1. Introduction
5G wireless technologies are a promising solution for many of the problems of current wireless networks, and especially of those concerning high-speed data transfers and ubiquitous connectivity requiring very low latency responses. Among these technologies,
spectrum extension through the use of
millimeter-wave (mmWave) band (30–300 GHz) with multiple GHz of unused bandwidth is one that has been receiving increasing attention [
1,
2]. Unfortunately, mmWave transmissions suffer from high propagation loss, sensitivity to blockage, atmospheric attenuation and diffraction loss, which brings in new unprecedented challenges to the implementation of communication systems at these high frequency bands. Tackling them requires well-thought
radio channel propagation models that are obtained through extensive measurements (using steerable antennas and channel sounders), or via software ray-tracing simulations.
In this paper, we are concerned with two important tasks that help generate better radio channel models. First, we emphasize the role of clustering algorithms in grouping the incoming rays at the receiver site. Second, equally important, is the validation of their results. Clustering is paramount for fast processing of the received rays, and thus for extracting channel parameters in an efficient manner when the volume of data generated through simulations is huge. We use the well-known k-means clustering algorithm, in which we replace the usual Euclidean distance metric with the multipath component distance (MCD). Thus, a multi-dimensional space is defined by the channel parameters of the multipath components (MPCs). This space—based on the Time-of-Arrival (ToA), azimuth and elevation of the Angle-of-Arrival (AoA) and Angle-of-Departure (AoD)—is fed into the clustering algorithms, to provide the partitioning of all MPCs. Our analysis quantifies the goodness of the clustering algorithms through the use of five cluster validity indices (CVIs) and three score fusion techniques. The results show that, by using only CVIs we sometimes fail to find the optimal clustering number K because the indices might capture only specific aspects of a clustering solution. Therefore, we combine the five CVIs in an ensemble that becomes a better predictor of clustering quality than any CVI taken separately.
As an application of the two major tasks (clustering and validation) mentioned above, in the second part of our study, we increase the frequency of the transmitted signal, to cover other useful bands in the mmWave spectrum (e.g., 38, 60 and 73 GHz), and we verify how the clustering solution changes. Since directivity is extremely important to offset the large path loss and shadowing loss of the higher frequency mmWave signals, we replace the initial antenna with another one with smaller beamwidth, but higher gain, and we check if our clustering solution changes noticeably.
The results of our paper show that while higher frequencies (60 and 73 GHz) generate a sparser environment at the receiver, the number of clusters does not vary by much for many receivers in our outdoor scenario. Nevertheless, there are exceptions related either to the receiver being at the edge of the cell, or being much closer to the transmitter, at the entrance on a street with tall buildings (on both sides) that create a tunneling effect. Therefore, the longer delays experienced by some MPCs or the multitude of rays due to more reflections and scattering increase the number of clusters in some spots.
In our study, the clustering solution for each receiver is found not only for different frequencies of the transmitted signal but also for different half-power beamwidth (HPBW) antennas. In this context, we show that the most representative MPCs (i.e., the cluster heads) discovered for the lowest mmWave frequency (28 GHz) transmissions have larger times-of-arrival (ToA) and a wider range of angles-of-arrival (AoA), while the antenna beamwidth does not affect much these statistics.
Finally, we analyze the root-mean-square (RMS) delay spread (DS), as an important indicator of the radio channel quality. It helps evaluate the time dispersive properties of the channel and gives an estimation of the maximum data rate for transmissions. Thus, we provide the distribution of the RMS DS values based on the values calculated for the cluster heads (CHs) identified in the clustering process. Our results show that the delay spread of the narrower antenna is smaller at both ends of the studied spectrum (28 and 73 GHz). We also report a smaller overall RMS delay spread for both antennas for the case of transmissions at 73 GHz. These results demonstrate the importance of directive antennas with higher gain that allow for higher data rates in the channel.
The rest of the paper is organized as follows.
Section 2 represents a brief primer on clustering techniques and the validation of their results. It also introduces the setup of our simulations.
Section 3 describes in detail the results obtained in our study.
Section 4 concludes the paper and opens the path for more research in this area.