Millimeter wave communication systems can provide high data rates, but the system performance may degrade significantly due to interruptions by mobile blockers, such as humans or vehicles. High-frequency interruptions and lengthy blockage durations will degrade the quality of the user's experience. A promising solution is to employ the macrodiversity of base stations (BSs), where the user equipment (UE) can handover to other available BSs if the current serving BS gets blocked. However, an analytical model to evaluate the system performance of dynamic blockage events in this setting is unknown. In this paper, we develop a line-of-sight (LOS) dynamic blockage model and evaluate the probability, duration, and frequency of blockage events considering all the links to the UE which are not blocked by buildings or the user's own body. For a dense urban area, we also analyze the impact of non-LOS links on blockage events. Our results indicate that the minimum density of the BS required to satisfy the quality of service requirements of ultra-reliable low-latency communication applications will be driven mainly by blockage and latency constraints, rather than coverage or capacity requirements.

Millimeter wave (mmWave) communication systems can provide high data rates but the system performance may degrade significantly due to mobile blockers and the user's own body. A high frequency of interruptions and long duration of blockage may degrade the quality of experience. For example, delays of more than about 10ms cause nausea to VR viewers. Macro-diversity of base stations (BSs) has been considered a promising solution where the user equipment (UE) can handover to other available BSs, if the current serving BS gets blocked. However, an analytical model for the frequency and duration of dynamic blockage events in this setting is largely unknown. In this paper, we consider an open park-like scenario and obtain closedform expressions for the blockage probability, expected frequency and duration of blockage events using stochastic geometry. Our results indicate that the minimum density of BS that is required to satisfy the Quality of Service (QoS) requirements of AR/VR and other low latency applications is largely driven by blockage events rather than capacity requirements. Placing the BS at a greater height reduces the likelihood of blockage. We present a closed-form expression for the BS density-height trade-off that can be used for network planning.

We analyze the theoretical properties of the recently proposed objective function for efficient online construction and training of multiclass classification trees in the settings where the label space is very large. We show the important properties of this objective and provide a complete proof that maximizing it simultaneously encourages balanced trees and improves the purity of the class distributions at subsequent levels in the tree. We further explore its connection to the three well-known entropy-based decision tree criteria, i.e., Shannon entropy, Gini-entropy and its modified variant, for which efficient optimization strategies are largely unknown in the extreme multiclass setting. We show theoretically that this objective can be viewed as a surrogate function for all of these entropy criteria and that maximizing it indirectly optimizes them as well. We derive boosting guarantees and obtain a closed-form expression for the number of iterations needed to reduce the considered entropy criteria below an arbitrary threshold. The obtained theorem relies on a weak hypothesis assumption that directly depends on the considered objective function. Finally, we prove that optimizing the objective directly reduces the multi-class classification error of the decision tree.

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