# Introduction to Wireless Systems–A Tutorial–Part II

Editor's Note:
Here isPart I of the article. Also, check out the Mobile Handset DesignLine site. During the publishing of this book excerpt, I'm putting up crossword puzzles for a chance to win your very own copy of this recently published book. Watch for the latest one in the blog section.

Cellular Concepts
Interference control is the key to allowing reuse of channels within a given geographic area. We therefore begin our discussion of cellular concepts by developing a simple model to predict the interference levels caused by geographically separated transmitters operating on a common channel.

Consider two cells whose base stations (BS1 and BS2 respectively) are separated by a distance D. Each base station has a circular coverage area of radius R as shown in Figure 4.1. Assume that the propagation environment is uniform within and completely surrounding the two cells and that the path-loss exponent is ½. Let the two base stations receive on the same channel, with center frequency f1 . Also shown in Figure 4.1 are two mobile units, MU1 and MU2 , served by base stations BS1 and BS2 respectively. The mobile units are located at the boundaries of their respective cells, each at distance R from its base station. To keep the discussion simple, we consider transmission on the reverse channel, from mobile unit to base station, only.

Figure 4.1 Cochannel interference from a Single Source

From our work in Chapter 3, the level of the signal received at base station BS1 from mobile unit MU1 can be expressed as:

where K1 is a constant that incorporates the transmitter power, the antenna gains, the antenna heights, and so on. The received signal level at base station BS1 from mobile unit MU2 can be written:

Now from the perspective of base station BS1 , P1 represents “signal” and
P2 is cochannel interference. The signal-to-noise-and-interference ratio at base station BS1 is:

Where Pn is thermal noise referred to the base station input. When the receiver noise is significantly greater than the interference–that is, when Pn > > P2 –we describe the system as “noise limited,” as explained earlier. For this case:

When the received noise is significantly less than the interference–that is, when Pn
< < P2 –the system is “interference limited.” Then we can write:

For identical mobile units transmitting at the same power level, the previous Equation becomes:

The locations of the mobile units in Figure 4.1 have been chosen to illustrate the worst case of signal-to-interference ratio (SIR). Mobile unit MU1 is at the perimeter of its cell, as far as possible from the base station serving it. Mobile unit MU2 is also at the perimeter of its cell, as
close to base station BS1 as it can get while remaining in the cell served by BS2 . It should be evident that for this geometry the signal-to-interference ratio would be the same if we calculated it at base station BS2 or at either mobile unit.

In a realistic cellular system there are likely to be more than two cells, and cochannel interference may come from more than one source. If there are J cells surrounding base station BS1 , each containing a mobile unit, and all of these mobile units are transmitting on the same channel, then the signal-to-interference ratio at BS1 can be written

where Pj , j = 2,…,J = 1 represent cochannel interference from mobile units in the surrounding cells. In the discussion that follows, we will see that in the most important case all of the interference sources are identical, and all are located at distances approximately D from the base station BS receiver. In this case Equation (4.9) becomes

The equation above suggests that the ratio of separation distance D to cell radius R is the predominant factor in determining the signal-to-interference ratio S/I. The ratio Q = D/R is usually termed the “frequency reuse ratio” or the “interference reduction factor.” Quality of service objectives for the cellular system will usually dictate that some minimum signal-to-interference ratio, say, S/I = ϒmin , be met throughout the area. This normally implies that D must exceed R by some factor greater than 1. Base stations BS1 and BS2 are then separated by enough distance that additional cells can be deployed between them. To avoid increasing the cochannel interference, these additional cells must operate on channel frequencies other than 1 . In this way an entire geographic area can receive contiguous coverage, while allowing frequency reuse at an acceptable level of cochannel interference.

When the number of available channels Nchan is sufficiently large, the channels may be organized into groups called “channel sets,” Fi = 1,..,N, and deployed among the cells as suggested by Figure 4.2. The assignment of sets of frequencies to each cell allows more than one subscriber to be serviced at a time in any given cell. The appropriate size of a channel set and the number of distinct channel sets then become design parameters.

Figure 4.2 Deployment of Channel Sets in Neighboring Cells

In the single-base-station approach, popular before the introduction of frequency reuse, the location of users within the coverage area was not a matter of concern. In a cellular system the geographical distribution of users may matter. Since the allocated group of channels is broken up into channel sets, each cell can service only a limited number of customers. If all of the customers happen to congregate in a single cell, it is likely that there will not be enough channels available in that cell to provide adequate service. In real-world cellular systems the downtown areas of cities are more likely to experience a higher density of customers, at least during the working day, than are the peripheral areas. The higher customer density in some cells can be managed either by assigning more channels to these cells or by making these cells smaller so that they include fewer customers. Increasing the number of channels in a channel set causes a decrease in the number of channel sets that are available.

The geometry of Figure 4.2 suggests that as the number of channel sets decreases, so does the separation distance D, leading to an increase in cochannel interference. On the other hand, decreasing the cell radius R requires more cells to cover the market area, leading to an increased investment in base station towers and transmitters. These considerations will be examined in detail later. For the present we will accept the simplest case and assume that subscribers are uniformly distributed throughout the market area.

Our design objectives require that the cellular system be capable of growth in both coverage area and user capacity. This implies that our system must have an ability to add cells to the periphery to expand the service area, and also an ability to add cells within the coverage area to increase the user capacity. It is certainly possible to lay out cells and assign channels in a way that is individually crafted for a given geographic area and customer distribution, but adding new cells for growth would then require custom reengineering. Such ad-hoc design could easily result in a need to redistribute cells and relocate base stations. Construction of a base station is costly and, in addition to the cost of erecting a tower, may involve the purchase of real estate and the approval of zoning boards. Consequently the capability to expand must be designed into the cellular system from the beginning. To facilitate expansion it is convenient to deploy cells that are uniform in shape and are located on a symmetric grid. We will now investigate the extent to which such a regular layout is possible and the principles on which the cell layout is based.

Given a specified service area, placing cells to cover that area requires that some assumption be made about the shape of the coverage regions of the individual base stations. The simplest assumption is that coverage regions will be circular, based on the principle that equal-level signal contours surrounding a transmitting antenna are circles with the base station at the origin. Given what we know about propagation, however, it is unlikely that real-world coverage areas will be circular in any but a statistical sense. In any specific instance, the shape of a coverage region is not circular but is rather somewhat amorphous and highly dependent on terrain and the location of surrounding obstacles. Keep in mind, however, that our objective in configuring cells is to provide a high likelihood that a mobile unit will be adequately served by its nearest base station. To accomplish this purpose, determining the shape of the actual coverage area is not as important as defining the boundaries over which the mobile unit will operate while communicating with the specific base station. Our approach, then, is to initially assume that the base station coverage areas are circular and to focus on developing an efficient method for locating and growing the cells. Historical experience has shown that once the cells are deployed, system parameters may be adjusted to provide adequate performance in the vast majority of circumstances without the need for extraordinary engineering efforts.

Figure 4.3 The Boundary between Two Circular Cells

Although we will assume that the coverage regions are circular, a little reflection will show that it is not possible to uniformly cover a geographic area with circles without having gaps or overlaps in coverage. We naturally seek to determine a layout pattern that has no gaps. Also, to ensure that the number of cells deployed is minimal, we wish to minimize the overlaps. Figure 4.3 shows two overlapping circular coverage regions. In the region of overlap there is a straight-line boundary that divides the locations for which the signal from base station BS1 is stronger than the signal from base station BS2 and vice versa. Consequently, if we cover our market area with overlapping circular coverage regions arranged on some kind of a regular grid, the actual cells will be polygons. Now it turns out that there are only three regular polygonal shapes for which it is possible to completely “tile” an area without overlaps or gaps. These shapes are the equilateral triangle, the square, and the hexagon: regular polygons of three, four, or six sides, respectively. Figure 4.4 shows the tile pattern for each of these polygons and also shows how a single polygon can be inscribed in a circle of radius R, the cell (or coverage) radius. Observe that within the circle of radius R the area covered by the hexagonal pattern is greatest.

Figure 4.4 Covering a Plane Area with Regular Polygons: (a) Equilateral Triangles; (b) Squares; (c) Hexagons

Next: Cellular Concepts Cont'd.

Bruce A. Black completed his B.S. at Columbia University, his S.M. at Massachusetts Institute of Technology, and his Ph.D. at the University of California at Berkeley, all in electrical engineering. Since 1983 he has been on the faculty of the Department of Electrical and Computer Engineering at Rose-Hulman Institute of Technology in Terre Haute, Indiana, where he has been advisor to Tau Beta Pi and is advisor to the Amateur Radio club (W9NAA). In 2004 he was named Wireless Educator of the Year by the Global Wireless Education Consortium. He is a member of Tau Beta Pi, Eta Kappa Nu, and Sigma Xi.

Philip S. DiPiazza received a B.E.E from Manhattan College in 1964, an M.E. in electrical engineering from New York University in 1965, and a Ph.D. (electrical engineering) from the Polytechnic Institute of New York in 1976. Dr. DiPiazza was responsible for the system integration and test of the first North American deployment of AMPS.. He is currently an Adjunct Professor at the Rose-Hulman Institute of Technology and a Senior Consultant with Award Solutions, Inc. Dr. DiPiazza is an advisor and member of the Global Wireless Educational Consortium and a member of the IEEE.

Bruce A. Ferguson received the B.S., M.S., and the Ph.D. degree in electrical engineering from Purdue University, West Lafayette, Indiana in 1987, 1988, and 1992 respectively. He is currently a Communication System Engineer with Northrop Grumman Space Technology. He has worked with space and ground communication systems and photonics at TRW Space and Electronics (now NGST), and taught at Rose-Hulman Institute of Technology and The University of Portland in Oregon. Dr. Ferguson is a member Eta Kappa Nu and IEEE.

David R. Voltmer received degrees from Iowa State University (B.S.), University of Southern California (M.S.), and The Ohio State University (Ph.D.), all in electrical engineering. During nearly four decades of teaching, Dr. Voltmer has maintained a technical focus in electromagnetics, microwaves, and antennas. His more recent efforts are directed toward the design process and project courses. He has served in many offices of the ERM division of ASEE and in FIE. Dr. Voltmer is an ASEE Fellow and a Life Senior member of IEEE.

Frederick C. Berry received the B.S., M.S., and D.E. degrees from Louisiana Tech University in 1981, 1983, and 1988 respectively. He taught in the Electrical Engineering Department at Louisiana Tech University from 1982 to 1995. Currently Dr. Berry is Professor and Head of the Electrical and Computer Engineering Department at Rose-Hulman Institute of Technology. In 2007 he became Executive Director of the Global Wireless Education Consortium. He is a member of Tau Beta Pi, Eta Kappa Nu, and Sigma Xi.

Title: Introduction to Wireless Systems ISBN: 0132447894 Chapter 4: Radio Frequency Coverage: Sysetms Engineering and Design

Reproduced by permission of Pearson Education, Inc., 800 East 96th Street, Indianapolis, IN 46240. Written permission from Pearson Education, Inc. is required for all other uses. The book can be purchased at: Purchase.

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