Small cell networks have recently been proposed as an important evolution path for the next-generation cellular networks. However, with more and more irregularly deployed base stations (BSs), it is becoming increasingly difficult to quantify the achievable network throughput or energy efficiency. In this paper, we develop an analytical framework for downlink performance evaluation of small cell networks, based on a random spatial network model, where BSs and users are modeled as two independent spatial Poisson point processes. A new simple expression of the outage probability is derived, which is analytically tractable and is especially useful with multi-antenna transmissions. This new result is then applied to evaluate the network throughput and energy efficiency. It is analytically shown that deploying more BSs or more BS antennas can always increase the network throughput, but the performance gain critically depends on the BS-user density ratio and the number of BS antennas. On the other hand, increasing the BS density or the number of transmit antennas will first increase and then decrease the energy efficiency if different components of BS power consumption satisfy certain conditions, and the optimal BS density and the optimal number of BS antennas can be found. Otherwise, the energy efficiency will always decrease. Simulation results shall demonstrate that our conclusions based on the random network model are general and also hold in a regular grid-based model.
Previous works that investigate the throughput, energy efficiency and their tradeoff have mainly focused on the point-to-point communication link or the single-cell case @cite_10 @cite_32 @cite_36 @cite_33 , while the interference from other cells are neglected. Meanwhile, the throughput analysis of conventional cellular networks has received lots of attention, and different models have been proposed, such as the Wyner model @cite_0 or the grid model @cite_35 @cite_3 . While the Wyner model is commonly used due to its tractability, it may lose the essential characteristics of real and practical networks @cite_26 . On the other hand, the regular grid model becomes intractable as the network size grows, and it cannot handle the irregular network structure in small cell networks. In general, it is quite challenging to accurately evaluate the performance of cellular networks, due to the complexity of the network topology, and effects of multi-path propagation. A more common way to evaluate cellular networks is by simulation. For example, in @cite_3 , different cellular network architectures were compared through simulation. While evaluating the network performance through simulation can provide insights on some specific settings, the results may not be extended to other scenarios and the computational complexity is rather high.
@cite_35 @cite_26 @cite_33 @cite_36 @cite_32 @cite_3 @cite_0 @cite_10
2150166076 2096536332 2102457283 1567643386
Cellular networks are usually modeled by placing the base stations on a grid, with mobile users either randomly scattered or placed deterministically. These models have been used extensively but suffer from being both highly idealized and not very tractable, so complex system-level simulations are used to evaluate coverage outage probability and rate. More tractable models have long been desirable. We develop new general models for the multi-cell signal-to-interference-plus-noise ratio (SINR) using stochastic geometry. Under very general assumptions, the resulting expressions for the downlink SINR CCDF (equivalent to the coverage probability) involve quickly computable integrals, and in some practical special cases can be simplified to common integrals (e.g., the Q-function) or even to simple closed-form expressions. We also derive the mean rate, and then the coverage gain (and mean rate loss) from static frequency reuse. We compare our coverage predictions to the grid model and an actual base station deployment, and observe that the proposed model is pessimistic (a lower bound on coverage) whereas the grid model is optimistic, and that both are about equally accurate. In addition to being more tractable, the proposed model may better capture the increasingly opportunistic and dense placement of base stations in future networks. Cellular networks are usually modeled by placing the base stations according to a regular geometry such as a grid, with the mobile users scattered around the network either as a Poisson point process (i.e. uniform distribution) or deterministically. These models have been used extensively for cellular design and analysis but suffer from being both highly idealized and not very tractable. Thus, complex simulations are used to evaluate key metrics such as coverage probability for a specified target rate (equivalently, the outage probability) or average sum rate. We develop general models for multi-cell signal-to-noise-plus-interference ratio (SINR) based on homogeneous Poisson point processes and derive the coverage probability, which is one minus the outage probability. Under very general assumptions, the resulting expressions for the SINR cumulative distribution function involve quickly computable integrals, and in some important special cases of practical interest these integrals can be simplified to common integrals (e.g., the Q-function) or even to exact and quite simple closed-form expressions. We compare our coverage predictions to the standard grid model and an actual base station deployment. We observe that the proposed model is pessimistic (a lower bound on coverage) whereas the grid model is optimistic. In addition to being more tractable, the proposed model may better capture the increasingly opportunistic and dense placement of base stations in urban cellular networks with highly variable coverage radii. How much information can one send through a random ad hoc network of n nodes, if overlaid with a cellular architecture of m base stations? This network model is commonly referred to as hybrid wireless networks and our paper analyzes the above question by characterizing its throughput capacity. Although several research efforts related to throughput capacity exist in the area of hybrid wireless networks, most of these solutions under-explore the capacity analysis. Their results particularly indicate that one can realize only a less than log or no gain on capacity, as compared to pure ad hoc networks, when ?? scales slower than some threshold. This unsatisfying capacity gain is due to the fact that the base stations were not properly exploited while formulating the capacity analysis. Moreover, these research efforts also assume an one-hop wireless uplink between a node and its associated base station. Nevertheless, with those power-constrained wireless nodes, this assumption clearly indicates an unrealistic scenario. In this paper, we establish the bounds on capacity and delay by resolving the issues in existing efforts and at the heart of our analysis lies a simple routing policy known as same cell routing policy. Our findings particularly stipulate that whether m = O(n over log n) or Ω(n over log n), each node can realize a throughput that scales, sublinearly or linearly, with m. This is in fact a significant result as opposed to previous efforts which claims that if m grows slower than some threshold, the benefit of augmenting those base stations to the original ad hoc network is insignificant. Our analysis also shows that for a maximum per node throughput Λ(n,m), the average end-to-end delay in a hybrid network can be bounded by Θ(Λ(n,m)n over m), which has an inverse relationship to m. 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.