Base station (BS) sleeping has emerged as a viable solution to enhance the overall network energy efficiency by inactivating the underutilized BSs. However, it affects the performance of users in sleeping cells depending on their BS association criteria, their channel conditions toward the active BSs, and scheduling criteria and traffic loads at the active BSs. This paper characterizes the performance of cellular systems with BS sleeping by developing a systematic framework to derive the spectral efficiency and outage probability of downlink transmission to the sleeping cell users taking into account the aforementioned factors. In this context, a user association scheme is also developed in which sleeping cell users associate to a BS with maximum mean channel access probability (MMAP). The MMAP-based user association scheme adapts according to traffic load and scheduling criteria at the active BSs. We consider greedy and round-robin schemes at active BSs for scheduling users in a channel. We also derive the analytical results for the conventional maximum received signal power (MRSP)-based user association scheme. Finally, we derive the statistics of the received signal and interference power to evaluate the downlink spectral efficiency of a given sleeping cell user. Numerical results provide a comparison between two user association schemes as a function of system parameters and demonstrate the efficacy of the MMAP-based association scheme in non-uniform traffic load scenarios.
Recently, few analytical frameworks have considered to derive the optimal density of sleeping BSs @cite_7 @cite_18 @cite_11 , proposed distributed sleeping mechanisms considering cognitive small cells @cite_12 , and developed different BS switching-off schemes @cite_21 @cite_14 . The development of such frameworks is highly desirable to capture the joint interplay among the network design parameters while extracting in-depth theoretical insights behind various observations and performance trends. A power minimization problem with coverage constraint for a randomly selected sleeping cell user is formulated in @cite_7 @cite_18 such that the BS density is optimized considering random and traffic load-based sleeping. To avoid coverage holes, power of all active BSs is assumed to increase equally regardless of the channel conditions of the sleeping cell users. Due to the complexity of closed-form solution, an optimal value of BS density is computed numerically. In @cite_11 , a BS density minimization problem is formulated with coverage constraints of users in sleeping cells. However, the expression for coverage includes two improper integrals and an infinite summation. Therefore, the authors opt to derive upper and lower bounds on the optimal BS density.
@cite_18 @cite_14 @cite_7 @cite_21 @cite_12 @cite_11
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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. This paper considers the joint optimization of frequency reuse and base-station (BS) bias for user association in downlink heterogeneous networks for load balancing and intercell interference management. To make the analysis tractable, we assume that BSs are randomly deployed as point processes in multiple tiers, where BSs in each tier have different transmission powers and spatial densities. A utility maximization framework is formulated based on the user coverage rate, which is a function of the different BS biases for user association and different frequency reuse factors across BS tiers. Compared to previous works where the bias levels are heuristically determined and full reuse is adopted, we quantitatively compute the optimal user association bias and obtain the closed-form solution of the optimal frequency reuse. Interestingly, we find that the optimal bias and the optimal reuse factor of each BS tier have an inversely proportional relationship. Further, we also propose an iterative method for optimizing these two factors. In contrast to system-level optimization solutions based on specific channel realization and network topology, our approach is off-line and is useful for deriving deployment insights. Numerical results show that optimizing user association and frequency reuse for multi-tier heterogeneous networks can effectively improve cell-edge user rate performance and utility. Energy efficiency (EE) is becoming an important design goal for wireless communication systems providing high spectral efficiency (SE). Both massive multi-input multi-output (MIMO) and small cell network (SCN) are expected to achieve high EE for high throughput cellular networks, though using different mechanisms. Massive MIMO improves EE by exploiting a large array gain, while SCN improves EE by deploying a large number of low-power base stations (BSs) to reduce the propagation loss and increase the opportunity of BS sleep. In this paper, we compare the EEs as well as the SEs of Massive MIMO and SCN. For a fair comparison, we consider a multi-cell network with the same user density, antenna density and average cell-edge signal-to-noise-ratio (SNR). Perfect channel information is assumed, and three BS sleep strategies are considered. Our analysis shows that the EE of SCN increases with the cell size shrinking, and the achievable SEs of SCN and Massive MIMO increase with the cell-edge SNR. When the number of cells is large, SCN is always more energy efficient than Massive MIMO. On the other hand, when the number of cells is small, Massive MIMO achieves higher EE than SCN when the circuit power consumptions of Massive MIMO are much lower than SCN. Base station (BS) sleeping is an effective way to improve the energy-efficiency of cellular networks. However, it may bring extra user-perceived delay. We conduct a theoretical study into the impact of BS sleeping on both energy-efficiency and user-perceived delay. We consider hysteresis sleep and three typical wake-up schemes, namely single sleep, multiple sleep, and @math -limited schemes. We model the system as an @math vacation queue, which captures the setup time, the mode-changing cost, as well as the counting or detection cost during the sleep mode. Closed-form expressions for the average power and the Laplace–Stieltjes transform of delay distribution are obtained. The impacts of system parameters on these expressions are analyzed. We then formulate an optimization problem to design delay-constrained energy-optimal BS sleeping policies. We show that the optimal solutions possess a special structure, thereby allowing us to obtain them explicitly or numerically by simple bisection search. In addition, the relationship between the optimal power consumption and the mean delay constraint is analyzed, so as to answer the fundamental question: how much energy can be saved by trading off a certain amount of delay? It is shown that this optimal relationship is linear only when the delay constraint is lower than a threshold. Numerical studies are also conducted, where the impact of detection or counting cost during the sleep mode is explored, and the delay distribution under the optimal policy is obtained. While the deployment of base stations (BSs) becomes increasingly dense in order to accommodate the growth in traffic demand, these BSs may be under-utilized during most hours except peak hours. The deactivation of these under-utilized BSs is regarded as the key to reducing network power consumption; however, the remaining active BSs should increase their transmit power in order to fill network coverage holes that result from BS switching off. This paper investigates the optimal balance between such beneficial and harmful effects of BS switching off in terms of minimizing the network power consumption, through comprehensively considering the spatial BS distribution, BS transmit power, BS power consumption behaviors, radio propagation environments, and frequency reuse. The suboptimal and approximated design problems are formulated as geometric programming and the numerical results demonstrate that the proposed suboptimal solutions for the spatial density, transmit power, and frequency reuse of remaining active BSs significantly contribute to reducing the power consumption of BSs. In this paper, traffic-aware sleeping control (SC) and power matching (PM) of a single base station (BS) in cellular networks are studied. The objective is to find the sleeping control and power matching configurations that achieve the Pareto optimal tradeoff between total power consumption and average delay. Two types of sleeping control schemes are considered: The BS goes to sleep whenever there is no active user, and wakes up when N users are assembled or after a period of multiple or single vacation time. We first discuss when to incorporate sleeping control into power matching energy efficiently. The explicit relationship between total power consumption and average delay with varying service rate is analyzed theoretically, indicating that sacrificing delay cannot always be traded for energy saving, and we also provide conditions under which the energy-optimal rate exists. Moreover, the optimal pair of sleeping parameter and service rate to achieve the optimal energy-delay tradeoff, and the energy consumption lower bound are also derived. Both the analytical and simulation results show that tolerable sacrifice of delay performance can be traded for substantial amount of energy saving given that careful designs were made according to our analysis. We develop a tractable, flexible, and accurate model for downlink heterogeneous cellular networks. It consists of K tiers of randomly-located base stations (BSs), where each tier may differ in terms of the average transmit power, the supported data rate and the BS density. This allows elements spanning traditional, micro, pico, and femtocell BSs to be simultaneously considered. Assuming a mobile user connects to its strongest BS, we derive its Signal-to-Interference-Ratio (SIR) distribution and use that to find the coverage (equivalently outage) probability over the entire network. We verify the accuracy of these analytical results through empirical comparisons with an actual 4G macro-cell network. With the exponential increase in mobile internet traffic driven by a new generation of wireless devices, future cellular networks face a great challenge to meet this overwhelming demand of network capacity. At the same time, the demand for higher data rates and the ever-increasing number of wireless users led to rapid increases in power consumption and operating cost of cellular networks. One potential solution to address these issues is to overlay small cell networks with macrocell networks as a means to provide higher network capacity and better coverage. However, the dense and random deployment of small cells and their uncoordinated operation raise important questions about the energy efficiency implications of such multi-tier networks. Another technique to improve energy efficiency in cellular networks is to introduce active sleep (on off) modes in macrocell base stations. In this paper, we investigate the design and the associated tradeoffs of energy efficient cellular networks through the deployment of sleeping strategies and small cells. Using a stochastic geometry based model, we derive the success probability and energy efficiency in homogeneous macrocell (single-tier) and heterogeneous K-tier wireless networks under different sleeping policies. In addition, we formulate the power consumption minimization and energy efficiency maximization problems, and determine the optimal operating regimes for macrocell base stations. Numerical results confirm the effectiveness of switching off base stations in homogeneous macrocell networks. Nevertheless, the gains in terms of energy efficiency depend on the type of sleeping strategy used. In addition, the deployment of small cells generally leads to higher energy efficiency but this gain saturates as the density of small cells increases. In a nutshell, our proposed framework provides an essential understanding on the deployment of future green heterogeneous networks. Random spatial models are attractive for modeling heterogeneous cellular networks (HCNs) due to their realism, tractability, and scalability. A major limitation of such models to date in the context of HCNs is the neglect of network traffic and load: all base stations (BSs) have typically been assumed to always be transmitting. Small cells in particular will have a lighter load than macrocells, and so their contribution to the network interference may be significantly overstated in a fully loaded model. This paper incorporates a flexible notion of BS load by introducing a new idea of conditionally thinning the interference field. For a K-tier HCN where BSs across tiers differ in terms of transmit power, supported data rate, deployment density, and now load, we derive the coverage probability for a typical mobile, which connects to the strongest BS signal. Conditioned on this connection, the interfering BSs of the i^ th tier are assumed to transmit independently with probability p_i, which models the load. Assuming — reasonably — that smaller cells are more lightly loaded than macrocells, the analysis shows that adding such access points to the network always increases the coverage probability. We also observe that fully loaded models are quite pessimistic in terms of coverage. Very recent studies showed that in a fully loaded dense small cell network (SCN), the coverage probability performance will continuously decrease with the network densification. Such new results were captured in IEEE ComSoc Technology News with an alarming title of "Will Densification Be the Death of 5G?". In this paper, we revisit this issue from more practical views of realistic network deployment, such as a finite number of active base stations (BSs) and user equipments (UEs), a decreasing BS transmission power with the network densification, etc. Particularly, in dense SCNs, due to an oversupply of BSs with respect to UEs, a large number of BSs can be put into idle modes without signal transmission, if there is no active UE within their coverage areas. Setting those BSs into idle modes mitigates unnecessary inter-cell interference and reduces energy consumption. In this paper, we investigate the performance impact of such BS idle mode capability (IMC) on dense SCNs. Different from existing work, we consider a realistic path loss model incorporating both line-of-sight (LoS) and non-line-of-sight (NLoS) transmissions. Moreover, we obtain analytical results for the coverage probability, the area spectral efficiency (ASE) and the energy efficiency (EE) performance for SCNs with the BS IMC and show that the performance impact of the IMC on dense SCNs is significant. As the BS density surpasses the UE density in dense SCNs, the coverage probability will continuously increase toward one, addressing previous concerns on "the death of 5G". Finally, the performance improvement in terms of the EE performance is also investigated for dense SCNs using practical energy models developed in the Green-Touch project. In this paper, we adopt stochastic geometry theory to analyze the optimal macro micro BS (base station) density for energy-efficient heterogeneous cellular networks with QoS constraints. We first derive the upper and lower bounds of the optimal BS density for homogeneous scenarios and, based on these, we analyze the optimal BS density for heterogeneous networks. The optimal macro micro BS density can be calculated numerically through our analysis, and the closed-form approximation is also derived. Our results reveal 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, the micro BSs are preferred, i.e., deploy more micro BSs for capacity extension or switch off certain macro BSs for energy saving. Otherwise, the optimal choice is the opposite. Our work provides guidance for energy efficient cellular network planning and dynamic operation control.1 Base station (BS) deployment in cellular networks is one of the fundamental problems in network design. This paper proposes a novel method for the cell planning problem for fourth-generation (4G) cellular networks using metaheuristic algorithms. In this approach, we aim to satisfy both cell coverage and capacity constraints simultaneously by formulating an optimization problem that captures practical planning aspects. The starting point of the planning process is defined through a dimensioning exercise that captures both coverage and capacity constraints. Afterward, we implement a metaheuristic algorithm based on swarm intelligence (e.g., particle swarm optimization or the recently proposed gray-wolf optimizer) to find suboptimal BS locations that satisfy both problem constraints in the area of interest, which can be divided into several subareas with different spatial user densities. Subsequently, an iterative approach is executed to eliminate eventual redundant BSs. We also perform Monte Carlo simulations to study the performance of the proposed scheme and compute the average number of users in outage. Next, the problems of green planning with regard to temporal traffic variation and planning with location constraints due to tight limits on electromagnetic radiations are addressed, using the proposed method. Finally, in our simulation results, we apply our proposed approach for different scenarios with different subareas and user distributions and show that the desired network quality-of-service (QoS) targets are always reached, even for large-scale problems. Femtocells are recognized as effective for improving network coverage and capacity and for reducing power consumption due to the reduced range of wireless transmissions. Although highly appealing, a plethora of challenging problems need to be addressed for fully harvesting its potential. In this paper, we investigate the problem of cell association and service scheduling in femtocell networks. In addition to the general goal of offloading traffic from the macrobase station (BS), we also aim at minimizing the latency of service requested by the users, while considering both open and closed access strategies. We show that the cell association problem is NP-hard, and propose several near-optimal solution algorithms for assigning users to BSs, including a sequential fixing algorithm, a rounding approximation algorithm, a greedy approximation algorithm, and a randomized algorithm. For service scheduling, we develop an optimal algorithm to minimize the average waiting time for the users associated with the same BS. The proposed algorithms are analyzed with respect to performance bounds, approximation ratios, and optimality, and are evaluated with simulations. Heterogeneous networks using a mix of macrocells and small cells are foreseen as one of the solutions to meet the ever increasing mobile traffic demand. Nevertheless, a massive deployment of small cell access points (SAPs) leads also to a considerable increase in energy consumption. Spurred by growing environmental awareness and the high price of energy, it is crucial to design energy efficient wireless systems for both macrocells and small cells. In this work, we evaluate a distributed sleep-mode strategy for cognitive SAPs and we analyze the trade-off between traffic offloading from the macrocell and the energy consumption of the small cells. Using tools from stochastic geometry, we define the user discovery performance of the SAP and derive the uplink capacity of the small cells located in the Voronoi cell of a macrocell base station, accounting for the uncertainties associated with random position, density, user activity, propagation channel, network interference generated by uncoordinated activity, and the sensing scheme. In addition, we define a fundamental limit on the interference density that allows robust detection and we elucidate the relation between energy efficiency and sensing time using large deviations theory. Through the formulation of several optimization problems, we propose a framework that yields design guidelines for energy efficient small cell networks. The issue of energy efficiency (EE) in Orthogonal Frequency-Division Multiple Access (OFDMA) wireless networks is discussed in this paper. Our interest is focused on the promising concept of base station (BS) sleep mode, introduced recently as a key feature in order to dramatically reduce network energy consumption. The proposed technical approach fully exploits the properties of stochastic geometry, where the number of active cells is reduced in a way that the outage probability, or equivalently the signal to interference plus noise (SINR) distribution, remains the same. The optimal EE gains are then specified with the help of a simplified but yet realistic BS power consumption model. Furthermore, the authors extend their initial work by studying a non-singular path loss model in order to verify the validity of the analysis and finally, the impact on the achieved user capacity is investigated. In this context, the significant contribution of this paper is the evaluation of the theoretically optimal energy savings of sleep mode, with respect to the decisive role that the BS power profile plays. Base station (BS) cooperation is set to play a key role in managing interference in dense heterogeneous cellular networks (HCNs). Non-coherent joint transmission (JT) is particularly appealing due to its low complexity, smaller overhead, and ability for load balancing. However, a general analysis of this technique is difficult mostly due to the lack of tractable models. This paper addresses this gap and presents a tractable model for analyzing non-coherent JT in HCNs, while incorporating key system parameters such as user-centric BS clustering and channel-dependent cooperation activation. Assuming all BSs of each tier follow a stationary Poisson point process, the coverage probability for non-coherent JT is derived. Using the developed model, it is shown that for small cooperative clusters of small-cell BSs, non-coherent JT by small cells provides spectral efficiency gains without significantly increasing cell load. Further, when cooperation is aggressively triggered intra-cluster frequency reuse within small cells is favorable over intra-cluster coordinated scheduling. Millimeter wave (mmWave) cellular systems will require high-gain directional antennas and dense base station (BS) deployments to overcome a high near-field path loss and poor diffraction. As a desirable side effect, high-gain antennas offer interference isolation, providing an opportunity to incorporate self-backhauling , i.e., BSs backhauling among themselves in a mesh architecture without significant loss in the throughput, to enable the requisite large BS densities. The use of directional antennas and resource sharing between access and backhaul links leads to coverage and rate trends that significantly differ from conventional UHF cellular systems. In this paper, we propose a general and tractable mmWave cellular model capturing these key trends and characterize the associated rate distribution. The developed model and analysis are validated using actual building locations from dense urban settings and empirically derived path loss models. The analysis shows that, in sharp contrast to the interference-limited nature of UHF cellular networks, the spectral efficiency of mmWave networks (besides the total rate) also increases with the BS density, particularly at the cell edge. Increasing the system bandwidth does not significantly influence the cell edge rate, although it boosts the median and peak rates. With self-backhauling, different combinations of the wired backhaul fraction (i.e., the fraction of BSs with a wired connection) and the BS density are shown to guarantee the same median rate (QoS). The energy consumption of the information and communication technology (ICT) industry, which has become a serious problem, is mostly due to the network infrastructure rather than the mobile terminals. In this paper, we focus on reducing the energy consumption of base stations (BSs) by adjusting their working modes (active or sleep). Specifically, the objective is to minimize the energy consumption while satisfying quality of service (QoS, e.g., blocking probability) requirement and, at the same time, avoiding frequent mode switching to reduce signaling and delay overhead. The problem is modeled as a dynamic programming (DP) problem, which is NP-hard in general. Based on cooperation among neighboring BSs, a low-complexity algorithm is proposed to reduce the size of state space as well as that of action space. Simulations demonstrate that, with the proposed algorithm, the active BS pattern well meets the time variation and the non-uniform spatial distribution of system traffic. Moreover, the tradeoff between the energy saving from BS sleeping and the cost of switching is well balanced by the proposed scheme. In this paper we develop a tractable framework for SINR analysis in downlink heterogeneous cellular networks (HCNs) with flexible cell association. The HCN is modeled as a multi-tier cellular network where each tier's base stations (BSs) are randomly located and have a unique transmit power, path loss exponent, spatial density, and bias towards admitting users. We implicitly assume every BS has full queues. From this model, we derive the outage probability of a typical user in the network, which can be viewed as a spatial average of SINR over all users in the network. We observe that deploying more or less BSs does not change the outage probability in interference-limited HCN with unbiased cell association, and observe how biasing affects the metric. 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.