Clustering Algorithms and Validation Indices for mmWave Radio Multipath Propagation

Transmissions in the mmWave spectrum benefit from a-priori knowledge of radio channel propagation models. This paper is concerned with one important task that helps provide a more accurate channel model, namely, the clustering of all multipath components arriving at the receiver. Our work focuses on directive transmissions in urban outdoor scenarios and shows the importance of the correct estimation of the number of clusters for mmWave radio channels simulated with a software ray-tracer tool. We investigate the effectiveness of k-means and k-power-means clustering algorithms in predicting the number of clusters through the use of cluster validity indices (CMIs) and score fusion techniques. Our investigation shows that clustering is a difficult task because the optimal number of clusters is not always given by one or by a combination of more CMIs. However, using score fusion methods, we find the optimal partitioning for the k-means algorithm based on the power and time of arrival of the multipath rays or based on their angle of arrival. When the k-power-means algorithm is used, the power of each arriving ray is the most important clustering factor, making the dominant received paths pull the other ones around them, to form a cluster. Thus, the number of clusters is smaller and the decision based on CMIs or score fusion factors easier to be taken.