On the statistics of SINR in cellular networks

This study focuses on the performance of device-to-device (D2D) communications in underlay cellular networks by analyzing key metrics such as successful transmission probability, coverage probability, and throughput.Under the homogeneous Poisson point process (PPP) spatial distribution of full-duplex (FD)-D2D users in cellular networks, stochastic geometry tools are used to derive approximate expressions for D2D users' coverage probability and throughput.In comparison to the conventional half-duplex (HD) communication mode, when the self-interference cancellation factor reaches -95 dB, there is a substantial improvement in the throughput of FD-D2D users, nearly doubling their gain.Additionally, experimental results demonstrate that the Newton iterative algorithm can be used to optimize the targeted signal-to-interference-plus-noise-ratio (SINR) threshold of users within the range of (10, 20) dB.

Due to its mathematical tractability, the homogeneous Poisson point process (PPP) has been employed to model wireless networks and analyze their performance widely. PPP falls short in modeling the effect of interference management techniques, which typically introduces some form of spatial mutual exclusion among base stations (BSs). Considering the spatial mutual exclusion between macro BSs s (BSs), in this paper, we studies the coverage performance of a two-tier heterogeneous cellular network (HCN) modeled by Poisson hard-core process (PHCP) and PPP. We first provide the approximate expression of coverage probability of the two-tier PHCP-PPP HCN with the use of PT-ASAPPP method, which stands for “per tier approximate signal to interference ratio (SIR) analysis based on PPP. In this method, each tier is approximated to PPP by using SIR gain. The concrete expression of the SIR gain G PHCP for PHCP model is derived through simulation and data fitting. Simulation results verify the correctness of theoretical analysis and the effectiveness of PT-ASAPPP method.

Heterogeneous cellular networks (HCNs) constitute a necessary step in the evolution of cellular networks. In this paper, we apply the signal-to-interference ratio (SIR) meta distribution framework for a refined SIR performance analysis of HCNs, focusing on K-tier heterogeneous cellular networks based on the homogeneous independent Poisson point process (HIP) model, with range expansion bias (offloading bias) in each tier. Expressions for the b-th moment of the conditional success probability for both the entire network and each tier are derived, based on which the exact meta distributions and the beta approximations are evaluated and compared. Key performance metrics including the mean success probability, the variance of the conditional success probability, the mean local delay and the asymptotic SIR gains of each tier are obtained. The results show that the biases are detrimental to the overall mean success probability of the whole network and that the b-th moment curve (versus the SIR threshold) of the conditional success probability of each tier can be excellently approximated by the horizontal shifted versions of the first moment curve of the single-tier PPP network. We also provide lower bounds for the region of the active probabilities of the base stations to keep the mean local delay of each tier finite.

In a Poisson Point Process (PPP) network model, in which the locations of Base Stations (BSs) are randomly distributed according to a Spatial Poisson Process, has been recently used as a tractable stochastic model to analyse the performance of downlink Heterogeneous Cellular Networks (HCNs). The HCN is modelled as a multi-tier cellular network where each tier is characterised by the transmission power level, propagation path loss exponent and density of BSs. The current works on HCN enabling Intercell Interference Coordination (ICIC) technique usually deal with Strict Frequency Reuse (FR) or Soft FR with a reuse factor of $\Delta=1$ in a Rayleigh fading channel. It has been assumed that all Base Stations (BSs) transmit continuously which leads to a reduction on the impact of number of users and RBs on network performance. In this paper, the performance of Soft FR with a reuse factor of $\Delta>1$ in Rayleigh-Lognormal fading channel is evaluated. The impact of the number of users and Resource Blocks (RBs) on Intercell Interference (ICI) are presented for Round Robin scheduling and indicator functions. The results show that there are opposite trends between coverage probability of Cell-Center User (CCU) and Cell-Edge User (CEU).

Cellular networks have a great transformation during the last decade. The traditional cellular network system is often overlaid with well-deployed BSs of proper power. However, more and more complex elements such as picocells, femtocells and relays have been introduced to cellular network system. BSs in these elements are unplanned, user-installed and randomly deployed. All of these things compose heterogeneous cellular networks (HCNs). In order to evaluate the performance of HCNs, people usually model the distribution of BSs in HCNs as spatial stochastic point process model. One of the most popular spatial models for these HCNs is Poisson Point Process (PPP) model. However the PPP model is not exact for some cases where BSs in PPP model may be too close to each other. In this paper, we propose a more reasonable and practical model called Matern-like point process (MLPP) model which imposes a certain minimal distance between any two BSs to overcome this problem. Simulations show that the coverage probability of the proposed model noticeably outperforms the PPP model. This improvement depends on the value of minimal distance. We also evaluate the system efficiency defined by the ratio of coverage probability and total power. The results show that the MLPP model has a significant improvement compared to PPP model.

The aim of this paper is to present a non‐linear statistical model to fit and forecast the signal‐to‐interference plus noise ratio (SINR) in two‐tier heterogeneous cellular networks which consist of macrocells and femtocells. Since in these networks the number and locations of femtocell base stations (FBS) are variable, SINR forecasting can be useful in some areas such as power control and handover management. So far, linear autoregressive (AR) models have commonly been used in forecasting the received signal strength (rss) in macrocellular networks. However, AR modelling results in high mean square error (MSE) when data are non‐linear. This paper focuses on SINR which takes into account signal strength, interference and noise effects. Moreover, macro‐femto cellular network is considered. The F ‐test results show that the SINR data are non‐linear, leading to use non‐linear models instead of AR model. A non‐linear logistic smooth threshold AR (LSTAR) model is utilised to model and forecast the SINR data. Kolmogorov–Smirnov (K‐S) test demonstrates that LSTAR provides good fitness to the SINR samples. The results indicate that LSTAR model achieves much better performance in modelling and forecasting of SINR data than the AR model.

In a conventional cellular network, a terminal receives signals not only from the base station of that cell, but also from other cell base stations. This inter-cell interference has more impact on the cell-edge users, in multi cell environment. The inter-cell interference degrades the performance of wireless systems. Using Base Station Cooperation, the ability of a mobile station to receive signals from multiple base stations can be utilized as an opportunity to improve the spectral efficiency and to get higher data rates for cell edge users. In multi cell environment using base station cooperation overall interference can be minimized marginally, whereas the interference within the cooperation region is largely reduced. This leads to a question whether it is worth doing cooperation all the time. However increase in terms of throughput may not always be enough to increase the throughput of each of the user .Hence for such a scenario the distinct cooperation scheme is used. The distinct cooperation is a joint transmission scheme in which the selection criterion is based on user’s signal to interference plus noise ratio (SINR) is proposed and the capacity achieved through cooperation is shared equally among the cell-edge users. Here we will analyze the normal operation, full cooperation and distinct cooperation scheme in the downlink environment for cell edge users in cellular network and we will compare and see which method improves the user capacity and data rate.KeywordsCooperative transmissionfull cooperationDistinct cooperationsignal to interference plus noise ratio (SINR)

The crushing demands for mobile data traffic drive the current cellular networks to become more heterogeneous, making the signal-to-interference ratio (SIR) distribution more difficult to analyze. In this paper we propose a simple approximative approach to the SIR distribution of heterogeneous cellular networks (HCNs) based on the ASAPPP method which stands for ``approximate SIR analysis based on the Poisson point process'' and the MISR (mean interference-to-signal ratio)-based gain for each individual tier of the HCN. The results demonstrate that this approach gives a tight approximation and asymptotically a lower bound for the coverage probability.

This article performs a unified analysis of three coordinated multipoint (CoMP) transmission strategies in the downlink of mmWave cellular networks, including the fixed-number base station (BS) cooperation (FNC), the fixed-region BS cooperation (FRC), and the interference-aware BS cooperation (IAC). We first develop a comprehensive framework for CoMP operation in cellular networks, and investigate the network performance under a Poisson point process (PPP) model together with mmWave spectrum. To show what fraction of users in the network achieve target reliability for a given signal to interference-plus-noise ratio (SINR)/signal-to-interference ratio (SIR), we derive the SINR/SIR meta distributions, and further obtain the coverage probability as well as mean local delay for the three cooperation strategies. A pivotal intermediate step to compute the performance metrics is the derivation of joint distributions of distances between a typical user and cooperative BSs. Our analysis demonstrates that parameters of blockage have a significant influence on the network performance for the three CoMP schemes. We find that the FRC scheme makes more users achieve the given link reliability for the scenario with a low density of BSs, while the IAC scheme provides better performance for the network with a high density of BSs. Moreover, the optimal CoMP scheme can be approximately selected by considering the nearest distance from the serving BS to user and the radius of the approximate line-of-sight (LoS) region in the cellular networks.

How many small cell (SC) access points (APs) are required to guarantee a chosen quality of service in a heterogeneous network? In this chapter, we answer this question considering two different network models. The first is the downlink of a finite-area SC network where the locations of APs within the chosen area are uniformly distributed. A key step in obtaining the closed-form expressions is to generalize the well-accepted moment matching approximation for the linear combination of lognormal random variables. For the second model, we focus on a two-layer downlink heterogeneous network with frequency reuse-1 hexagonal macro cells (MCs), and SC APs that are placed at locations that do not meet a chosen quality of service from macro base stations (BSs). An important property of this model is that the SC AP locations are coupled with the MC coverage. Here, simple bounds for the average total interference within an MC makes the formulation possible for the percentage of MC area in outage, as well as the required average number of SCs (per MC) to overcome outage, assuming isolated SCs. Introduction Heterogeneous cellular networks (HCNs) are being considered as an efficient way to improve system capacity as well as effectively enhance network coverage [1, 2]. Comprising multiple layers of access points (APs), HCNs encompass a conventional macro cellular network (first layer) overlaid with a diverse set of small cells (SCs) (higher layers). Cell deployment is an important problem in heterogeneous networks, both in terms of the number and positioning of the SCs. Traditional network models are either impractically simple (such as the Wyner model [3]) or excessively complex (e.g., the general case of random user locations in a hexagonal lattice network [4]) to accurately model SC networks. A useful mathematical model that accounts for the randomness in SC locations and irregularity in the cells uses spatial point processes, such as Poisson point process (PPP), to model the location of SCs in the network [5–10]. The independent placement of SCs from the MC layer, has the advantage of analytical tractability and leads to many useful SINR and/or rate expressions. However, even assuming that wireless providers would deploy SCs to support mobile broadband services, the dominant assumption remains that SCs are deployed randomly and independent of the MC layer [11].

Multi-hop heterogeneous cellular networks (MHCNs) consist of conventional macro cellular networks overlaid with an irregular deployment of low-power base stations (BSs), where the communication between BSs and mobile users can be established through a single hop or multiple hops. By modeling different kinds of randomly located BSs as K tiers of independent homogeneous Poisson Point Processes, we first explore the capacity of downlink MHCNs and derive the expression of capacity under Rayleigh fading channels. Particularly, the capacity gain achieved by cell splitting and multi-hop relaying is quantified for the first time. We then study the effects of BS density, transmit power, and signal-to-interference-plus-noise-ratio (SINR) threshold on the capacity of MHCNs. More importantly, we obtain the spectral efficiency enhancement condition under which the increase of BS density and transmit power improve the spectral efficiency, thereby enhancing the capacity. One interesting observation is that at a given SINR threshold, the capacity increases with BS density when all the tiers have the same SINR threshold. Moreover, the capacity of some special networks (i.e., heterogeneous cellular networks, multi-hop cellular networks, and conventional cellular networks) are derived directly by specializing some system parameters in our results. Finally, numerical studies and simulations are conducted to validate our analysis.

In this paper, we establish a general heterogeneous cellular network (HCN) model based on stochastic geometry and employ the accurate signal-to-interference-ratio (SIR) approximation of the ASAPPP (approximate SIR analysis based on the Poisson point process) technique to investigate spectrum allocation problems for general HCNs. Firstly, a spectrum partitioning problem where each tier uses a dedicated band is formulated to maximize the area spectral efficiency. The solution is obtained by approximating the problem with the ASAPPP method, deriving the optimal SIR thresholds, and solving a simple linear program to give the optimal spectrum allocation. Without a spectral efficiency constraint for each tier, the area spectral efficiency is maximized if the entire bandwidth is allocated to a single tier. Secondly it is shown that the proposed algorithm can also be used to solve the spectrum sharing optimization problem, where bands can be shared between tiers.

In this paper, we present mathematical frameworks for error performance analysis in interference limited networks such as cellular networks. Due to the increasing irregularity in the spatial deployment of nodes in the emerging heterogeneous cellular networks (HCNs), we employ stochastic geometry approach by abstracting the node locations as a homogeneous Poisson point process (PPP). First, we characterize the average error probability of an intended communication link with a given transmitter-receiver separation, which is subject to interference from these Poisson distributed nodes. More specifically, we develop uniform approximation (UA), which is highly accurate over the whole range of signal-to-interference ratio (SIR) and hence, serve as an alternative to existing complex analytical results. Error probability UAs for both single-antenna and maximal ratio combining (MRC) receivers are derived in this paper. Next, we evaluate the average error probability of any typical user in the network, which is served by the node providing the maximum received power. Mellin-transform based method is proposed in this case, which often yield closed-form solution. An example of BPSK modulation is given in the paper.

Due to cell planning in a cellular communication network, it is difficult for a mobile user in a cell to get ranging measurements from other neighboring cells. Consequently, it is necessary to enhance signal sensitivity using long integration techniques so that the user position is obtained by trilateration. In order to maximize integration gain in coherent/noncoherent hybrid long integration, it is desirable to make SNR (signal to noise ratio) after coherent integration become as large as possible. Because SIR (signal to interference ratio) is not improved by the long integration, however, it is needed to mitigate CCI (Co-Channel Interference) so that the resultant hearability can be enhanced for weak signals. This paper presents a hybrid long integration scheme in presence of CCI. SNIR (signal to noise plus interference ratio) is employed to explain the loss induced by interference as well as noise. Together with interference cancellation and residual frequency estimation technique, design procedure of hybrid long integration is proposed to maximize SNIR. Simulation results show that hearability is greatly improved at most of cell coverage when the proposed method is used.

The evolution of cellular networks from one generation to another has led to the deployment of multiple radio access technologies (such as 2G/2.5G/3G/4G) in the same geographical area. This scenario is termed heterogeneous cellular networks. In heterogeneous cellular networks, radio resources can be jointly or independently managed. When radio resources are jointly managed, joint call admission control algorithms are needed for making radio access technology selection decisions. This chapter gives an overview of joint call admission control in heterogeneous cellular networks. It then presents a model of load-based joint call admission control algorithm. Four different scenarios of call admission control in heterogeneous cellular networks are analyzed and compared. Simulations results are given to show the effectiveness of call admission control in the different scenarios. The coexistence of different cellular networks in the same geographical area necessitates joint radio resource management (JRRM) for enhanced QoS provisioning and efficient radio resource utilization. The concept of JRRM arises in order to efficiently manage the common pool of radio resources that are available in each of the existing radio access technologies (RATs) (Perez-Romero et al, 2005). In heterogeneous cellular networks, the radio resource pool consists of resources that are available in a set of cells, typically under the control of a radio network controller or a base station controller. There are a number of motivations for heterogeneous wireless networks. These motivations are (1) limitation of a single radio access technology (RAT), (2) users’ demand for advanced services and complementary features of different RATs, and (3) evolution of wireless technology. Every RAT is limited in one or more of the following: data rate, coverage, security-level, type of services, and quality of service it can provide, etc. (Vidales et al, 2005). A motivation for heterogeneous cellular networks arises from the fact that no single RAT can provide ubiquitous coverage and continuous high QoS levels across multiple smart spaces, e.g. home, office, public smart spaces, etc. Moreover, increasing users’ demand for advanced services that consume a lot of network resources has made network researchers developed more and more spectrally efficient multiple access and modulation schemes to support these services. Consequently, wireless networks have evolved from one generation to another. However, due to huge investment in existing RATs, operators do not readily discard their existing RATs when they acquire new ones. This situation has led to coexistence of multiple RATs in the same geographical area.