Shotgun Cellular Systems Research Articles

Physical layer security in shotgun cellular systems over correlated/independent shadow fading channels

The shotgun cellular systems (SCSs) (modeling, generally, a dense cellular or wireless data network deployment and non-ideal regular hexagonal grid with site-acquisition difficulties, variable traffic load) are wireless communication systems with randomly placed base stations (BSs) over the entire plane according to a stochastic (e.g., Poisson) point process in n dimensions (n = 1, 2, and 3). Due to the good performance and the importance of the SCSs in today’s communications, the physical layer security of these systems is practically of importance, specifically, in more realistic channel propagation models. In this paper, by assuming that the channel coefficients are known at the receiver, we analyze the performance of the physical layer security for the classic Wyner’s three-node model in the SCSs over correlated/independent log-normal shadow fading channels. For this purpose, first, we calculate the signal-to-interference-plus-noise ratio (SINR) performance at a mobile station (MS) in an SCS. Then, the average secrecy capacity (ASC), the probability of non-zero secrecy capacity (PNSC), the secure outage probability (SOP), and the lower bound of SOP (LSOP) are obtained, and also, their approximated closed-form expressions are derived. Finally, analytical results are validated numerically.

Generalized carrier to interference ratio analysis for shotgun cellular systems in multiple dimensions over composite Rayleigh–Lognormal (Suzuki) fading

This paper analyzes the carrier-to-interference ratio (CIR) of the so-called shotgun cellular systems (SCSs) in $$\tau $$ dimensions ( $$\tau =1, 2,$$ and 3). SCSs are wireless communication systems with randomly placed base stations (BSs) over the entire plane according to a Poisson point process in $$\tau $$ dimensions. Such a system can model a dense cellular or wireless data network deployment, where locations of BSs end up being close to random due to constraints other than optimal coverage. In this paper we apply SCSs in $$\tau $$ dimensions and also, in addition to path-loss and shadow fading, consider Rayleigh fading as a most commonly used distribution to model multi-path fading, and analyze the CIR over the composite fading channel [i.e., Rayleigh–Lognormal (or Suzuki) fading channel], and determine a generalized expression for the distribution of CIR and obtain the tail probability of CIR.

Carrier to interference ratio analysis in shotgun cellular systems over a generalized shadowing distribution

Shotgun cellular systems (SCSs) are wireless communication systems with randomly placed base stations (BSs) over the entire plane according to a two-dimensional Poisson point process. Such a system can model a dense cellular or wireless data network deployment, where the BS locations end up being close to random due to constraints other than optimal coverage. SCSs have been studied by considering path-loss and independent shadowing paths between BS to mobile station (MS) pairs in the channel models. In this paper, we consider correlated shadowing paths between BS to MS pairs as a most important factor, and analyze the carrier to interference ratio (CIR), in a SCS over this correlation, and determine an expression for distribution of CIR, and obtain the tail probability of the CIR.

Carrier to interference ratio, rate and coverage analysis in shotgun cellular systems over composite fading channels

Wireless communication performance in shotgun cellular system (SCS: wireless communication system with randomly placed base stations) is analysed. Aiming at this analysis, (i) the carrier to interference ratio (CIR), as an important measure in a cellular network, is considered in the downlink (path-loss, shadowing and multi-path) fading channel. Since direct calculating of the distribution of CIR is complicated, a related mathematical equation is determined through which the probability density function (PDF) of CIR can be calculated. And then, as a special case, the tail probability of CIR is obtained. (ii) A normal approximation for inverse of CIR is proposed which is applicable for calculating a tractable PDF for the downlink CIR. The analytically calculated and the approximate PDFs of CIR are compared with numerical PDFs. (iii) The distribution of the downlink rate and a lower bound for the average rate; the analytical expression for coverage of a user in an SCS based on its received CIR, and an average value for coverage are calculated. (iv) Simulation results show that the closed form and approximate PDFs over different models are close to numerical ones.

Downlink Performance Analysis for a Generalized Shotgun Cellular System

In this paper, we analyze the signal-to-interference-plus-noise ratio (SINR) performance at a mobile station (MS) in a random cellular network. The cellular network is formed by base stations (BSs) placed in a one-, two-, or three-dimensional space according to a possibly non-homogeneous Poisson point process, which is a generalization of the so-called shotgun cellular system. We develop a sequence of equivalence relations for the SCSs and use them to derive semi-analytical expressions for the coverage probability at the MS when the transmissions from each BS may be affected by random fading with arbitrary distributions as well as attenuation following arbitrary path-loss models. For homogeneous Poisson point processes in the interference-limited case with power-law path-loss model, we show that the SINR distribution is the same for all fading distributions and is not a function of the base station density. In addition, the influence of random transmission power, power control, and multiple channel reuse groups on the downlink performance is also discussed. The techniques developed for the analysis of SINR have applications beyond cellular networks and can be used in similar studies for cognitive radio networks, femtocell networks, and other heterogeneous and multi-tier networks.

Cellular performance bounds via shotgun cellular systems

This paper considers two-dimensional interference-limited cellular radio systems. It introduces the shotgun cellular system that places base stations randomly and assigns channels randomly. Such systems are shown to provide lower bounds to cellular performance that are easy to compute, independent of shadow fading, and apply to a number of design scenarios. Traditional hexagonal systems provide an upper performance bound. The difference between upper and lower bounds is small under operating conditions typical in modern TDMA and CDMA cellular systems. Furthermore, in the strong shadow fading limit, the bounds converge. To give insights into the design of practical systems, several variations are explored including mobile access methods, sectorizing, channel assignments, and placement with deviations. Together these results indicate cellular performance is very robust and little is lost in making rapid minimally planned deployments.