The Distribution of Path Losses for Uniformly Distributed Nodes in a Circle

Abstract

When simulating a wireless network, users/nodes are usually assumed to be distributed uniformly in space. Path losses between nodes in a simulated network are generally calculated by determining the distance between every pair of nodes and applying a suitable path loss model as a function of this distance (power of distance with an environment-specific path loss exponent) and adding a random component to represent the log-normal shadowing. A network with nodes consists of path loss values. In order to generate statistically significant results for system-level simulations, Monte Carlo simulations must be performed where the nodes are randomly distributed at the start of every run. This is a time-consuming operation which need not be carried out if the distribution of path losses between the nodes is known. The probability density function (pdf) of the path loss between the centre of a circle and a node distributed uniformly within a the circle is derived in this work.

Dynamic Fractional Frequency Reuse Diversity Design for Intercell Interference Mitigation in Nonorthogonal Multiple Access Multicellular Networks

“…Users are considered to be uniformly distributed in the service area of a cell as is the case in most practical scenarios and as shown in [40]. After distinguishing the edge and center users, power and frequency channel allocation will take place, ensuring that user fairness is maintained across the cell for each cell in the network.…”

Studying Optimal Design of Strict Fractional Frequency Reuse in OFDMA Cellular System

“…It consists of three macro cells in which each cell is partitioned into center and edge zone. The resource allocation between interior and celledge users is proportional to the square of the ratio of interior radius and the cell radius is represented by R. this is when user locations are assumed to be uniformly distributed [11]. One of the most important design parameters here is the radius of the center zone of the macro-cell.…”

Hexagonal vs Circular Cell Shape: A Comparative Analysis and Evaluation of the Two Popular Modeling Approximations

“…In this case, the path loss pdf between a node distributed uniformly within a circular cell with radius R and the center of the cell is (Baltzis, 2010b) () is the generalized Reimann's zeta function (Gradshteyn & Ryzhik, 1994). In the absence of small-scale fading, (12) is simplified (Bharucha & Haas, 2008) . In the case of hexagonal instead of circular cells, the path loss pdf (in the absence of smallscale fading; the incorporation of this factor is a topic for a potential next stage of future work extension) is (Baltzis, 2010a) () …”

“…We further see that the inradius circular pdf and cdf are closer to the hexagonal ones compared with the circumradius curves. Let us now consider a cellular system with typical UMTS air interface parameters (Bharucha & Haas, 2008). In particular, we set 3 γ = and L 0 = 37dB while shadowing deviation equals to 6dB or 12dB.…”

“…Proposals based on neural network techniques are also of great interest (Cerri et al 2004, Popescu et al, 2006Östlin et al, 2010). Approximate analytical methods that reduce significantly the computational requirements and the cost of the simulations can also be found in the published literature (Bharucha & Haas, 2008;Baltzis, 2010a,b). In this chapter, we discuss and evaluate the hexagonal and the circular cell shape modeling approximations in a cellular network.…”