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Meeting the diverse delay requirements of emerging wireless applications is one of the most critical goals for the design of ultradense networks. Though the delay of point-to-point communications has been well investigated using classical queueing theory, the delay of multi-point to multi-point communications, such as in ultradense networks, has not been explored in depth. The main technical difficulty lies in the interacting queues problem, in which the service rate is coupled with the statuses of other queues. In this article, we elaborate on the main challenges in the delay analysis in ultradense networks. Several promising approaches, such as introducing the dominant system and the simplified system, to bypass these difficulties are proposed and summarized to provide useful guidance.

Heterogeneous cellular networks (HetNets) are to be deployed for future wireless communication to meet the ever-increasing mobile traffic demand. However, the dense and random deployment of small cells and their uncoordinated operation raise important concerns about energy efficiency. In this paper, we consider the base station (BS) cooperation solution for improving energy efficiency of the HetNets where BSs from each tier within the cooperative cluster jointly transmit the same data to a typical user. Firstly, based on the proposed clustering model, we precisely derive the ergodic rate expression using tools from stochastic geometry. Furthermore, we formulate a power minimization problem with minimum ergodic rate constraint and derive a closed-form approximated result of the optimal cooperative radii. Building upon these results, we could effectively address the problem how to design appropriate cooperative radii, taking into account the trade-off of ergodic rate and energy efficiency. Simulation results also indicate that under the proposed clustering model, deploying a two-tier HetNet is more energy-saving compared to a macro-only network.

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Backpropagation-based visualizations have been proposed to interpret convolutional neural networks (CNNs), however a theory is missing to justify their behaviors: Guided backpropagation (GBP) and deconvolutional network (DeconvNet) generate more human-interpretable but less classsensitive visualizations than saliency map. Motivated by this, we develop a theoretical explanation revealing that GBP and DeconvNet are essentially doing (partial) image recovery which is unrelated to the network decisions. Specifically, our analysis shows that the backward ReLU introduced by GBP and DeconvNet, and the local connections in CNNs are the two main causes of compelling visualizations. Extensive experiments are provided that support the theoretical analysis.