Cell phone network design
Cell phone network design refers to the systematic organization and technology behind wireless communication systems that enable cell phones to connect and communicate effectively. Central to this design is the division of coverage areas into hexagonal cells, each served by a cell tower, allowing efficient use of radio frequencies. As cell phones transmit data over short distances, typically ranging from half a mile in urban settings to five miles in rural areas, low-power transmitters are utilized to minimize interference and maximize call capacity.
Mathematical principles, including graph theory concepts like the Four Color Theorem, play a critical role in ensuring that neighboring cells do not operate on the same frequencies, thus preventing signal overlap. Over time, cell technology has evolved from analog systems to digital formats, significantly enhancing the number of simultaneous calls that can be carried. The introduction of data compression techniques has further advanced network capabilities, with newer generations of technology, such as 3G and 4G, offering faster transmission speeds and improved data handling.
Overall, effective cell phone network design is crucial in accommodating the growing demand for mobile communication and ensuring that users experience reliable, high-quality service across diverse geographical areas.
Cell phone network design
Summary: Mathematics is involved in the design of the cell network and the assignment of calls to frequencies, as well as in data compression and error compression.
Cell phones have grown from a novelty, to a luxury, to a virtual necessity since the 1990s, with the number of cell phone subscribers in the United States growing from about 91,000 in 1985 to 276 million in 2009. Part of the reason that cell phones have become so reliable, cheap, and secure has to do with mathematics. Mathematics is involved in the design of the cell network and the assignment of calls to frequencies (or channels), as well as data compression and error compression that allow a large number of clear calls to be carried over a small bandwidth. The concept of a tree from graph theory can be used to understand cell phone networks, which are challenging because of the large amount of data and links. Mathematicians like Vincent Blondel analyze millions of users and months of communication.
Cellular Radio Networks
Cell phones work by communicating via radio signal with a nearby cell phone tower. In a cellular radio network, the type of system used for cell phone coverage, the land area to be supplied with coverage is divided into regular shaped regions (or “cells”), each of which has a corresponding radio base station or cell tower. Phones within a particular cell connect via radio signal to the tower for that cell, which then connects to the public telephone network through a switch. The range of a tower may be about one-half mile in urban areas up to about five miles in flat rural areas.
Because of this relatively short transmission range, cell phones and towers can use low power transmitters. In addition to allowing phones to be small and use smaller batteries, the low power also means the radio frequencies can be reused by towers not too far away from each other without any interference between the transmissions. This function allows cell phone networks to carry a larger number of calls in a smaller bandwidth. Typically, cell companies will divide their coverage area into regularly shaped cells or regions with each one covered by a single tower. In fairly flat areas, these regions are usually hexagonal in shape—an idea developed by Bell Labs engineers W. Rae Young and Douglas Ring in the middle of the twentieth century.
The frequencies used by a particular tower for transmissions in its region cannot be used by any of the six regions with which it shares a boundary. The Four Color Theorem from graph theory indicates that only four frequencies are needed to ensure that regions that share a boundary do not use the same frequency. However, companies usually want to further buffer the distance between reuse of the same frequency, so they divide the frequencies up into seven bundles and use a different one on each of the six cells sharing a boundary with a given cell.
Cell Phone Channels
During the twentieth century, there were many discussions among professionals at the Federal Communications Commission regarding the possibility of opening up frequencies for phone use. Cellular networks began to appear around the world. For instance, Japan offered a 1G system in 1979, and, in 1983, AT&T and Ameritech tested a commercial cellular system in Chicago. Much of the advancement in cell network technology has been focused on the frequency band within a cell, which must be divided up to carry several calls at the same time. In first-generation cell technology, calls were transmitted in analog, which allowed only one call per frequency. Typically, a cell phone carrier was assigned 832 radio frequencies to use in a city. Each call was full duplex, meaning that it used two frequencies: one to transmit and one to receive.
Thus, typically there were 390 voice channels with the remaining 42 radio frequencies used for control channels that were used to locate and communicate with phones but not to carry calls. If the 395 voice channels were divided into seven frequency bundles, that made 56 voice channels per region. So if more than 56 calls were in progress in a given region at a given time, then one of the calls would be disconnected or dropped. Fortunately, first-generation technology is no longer in use. With second-generation (2G) cell technology, calls were no longer analog signals but were converted to a digital (0 and 1) format. This shift is similar to the change from cassette tapes to compact discs in the recording industry.
The greatest advantage to digital technology is that it allows for sophisticated data compression techniques to be used without losing acceptable call quality. Data compression allows for between three and 10 digital calls to be carried in the bandwidth necessary for a single analog call. Further advancements in compression have allowed for even newer third-generation (3G) technology. 3G networks have much faster transmission speeds and allow the use of smartphones that can transmit data fast enough to surf the Internet, send and receive e-mail, and even instant message with a cell phone. Newer 4G technology adds even more speed and capacity to cell phone networks.
Bibliography
Agar, Jon. Constant Touch: A Global History of the Mobile Phone. Cambridge, UK: Icon Publishers, 2003.
Brain, Marshall, Jeff Tyson, and Julia Layton. “How Cell Phones Work.” HowStuffWorks. November 14, 2000. http://electronics.howstuffworks.com/cell-phone.htm.