteristics of antenna elements were different. Therefore, it was globally non-stationary on the Massive MIMO antenna array. As to the closely placed elements, it is easily understood that the fadings were similar due to the same shadow regions they were located in. Thus, the sub-channel can be considered as stationary covered by the same shadow regions. Generally, there are two methods to map out the stationary intervals. The first is the averaging method. According to the empirical model, the antenna elements can be divided into several subsets. Here, every subset is composed of a fixed number of elements. This method operates easily, which ignores the impact of specific propagation scenarios, but as a trade-off, it's at low accuracy. The second is the method of inspection. That is to say, we can estimate the parameters of the multi-path cluster according to the measurement results [21], then we extract the visible region of the multi-path cluster, furthermore grouping the antenna into a subset to ensure the channels are stationary within the groups. Here, a group of antenna elements is covered by a visible region in sight of radio propagation. As a result, the boundaries of the visible region are formed, and we should note that groups are irregularly divided. The method of inspection is based on the division of the antenna stationary subinterval, which greatly depends on the operator's observation and judgement. In addition, the larger the physical size of the array is, the more difficult the actual operation. In order to overcome the limitations of these methods, we introduce the automatic clustering algorithm, named ECD (element channel distance) algorithm based on the traditional MCD (multipath component distance) algorithm applied in mathematics [22; 23; 24] and clustering algorithm applied in pattern recognition [25; 26]. Clustering is to classify data objects into multiple subsets according to certain rules. Considering the special characteristics of radio channels, we develop the traditional algorithms by introducing the continuous coverage of the visible area of the cluster on the dimension of the extended antenna array. Objects in the same subset have higher similarity, while objects in different subsets have lower coupling. Distance algorithm is the most popular criterion in multi-path clustering  
Figure 5: Stationary and nonstationary channel correlation matrix. **(a)** The WSSUS correlation matrix; **(b)** the non-WSSUS correlation matrix. to model the radio channel. The multi-path with similar distances is divided into the same cluster. In practice, the distance refers to the compound distance of multi-path parameters, at the same time, the contributions of those parameters are fully considered in the way of the weighting coefficient. This is a scientific and highly efficient clustering method based on machine learning and artificial intelligence. First of all, we should understand that the goal of clustering is to divide all measurement data into several subsets, which required high correlation within them and low coupling between them. As a result, subsets or so-called clusters are composed of multipaths, which have similar elements, including energy, delay, angle, etc. Secondly, we should make clear that the foundation of clustering has a rich supply of data, which is not only raw data in the measurement but also the channel parameters of each antenna estimated from certain algorithms, SAGE algorithm as example, and the parameters including power, delay, angle and others. All these are called preprocessed data. Finally, the stationary subinterval programming is carried out, which is to divide the original set of preprocessed data into some classes with similar attributes by using certain criteria.