Millimeter wave (mmWave) signals are much more sensitive to blockage, which results in a significant increase of the outage probability, especially for the users at the edge of the cells. In this paper, we exploit the technique of base station (BS) cooperation to improve the performance of the cell-edge users in the downlink transmission of mmWave cellular networks. We design two cooperative schemes, which are referred to as fixed-number BS cooperation (FNC) scheme and fixed-region BS cooperation (FRC) scheme, respectively. In FNC scheme, the cooperative BSs consist of the M nearest BSs around the served cell-edge users, and in FRC scheme, the cooperative BSs include all the BSs located within a given region. We derive the expressions for the average rate and outage probability of a typical cell-edge user located at the origin based on the stochastic geometry framework. To reduce the computational complexity of our analytical results for the outage probability, we further propose a Gamma approximation based method to provide approximations with satisfying accuracy. Our analytical results incorporate the critical characteristics of mmWave channels, i.e., the blockage effects, the different path loss of LOS and NLOS links and the highly directional antenna arrays. Simulation results show that the performance of the cell-edge users is greatly improved when mmWave networks are combined with the technique of BS cooperation.
The stochastic geometry framework has been widely adopted to analyze the network-wide performance of cellular networks, including the works in @cite_40 @cite_30 @cite_16 @cite_37 @cite_18 . In @cite_40 @cite_16 , the authors modeled the random locations of the BSs as a homogeneous poisson point process (HPPP). And based on this model, the outage probability of a typical user was derived in single tier cellular network @cite_16 and in multiple tiers heterogeneous networks (HetNets) @cite_37 @cite_30 @cite_18 . Compared with the traditional grid model, using HPPP to model the locations of BSs and mobile users provides analytical tractability while guarantees satisfying accuracy of the analytical results @cite_40 .
@cite_30 @cite_18 @cite_37 @cite_40 @cite_16
2167353407 2065735671 2121822142 1960633731
The spatial structure of base stations (BSs) in cellular networks plays a key role in evaluating the downlink performance. In this paper, different spatial stochastic models (the Poisson point process (PPP), the Poisson hard-core process (PHCP), the Strauss process (SP), and the perturbed triangular lattice) are used to model the structure by fitting them to the locations of BSs in real cellular networks obtained from a public database. We provide two general approaches for fitting. One is fitting by the method of maximum pseudolikelihood. As for the fitted models, it is not sufficient to distinguish them conclusively by some classical statistics. We propose the coverage probability as the criterion for the goodness-of-fit. In terms of coverage, the SP provides a better fit than the PPP and the PHCP. The other approach is fitting by the method of minimum contrast that minimizes the average squared error of the coverage probability. This way, fitted models are obtained whose coverage performance matches that of the given data set very accurately. Furthermore, we introduce a novel metric, the deployment gain, and we demonstrate how it can be used to estimate the coverage performance and average rate achieved by a data set. Stochastic geometry models for wireless communication networks have recently attracted much attention. This is because the performance of such networks critically depends on the spatial configuration of wireless nodes and the irregularity of the node configuration in a real network can be captured by a spatial point process. However, most analysis of such stochastic geometry models for wireless networks assumes, owing to its tractability, that the wireless nodes are deployed according to homogeneous Poisson point processes. This means that the wireless nodes are located independently of each other and their spatial correlation is ignored. In this work we propose a stochastic geometry model of cellular networks such that the wireless base stations are deployed according to the Ginibre point process. The Ginibre point process is one of the determinantal point processes and accounts for the repulsion between the base stations. For the proposed model, we derive a computable representation for the coverage probability—the probability that the signal-to-interference-plus-noise ratio (SINR) for a mobile user achieves a target threshold. To capture its qualitative property, we further investigate the asymptotics of the coverage probability as the SINR threshold becomes large in a special case. We also present the results of some numerical experiments. Stochastic geometry proves to be a powerful tool for modeling dense wireless networks adopting random MAC protocols such as ALOHA and CSMA. The main strength of this methodology lies in its ability to account for the randomness in the nodes' location jointly with an accurate description at the physical layer, based on the SINR, that allows to consider also random fading on each link. Existing models of CSMA networks adopting the stochastic geometry approach suffer from two important weaknesses: 1) they permit to evaluate only spatial averages of the main performance measures, thus hiding possibly huge discrepancies in the performance achieved by individual nodes; 2) they are analytically tractable only when nodes are distributed over the area according to simple spatial processes (e.g., the Poisson point process). In this paper we show how the stochastic geometry approach can be extended to overcome the above limitations, allowing to obtain node throughput distributions as well as to analyze a significant class of topologies in which nodes are not independently placed. Heterogeneous cellular networks (HCNs) with embedded small cells are considered, where multiple mobile users wish to download network content of different popularity. By caching data into the small-cell base stations, we will design distributed caching optimization algorithms via belief propagation (BP) for minimizing the downloading latency. First, we derive the delay-minimization objective function and formulate an optimization problem. Then, we develop a framework for modeling the underlying HCN topology with the aid of a factor graph. Furthermore, a distributed BP algorithm is proposed based on the network's factor graph. Next, we prove that a fixed point of convergence exists for our distributed BP algorithm. In order to reduce the complexity of the BP, we propose a heuristic BP algorithm. Furthermore, we evaluate the average downloading performance of our HCN for different numbers and locations of the base stations and mobile users, with the aid of stochastic geometry theory. By modeling the nodes distributions using a Poisson point process, we develop the expressions of the average factor graph degree distribution, as well as an upper bound of the outage probability for random caching schemes. We also improve the performance of random caching. Our simulations show that 1) the proposed distributed BP algorithm has a near-optimal delay performance, approaching that of the high-complexity exhaustive search method; 2) the modified BP offers a good delay performance at low communication complexity; 3) both the average degree distribution and the outage upper bound analysis relying on stochastic geometry match well with our Monte-Carlo simulations; and 4) the optimization based on the upper bound provides both a better outage and a better delay performance than the benchmarks.