To understand the spatial deployment of base stations (BSs) is the first step to analyze the performance of cellular networks and further design efficient networking protocols. Poisson point process (PPP), which has been widely adopted to characterize the deployment of BSs and established the reputation to give tractable results in the stochastic geometry analyses, usually assumes a static BS deployment density in homogeneous PPP (HPPP) models or delicately designed location-dependent density functions in in-homogeneous PPP models. However, the simultaneous existence of attractiveness and repulsiveness among BSs practically deployed in a large-scale area defies such an assumption, and the @math -stable distribution, one kind of heavy-tailed distributions, has recently demonstrated superior accuracy to statistically model the varying BS density in different areas. In this paper, we start with these new findings and investigate the intrinsic feature (i.e., the spatial self-similarity) embedded in the BSs. Afterwards, we refer to a generalized PPP setup with @math -stable distributed density and theoretically derive the related coverage probability. In particular, we give an upper bound of the derived coverage probability for high signal-to-interference-plus-noise ratio thresholds and show the monotonically decreasing property of this bound with respect to the variance of BS density. Besides, we prove that our model could reduce to the single-tier HPPP for some special cases and demonstrate the superior accuracy of the @math -stable model to approach the real environment.
As discussed later in Section , the PPP model has provided many useful performance trends. However, the concern about total independence between nodes (e.g., BSs) has never stopped. Hence, in order to reduce the modeling gap between the single-tier HPPP model and the practical BS deployment, some researchers have adopted two-tier or multiple tier HPPP models @cite_70 @cite_91 @cite_54 @cite_6 @cite_63 @cite_67 @cite_81 @cite_69 . Though these models may lead to some tractable results, but it lacks the reasonable explanation to divide the gradually deployed and increasingly denser heterogeneous cells @cite_34 into different tiers. On the contrary, the @math -stable model contributes to understanding the spatial self-similarity and bridging the gap between cellular networks and other social behavior-based complex networks.
@cite_67 @cite_69 @cite_91 @cite_70 @cite_54 @cite_6 @cite_81 @cite_63 @cite_34
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In this paper, the optimal BS (Base Station) density for both homogeneous and heterogeneous cellular networks to minimize network energy cost is analyzed with stochastic geometry theory. For homogeneous cellular networks, both upper and lower bounds of the optimal BS density are derived. For heterogeneous cellular networks, our analysis reveals the best type of BSs to be deployed for capacity extension, or to be switched off for energy saving. Specifically, if the ratio between the micro BS cost and the macro BS cost is lower than a threshold, which is a function of path loss and their transmit power, then the optimal strategy is to deploy micro BSs for capacity extension or to switch off macro BSs (if possible) for energy saving with higher priority. Otherwise, the optimal strategy is the opposite. The optimal combination of macro and micro BS densities can be calculated numerically through our analysis, or alternatively be conservatively approximated with a closed-form solution. Based on the parameters from EARTH, numerical results show that in the dense urban scenario, compared to the traditional macro-only homogeneous cellular network with no BS sleeping, deploying micro BSs can reduce about 40 of the total energy cost, and further reduce up to 35 with BS sleeping capability. In this paper, a new mathematical framework to the analysis of millimeter wave cellular networks is introduced. Its peculiarity lies in considering realistic path-loss and blockage models, which are derived from recently reported experimental data. The path-loss model accounts for different distributions of line-of-sight and non-line-of-sight propagation conditions and the blockage model includes an outage state that provides a better representation of the outage possibilities of millimeter wave communications. By modeling the locations of the base stations as points of a Poisson point process and by relying on a noise-limited approximation for typical millimeter wave network deployments, simple and exact integral as well as approximated and closed-form formulas for computing the coverage probability and the average rate are obtained. With the aid of Monte Carlo simulations, the noise-limited approximation is shown to be sufficiently accurate for typical network densities. The noise-limited approximation, however, may not be sufficiently accurate for ultra-dense network deployments and for sub-gigahertz transmission bandwidths. For these case studies, the analytical approach is generalized to take the other-cell interference into account at the cost of increasing its computational complexity. The proposed mathematical framework is applicable to cell association criteria based on the smallest path-loss and on the highest received power. It accounts for beamforming alignment errors and for multi-tier cellular network deployments. Numerical results confirm that sufficiently dense millimeter wave cellular networks are capable of outperforming micro wave cellular networks, in terms of coverage probability and average rate. The deployment of femtocells in a macrocell network is an economical and effective way to increase network capacity and coverage. Nevertheless, such deployment is challenging due to the presence of inter-tier and intra-tier interference, and the ad hoc operation of femtocells. Motivated by the flexible subchannel allocation capability of OFDMA, we investigate the effect of spectrum allocation in two-tier networks, where the macrocells employ closed access policy and the femtocells can operate in either open or closed access. By introducing a tractable model, we derive the success probability for each tier under different spectrum allocation and femtocell access policies. In particular, we consider joint subchannel allocation, in which the whole spectrum is shared by both tiers, as well as disjoint subchannel allocation, whereby disjoint sets of subchannels are assigned to both tiers. We formulate the throughput maximization problem subject to quality of service constraints in terms of success probabilities and per-tier minimum rates, and provide insights into the optimal spectrum allocation. Our results indicate that with closed access femtocells, the optimized joint and disjoint subchannel allocations provide the highest throughput among all schemes in sparse and dense femtocell networks, respectively. With open access femtocells, the optimized joint subchannel allocation provides the highest possible throughput for all femtocell densities. In a two-tier heterogeneous network (HetNet) where femto access points (FAPs) with lower transmission power coexist with macro base stations (BSs) with higher transmission power, the FAPs may suffer significant performance degradation due to inter-tier interference. Introducing cognition into the FAPs through the spectrum sensing (or carrier sensing) capability helps them avoiding severe interference from the macro BSs and enhance their performance. In this paper, we use stochastic geometry to model and analyze performance of HetNets composed of macro BSs and cognitive FAPs in a multichannel environment. The proposed model explicitly accounts for the spatial distribution of the macro BSs, FAPs, and users in a Rayleigh fading environment. We quantify the performance gain in outage probability obtained by introducing cognition into the femto-tier, provide design guidelines, and show the existence of an optimal spectrum sensing threshold for the cognitive FAPs, which depends on the HetNet parameters. We also show that looking into the overall performance of the HetNets is quite misleading in the scenarios where the majority of users are served by the macro BSs. Therefore, the performance of femto-tier needs to be explicitly accounted for and optimized. With the exponential increase in high rate traffic given by a new generation of wireless devices, data is expected to overwhelm cellular network capacity in the near future. Femtocell networks have been recently proposed as an efficient and cost-effective approach to provide unprecedented levels of network capacity and coverage. However, the dense and random deployment of femtocells and their uncoordinated operation raise important questions concerning interference pollution and spectrum allocation. Motivated by the flexible subchannel allocation capabilities of cognitive radio, we propose a cognitive hybrid division duplex (CHDD) that is suitable for heterogeneous networks in future mobile communication systems. Specifically, our CHDD scheme has a pair of frequency bands to perform frequency division duplex (FDD) on the macrocell, while time division duplex (TDD) is simultaneously operated in these bands by underlaid cognitive femtocells. By doing so, the proposed CHDD scheme exploits the advantages of both FDD and TDD schemes: operating in FDD at the macrocell tier controls inter-tier interference, whereas operating in TDD at the femtocell tier provides to femtocells the flexibility of adjusting uplink and downlink rates together with opportunistic access benefits. Using tools from stochastic geometry, we provide a methodology on how to design efficient switching mechanisms for cognitive TDD operation of femtocells. In particular, we derive closed-form expressions for the success probability and the area spectral efficiency of the proposed CHDD scheme when the macro tier is in downlink and uplink mode. Furthermore, we propose an open access policy as a means to improve the performance of macrocell transmissions. Our analysis and numerical results show the effectiveness of introducing cognition in femtocells so as to improve the system performance of two-tier femtocell networks. Cellular networks are in a major transition from a carefully planned set of large tower-mounted base-stations (BSs) to an irregular deployment of heterogeneous infrastructure elements that often additionally includes micro, pico, and femtocells, as well as distributed antennas. In this paper, we develop a tractable, flexible, and accurate model for a downlink heterogeneous cellular network (HCN) consisting of K tiers of randomly located BSs, where each tier may differ in terms of average transmit power, supported data rate and BS density. Assuming a mobile user connects to the strongest candidate BS, the resulting Signal-to-Interference-plus-Noise-Ratio (SINR) is greater than 1 when in coverage, Rayleigh fading, we derive an expression for the probability of coverage (equivalently outage) over the entire network under both open and closed access, which assumes a strikingly simple closed-form in the high SINR regime and is accurate down to -4 dB even under weaker assumptions. For external validation, we compare against an actual LTE network (for tier 1) with the other K-1 tiers being modeled as independent Poisson Point Processes. In this case as well, our model is accurate to within 1-2 dB. We also derive the average rate achieved by a randomly located mobile and the average load on each tier of BSs. One interesting observation for interference-limited open access networks is that at a given , adding more tiers and or BSs neither increases nor decreases the probability of coverage or outage when all the tiers have the same target-SINR. Partial Spectrum Reuse (PSR) in the second tier of two-tier heterogeneous cellular networks has a potential to improve spectrum efficiency by reducing inter-cell interference, and thus energy efficiency as well by deploying less or switching off more Base Stations (BSs). In this paper, we analyze the optimal PSR factor, defined as the portion of spectrum reused by micro cells in two-tier heterogeneous networks, which is not in an explicit form generally. Then, a closed-form limit of the optimal PSR factor is derived as the ratio of the user rate requirement over the whole system spectrum bandwidth is approaching zero, based on which a threshold of the micro-BS energy cost is also derived to determine which type of BSs is preferable. Specifically, one should deploy more micro BSs or switch off more macro BSs if the micro-BS energy cost is lower than the threshold. Otherwise, the optimal choice is the opposite. This threshold with the PSR scheme is higher than that without PSR scheme, i.e., PSR can improve both spectrum efficiency and energy efficiency. Numerical results show that adopting PSR can reduce the network energy consumption by up to 50 when the transmit power of macro BSs is 10dB higher than that of micro BSs. Traditional ultra-dense wireless networks are recommended as a complement for cellular networks and are deployed in partial areas, such as hotspot and indoor scenarios. Based on the massive multiple-input multi-output antennas and the millimeter wave communication technologies, the 5G ultra-dense cellular network is proposed to deploy in overall cellular scenarios. Moreover, a distribution network architecture is presented for 5G ultra-dense cellular networks. Furthermore, the backhaul network capacity and the backhaul energy efficiency of ultra-dense cellular networks are investigated to answer an important question, that is, how much densification can be deployed for 5G ultra-dense cellular networks. Simulation results reveal that there exist densification limits for 5G ultra-dense cellular networks with backhaul network capacity and backhaul energy efficiency constraints.