## 1 Introduction
### Motivation and Contributions  
Inspired by all of the above, we have conducted a measurement campaign on VR video frame freeze length, referred to as freeze length in the sequel for brevity, using a commercial TPCAST wireless VR solution. Apart from latency, video freezes and their durations or lengths are also important temporal performance indicators that impact on the QoE of networked VR applications and services. Based on the video traces collected in this experimental study, the following research questions are pursued in this paper:  
1. What are the statistical characteristics of the number of freezes, freeze intensities, and freeze lengths to be dealt with in wireless VR solutions? 2. What are the statistical models that form a compact representation of the measured freeze events? The research reported in this paper utilizes a wireless VR testbed which is based on the commercial TPCAST wireless adapter together with the HTC Vive HMD. This hardware has been chosen because TPCAST has been specifically developed and optimized for the HTC Vive HMD. In the meantime, a TPCAST adaptor is also available for the Oculus Rift HMD. The TPCAST wireless VR testbed can be used as a measurement environment that allows obtaining real data on temporal impairments observed in a commercial network solution rather than needing to focus on optimizing the wireless VR technology itself. The related work reported above has extensively assessed throughput and latency issues of wireless VR systems while little has been reported on freezes and freeze lengths. The comprehensive experimental study reported in this paper hence focuses on measuring freeze characteristics and their statistical analysis and modeling. The statistical models of the freeze characteristics may be included in wireless VR simulators supporting the development of physical layer, medium access layer, and higher layer functionalities. They also may serve as network-disturbance models for VR QoE studies, e.g., generating realistic freeze events in wireless VR stimuli to support the development of perceptual quality measures, similar as is done for conventional videos [21; 22]. The main contributions of this paper are summarized as follows:  
* A comprehensive description of the experimental setup of the wireless VR TPCAST testbed is provided including room topology and its structuring into quadrants,relevant hardware components and functions of the TPCAST-based wireless VR testbed, rotational movement procedure of the full-swivel chair adopted to realize the HMD rotational movement pattern, and the six distances imposed on the placements of the transmitter and receiver of the wireless link. * The number of freezes and freeze lengths deduced from the VR video traces that were recorded in the measurement campaign are reported both accumulated over the four quadrants as well as focusing on each of the four quadrants. This analysis is provided for the six considered distances. * Histograms of the freeze lengths measured in frames are provided for different distances between transmitter and receiver to shed light on the density of the underlying distributions of the measured data. Measures of the central tendency of freeze lengths are provided to support the statistical modeling of the freeze lengths. * Cumulative complementary histograms (CCHs) of the freeze length both accumulated over the four quadrants and quadrant-specific CCHs are provided. The CCHs reveal those scenarios which cause tails beyond the central part of the distributions of the freeze length. * Exponential distributions and their equivalent geometric distributions are obtained as statistical models for the freeze length characteristics using curve fitting along with their goodness of fit. The remainder of this paper is organized as follows. The experimental setup is described in Section 2 including the TPCAST wireless VR testbed, VR video traffic, room topology, and measurement procedure.