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.