Cell switch-off (CSO) is an important approach to reducing energy consumption in cellular networks during off-peak periods. CSO addresses the research question of which cells to switch off when. Whereas online CSO, based on immediate user demands and channel states, is problematic to implement and difficult to model, off-line CSO is more practical and tractable. Furthermore, it is known that regular cell layouts generally provide the best coverage and spectral efficiency, which leads us to prefer regular static (off-line) CSO. We introduce sector-based regular CSO patterns for the first time. We organize the existing and newly introduced patterns using a systematic nomenclature; studying 26 patterns in total. We compare these patterns in terms of energy efficiency and the average number of users supported, via a combination of analysis and simulation. We also compare the performance of CSO with two benchmark algorithms. We show that the average number of users can be captured by one parameter. Moreover, we find that the distribution of the number of users is close to Gaussian, with a tractable variance. Our results demonstrate that several patterns that activate only one out of three sectors are particularly beneficial; such CSO patterns have not been studied before.

The LTE random access procedures proposed in 3GPP for Machine Type Communication in current cellular systems may become overwhelmed when too many machine devices attempt to upload their data. In this paper, we propose a two-hop cluster random access based on slotted ALOHA communication. In each cluster, a cluster head (CH) is selected according to the channel gains. The CH aggregates data from cluster members and then initiates the LTE random access procedure to the base station. Due to the offloading from the random access channel to the slotted ALOHA, the number of contending devices is reduced, which alleviates the collision problem and results in better performance. The simplification of access procedure can also significantly decrease the energy consumption. We define a clustering metric for machine locations and we examine the impact of the metric on the performance. The simulation results show that as machine locations become more clustered, the overall performance improves.

Energy saving in cellular networks can be achieved by implementing the cell switch-off (CSO) approach in periods of light traffic. Regular static CSO (CSO patterns) is a type of CSO where the set of active cells is predetermined such that they are located on a regular grid. It is known that regular cell layouts generally provide the best coverage and downlink SINR. Furthermore, CSO patterns assure that interfering cells are as far away as possible and help in modeling interference accurately. Existing lit- erature on CSO patterns focuses only on site-level CSO (switching off entire BSs); however, significant gains can sometimes be obtained from sector-level CSO patterns (switching off individual sectors). This paper is the first to introduce and investi- gate sector- based regular CSO patterns by providing illustrative examples. We compare the performances of different CSO patterns in terms of the number of supported users. Also, we analytically compare site- based versus sector-based CSO patterns in terms of power saving. Our results show that patterns with only one of the three sectors active (each with the same orientation) can support the most users per sector, due to a favourable interference situation.

In this paper, we give qualitative and quantitative arguments for the use of perturbed triangular lattice (PTL) models for generating base station deployments with any amount of spatial regularity, which is useful notably in modeling different tiers of HetNets. We use the coefficient of variation of three spatial properties of point processes to measure the regularity of two common types of PTL: uniform on disc and Gaussian. From these measurements, we are able to derive a simple formula that allows matching and interchanging the two PTL models, within about 0.1 dB error in SIR.

Wireless cellular network planning benefits from accurate and realistic, yet relatively simple and manageable, spatial traffic models. User locations in cellular networks are often modeled as homogeneous (uniform) Poisson point processes (PPPs). However, the real user distributions are seldom purely homogeneous. Network users are usually concentrated at social attractors such as residential and office buildings, shopping malls, and bus stations. Wireless spectral efficiency depends significantly on the users' spatial heterogeneity, and thus relevant spatial traffic generators and models are important. In future (5G) networks, for which device-to-device (D2D), millimeter-wave (mmWave), and small-cell deployments in Heterogeneous Networks (HetNets), are promising technologies, it will become more important to have spatial traffic models which can represent the broad possibilities from completely homogeneous cases (e.g., a deterministic lattice) to extremely heterogeneous cases (e.g., highly clustered scenarios). In this paper, we study the spatial traffic heterogeneity of outdoor users in the denser areas of the city center of Paris, France. The building shape data is freely available from the OpenStreetMaps project. We measure the heterogeneity via a second-order statistic: the Coefficient of Variation (CoV) of two spatial metrics of the resulting point process: the Voronoi cell areas and the Delaunay cell edge lengths. The expected value of the CoV of these metrics allows us to study how the heterogeneity increases with the density of users. Moreover, we find that the statistical distribution of both these metrics is close to Weibull. Our results illustrate that the topology of the buildings in the city imposes a significant degree of heterogeneity on the spatial distribution of the wireless traffic.

We examine the statistical distribution of the interference produced by a cluster of many co-channel interferers: e.g., a sensor network, or a city full of active wireless devices and access points. We consider a clustered interferer layout and analyze the interference as experienced at a given point outside (and not immediately near to) the interferer area. We model the propagation paths as experiencing power law attenuation and lognormal correlated shadowing, with pairwise correlations depending on the relative positions of the two interferers. It has already been shown in literature that adding correlation to the shadowing model can give significantly different, and more realistic, results. Our solution is mostly analytical, with only a small amount of numerical integration required. Whereas both simulation and other analytical methods become very computationally demanding as the number of interferers grows, our method's complexity is independent of the number of interferers, and its precision actually improves when their number increases.

We analyze the uplink outage probability at the randomly, but not necessarily independently nor homogeneously, distributed cellular network receivers caused by an overlaid secondary ad hoc network. Unlike the previous works that assumed exact circular exclusion regions (or guard zones), we incorporate a sensing mechanism to decrease the significant effect of the nearby interferers. We consider Rayleigh-faded links, large-scale power control, and the knowledge of the initial outages in the absence of the secondary network. We derive an upper bound on the outage probability and show it to be tight when the co-channel primary receivers are separated by relatively significant distances, which is inherently the case for the cellular network. Furthermore, we derive a closed-form expression that shows the significant impact of the sensing mechanism on the spectrum sharing gains.. Additionally, we optimize the decision threshold, which is used by secondary network users to decide whether to transmit or not, in order to maximize the spectrum sharing gains under the given outage constraints.

A closed-form expression for the outage probability at a receiver in the primary network due to a uniform annular sector distribution of secondary transmitters is derived in a Rayleigh fading environment. This may include an exclusion region, and a finite or infinite outer radius. Conversely, under a given constraint on the outage probability, spectrum sharing opportunities are analyzed with respect to the field size and are shown to be significantly dependent on the exclusion region. Conditions are obtained for which an infinite field size assumption can or cannot lead to the loss of spectrum sharing opportunity. Additionally, the spectrum sharing gains (the maximum average number of secondary transmitters) are derived for the secondary network for different spatial deployments. It is worth mentioning that other than networks sharing spectrum, the derived results are applicable to any set of interferers from the same network or other networks around any receiver of study.

As the number of wireless devices sharing a radio band increases, so does the number N of potential co-channel interferers. The receiver performance is then strongly dependent on the total received interference power. While the statistics of this power have previously been studied under the channel assumption of independent shadowing, it is easy to show that for large N the correlation among the shadowing paths cannot be neglected. While this correlation may be simulated by matrix decomposition, we show that an alternative approximately equivalent algorithm using shadowing fields can achieve simulation performance that scales much better with N and has additional advantages.

We propose a new method for calculating a tight approximation to the distribution of the sum of independent lognormal random variables. We make use of a three-parameter modified-power-lognormal distribution function as the approximating distribution. We use theoretical results from our previous work on the tails of the distribution of the sum of lognormals to match the slope of the modified-power-lognormal function at both tails. This would not have been possible with many of the recently-proposed distribution functions, which do not behave properly in the tails. We then also use moment-matching to find the best curve match. Our method is mostly closed-form, requiring only one simple numerical integral. We compare our method with those in literature in terms of complexity and accuracy. We conclude that our method is more accurate than the simple (closed-form) methods, and much simpler to understand and implement than the more accurate methods which rely heavily on numerical integration.

We prove that the distribution of the sum of N identically distributed jointly lognormal random variables, where all pairs have the same strictly positive correlation coefficient, converges to a lognormal with known parameters as N becomes large. We confirm our theorem by simulations and give an application of the theorem.

We examine the statistical distribution of the interference produced by a cluster of very many co-channel interferers, e.g., a sensor network, or a city full of active wireless devices and access points. We consider an arbitrary statistical interferer layout and consider the interference as experienced at a given point outside (and not immediately near to) the interferer area. We model the paths as experiencing power law attenuation and lognormal correlated shadowing. It has been shown in literature that adding correlation to the shadowing model can give qualitatively different (and probably more realistic) results. Our results are mostly analytical, with a small amount of numerical integration required. Whereas simulations of very many correlated interferers are very computationally heavy, our method's complexity is independent of the number of interferers, and its precision in fact improves when increasing the number of terms.

Finding the distribution of the sum of lognormal random variables is an important mathematical problem in wireless communications, as well as in many other fields. While several methods exist to approximate this distribution, their performance tends to deteriorate in both tails. Finding a good overall fit remains an open problem. Other disadvantages of these methods are their complexity and, in some cases, their limitation to particular scenarios. In this paper we examine the sum of independent lognormal random variables with arbitrary parameters. We define the concept of best lognormal fit to a tail and show what it means in terms of convergence. We restate a known result about asymptotes to the higher tail of the distribution. To our knowledge, the lower tail has not yet been studied. We give a simple closed-form expression for an asymptote to the lower tail. We also show that known methods for finding the sum of lognormals use distribution functions that do not have this asymptotic behaviour in the tails. Our results are complementary to the existing knowledge, which together can combine to solve the problem of the sum of lognormals simply and exactly. We support our results by simulations.