• Underlying context

    Initial setting

    The popularity of cell phones continues to grow.  How do these things work?  How do companies determine the monthly charges? Mathematics helps us to understand the cell phone business and to make wise choices. Among the important ideas with this technology is placement of cell phone towers and techniques for transmitting data effectively.

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    Detailed context

     

    Cell phone communication depends upon the use of cell phone towers. The placement of towers is determined by their power, the desired quality of the service provided, the number of users, and the location of the users.  The goal is to cover the area as big as possible. Generally, the displacement of towers has a range of possibilities.

    People who work with cell phones know that the area covered by a tower – that is, the area in which people can use the tower directly – may have an unusual geometric shape.  However, to make their work easier to talk about mathematically, they often use a circle to model the area covered by a single tower. The circular shape is the ideal power coverage area.  Because multiple towers are used in reality, people who look at the arrangements of towers use hexagons and tessellations to model the placement of multiple towers. Hexagonal shaped cells are artificial and do not represent the real world tower area, but using hexagons simplifies planning and design of a cellular system. The real cell shape will keep changing due to prevailing conditions, such as the weather within the tower’s coverage area. Examples of these various geometric patterns appear at http://www.doc.ic.ac.uk/~nd/surprise_96/journal/vol1/pr4/article1.html.  The area that a tower covers is called a cell.

    If call handoff and roaming are not considered, the farthest distance from a tower that a cell phone can still work is dependent on the area that can be covered by the tower. Handoff refers to switching a call from the current cell to the next cell.  When there is a cal in progress and the cellular system senses the mobile user passing from one cell to another, the call is switched “on the fly,” without dropping the call in progress.  The system uses continuous measurements of signal strength received from the individual cell sites to manage the handoff. Roaming means a cell phone can be used within a cell in which the cell phone is not registered. Typically, towers are spaced around 1 to 2 miles apart, but towers can be spaced up to 20 miles in rural areas. In areas with a higher number of users or areas with many obstacles (such as tall buildings), towers may be spaced closer together.

    Cell phone calls happen because the technology changes the words that people say into a signal that can be transmitted and then changes that signal back into something people can hear.  A/D conversion means to convert an analog signal (like voice) to its digital form (how the data travel). Generally, an analog signal is converted into a digital stream of 0s and 1s by sampling and quantifying the analog data.  The techniques for this process can be complicated.  Good techniques allow much data to be transmitted very quickly.  Data compression refers to the techniques for reducing all of these 0s and 1s into a shorter sequence of 0s and 1s. It involves probability and statistics and logical operations like AND, OR, and NOT.

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    Context Q&A

    As more people use cell phones and other types of communication, questions arise.  Here are some questions that have been posed as people think about the technology used in this module.

    Q1:      What matters when it comes to the quality of cell phones?

    For those which can send/receive email, image, and video, the transmission speed and the security during wireless communication are becoming critical. Transmission speed is the number of data bits that can be transmitted (sent) per second (bits/sec). It depends on the available bandwidth of the channel. For example, voice can be sent in as little as 8000 bits per second. Security is usually provided by a service provider; the cell phone has to be registered properly before it can be used.

    Q2:      Is it true that certain cellular phone carriers have more towers that will lead to a better quality of sound?

    Not necessarily. Having more towers might mean that the towers are located closer to each other, which will probably cause an increase in co-channel interference (interference from other towers using the same channel frequency).  The interference also depends on whether different towers use the same bandwidth.