Chiranjib Saha

Enriched

One of the principal underlying assumptions of current approaches to the analysis of heterogeneous cellular networks (HetNets) with random spatial models is the uniform distribution of users independent of the base station (BS) locations. This assumption is not quite accurate, especially for user-centric capacity-driven small cell deployments where low-power BSs are deployed in the areas of high user density, thus inducing a natural correlation in the BS and user locations. In order to capture this correlation, we enrich the existing

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-Tier HetNet Model to Enable the Analysis of User-Centric Small Cell Deployments

-tier Poisson point process (PPP) HetNet model by considering user locations as Poisson Cluster Process with the BSs at the cluster centers. In particular, we provide the formal analysis of the downlink coverage probability in terms of a general density function describing the locations of users around the BSs. The derived results are specialized for two cases of interest: 1) Thomas cluster process, where the locations of the users around BSs are Gaussian distributed and 2) Matérn cluster process, where the users are uniformly distributed inside a disc of a given radius. Tight closed-form bounds for the coverage probability in these two cases are also derived. Our results demonstrate that the coverage probability decreases as the size of user clusters around BSs increases, ultimately collapsing to the result obtained under the assumption of PPP distribution of users independent of the BS locations when the cluster size goes to infinity. Using these results, we also handle mixed user distributions consisting of two types of users: 1) uniformly distributed and 2) clustered around certain tiers.

Enhanced Multiobjective Evolutionary Algorithm Based on Decomposition for Solving the Unit Commitment Problem

In this paper, a multiobjective evolutionary algorithm based on decomposition (MOEA/D) is proposed to solve the unit commitment (UC) problem as a multiobjective optimization problem (MOP) considering minimizing cost and emission as the multiple objectives. Since UC problem is a mixed-integer optimization problem, a hybrid strategy is integrated within the framework of MOEA/D such that genetic algorithm (GA) evolves the binary variables, while differential evolution (DE) evolves the continuous variables. Further, a novel nonuniform weight-vector distribution (NUWD) strategy is proposed and an ensemble algorithm based on combination of MOEA/D with uniform weight-vector distribution (UWD) and NUWD strategy is implemented to enhance the performance of the presented algorithm. Extensive case studies are presented on different test systems and the effectiveness of the hybrid strategy, the NUWD strategy, and the ensemble algorithm is verified through stringent simulated results. Further, exhaustive benchmarking against the algorithm proposed in the literature is presented to demonstrate the superiority of the proposed algorithm.

Nearest-Neighbor and Contact Distance Distributions for Thomas Cluster Process

We characterize the statistics of nearest-neighbor and contact distance distributions for Thomas cluster process (TCP), which is a special case of Poisson cluster process. In particular, we derive the cumulative distribution function of the distance to the nearest point of TCP from a reference point for three different cases: 1) reference point is not a part of the point process; 2) it is chosen uniformly at random from the TCP; and 3) it is a randomly chosen point from a cluster chosen uniformly at random from the TCP. While the first corresponds to the contact distance distribution, the other two provide two different viewpoints for the nearest-neighbor distance distribution. Closed-form bounds are also provided for the first two cases.

Downlink coverage probability of K-tier HetNets with general non-uniform user distributions

Current approaches to the analysis of heterogeneous cellular networks (HetNets) with random spatial models assume users to be distributed according to a homogeneous Poisson Point Process (PPP) independently of the base station (BS) locations. In reality, however, current deployments are capacity-driven, which correlates the BS and user locations. In this paper, we develop tools for the downlink analysis of HetNets with general nonuniform user distributions by enriching the K-tier PPP HetNet model. Instead of being PPP distributed, the user locations are modeled by a Poisson cluster process with the cluster centers being the BSs. In particular, we provide the first formal analysis of the downlink coverage probability in terms of a general density function describing the locations of users around the BSs. All the results are specialized to a particular case of a Thomas cluster process, where the locations of the users around BSs are Gaussian distributed. Our results concretely demonstrate that the coverage probability decreases with the increasing variance of the user location distribution, ultimately collapsing to the result for the PPP user distribution when the variance goes to infinity.

Poisson cluster process: Bridging the gap between PPP and 3GPP HetNet models

The growing complexity of heterogeneous cellular networks (HetNets) has necessitated the need to consider variety of user and base station (BS) configurations for realistic performance evaluation and system design. This is directly reflected in the HetNet simulation models considered by standardization bodies, such as the third generation partnership project (3GPP). Complementary to these simulation models, stochastic geometry-based approach modeling the user and BS locations as independent and homogeneous Poisson point processes (PPPs) has gained prominence in the past few years. Despite its success in revealing useful insights, this PPP-based model is not rich enough to capture all the spatial configurations that appear in real-world HetNet deployments (on which 3GPP simulation models are based). In this paper, we bridge the gap between the 3GPP simulation models and the popular PPP-based analytical model by developing a new unified HetNet model in which a fraction of users and some BS tiers are modeled as Poisson cluster processes (PCPs). This model captures both non-uniformity and coupling in the BS and user locations. For this setup, we derive exact expression for downlink coverage probability under maximum signal-to-interference ratio (SIR) cell association model. As intermediate results, we define and evaluate sum-product functionals for PPP and PCP. Special instances of the proposed model are shown to closely resemble different configurations considered in 3GPP HetNet models. Our results concretely demonstrate that the performance trends are highly sensitive to the assumptions made on the user and SBS configurations.

D2D Underlaid Cellular Networks with User Clusters: Load Balancing and Downlink Rate Analysis

In this paper we develop a comprehensive analytical framework for a cellular network enhanced with in-band device-to-device (D2D) communication capability where the D2D links reuse the downlink resources of the cellular links. The locations of the cellular base stations (BSs) are modeled as a Poisson point process (PPP). The user positions are modeled as a Thomas cluster process (TCP) to capture the inherent tendency of users to be located at close proximity to each other. The bandwidth allocated to D2D transmission is fixed and to cellular transmission is dynamic dependent on the load (the number of users) served by the macro BS. The users inside a cluster can either establish a D2D connection with a potential D2D transmitter (Tx) containing the file of interest within the same cluster if it is located closer than certain distance threshold or otherwise connects to the cellular network. By increasing this distance threshold, cellular traffic can be offloaded to D2D connections which in turn increases the interference from simultaneously active D2D Txs. We characterize the downlink rate coverage probability for this setup. Our analysis shows that there exists an optimum distance threshold for which rate coverage is maximized.