Background on Cellular Networks and Cell Phone Signals.

 Keywords in the following discussion. AM Base station Carrier wave Cell Cell phone Cellular network Channel Collisions Digital transmission Duplex channel Electromagnetic spectrum Electromagnetic wave FM Frequency Handing off Hertz Hexagon Modulation Radio Radio wave Sine wave Sound waves Telephone

A cell phone is just a sophisticated radio that is a combination of the telephone (Alexander Graham Bell, 1876) and the radio (Nikolai Tesla, 1880's and Guglielmo Marconi, 1894). The key to its versatility and popularity is the way that the cellular system of communication is implemented so that a high volume of simultaneous communication traffic can be supported at a relatively low cost.  Here we provide a brief discussion on cell phone communication signals and cellular networks to provide a foundation for the "Math Problem" in this demo.

Since a cell phone is a radio it works through a system of radio waves (also called electromagnetic waves) to receive and transmit signals that correspond to speech, fax, computer data, or video. A radio wave used for such communications is referred to as a carrier wave. A carrier wave produced to carry information is just a sine wave. A sine wave simply repeats itself over and over, hence conveys a small amount of information. However, the carrier wave can be switched on and off and this was the foundation for Morse code. (See the Auxiliary Resources on the main page.) If the carrier wave is to convey a substantial amount of information, then the carrier wave is subjected to a process called modulation. This is the basis for common radio waves like AM (amplitude modulation) and FM (frequency modulation). The type of modulation applied to a carrier wave varies in accordance with the type of information to be carried (or transmitted).

The frequency of a carrier wave is the number of times per second the wave oscillates. Frequencies are measured in hertz or Hz, where 1 Hz is one oscillation per second, 1 kHz (kilo hertz) is 1000 oscillations per second, 1 MHz (mega hertz) is a million oscillations per second, and 1 GHZ (giga hertz) is 1 billion oscillations per second. Different frequencies of carrier waves are used for AM and FM radio, TV, cellular communications, and microwave communication. For example, when you tune your FM radio to 101.1, it means that your radio is receiving signals from a radio station emitting carrier waves at a frequency of 101.1 million waves per second, or 101.1 MHz. Figure 1 shows the "electromagnetic spectrum", that is the frequencies for various types of carrier waves.

Figure 1. (Adapted from FCC OET Bulletin 56.)

Creating a visual demo of carrier waves of various frequencies that are used in radio transmission is not really feasible since we would need to count the number of waves passing a point during a 1 second time interval. Instead we can use sound waves to illustrate various frequencies.

"Sound is the quickly varying pressure wave traveling through a medium. When sound travels through air, the atmospheric pressure varies periodically. The number of pressure variations per second is called the frequency of sound, and is measured in Hertz (Hz) which is defined as cycles per second."

"The higher the frequency, the more high-pitched a sound is perceived. The sounds produced by drums have much lower frequencies than those produced by a whistle, as shown in the following diagrams." (See the URL below.) http://www.epd.gov.hk/epd/noise_education/web/ENG_EPD_HTML/m1/intro_5.html

To hear sounds of various frequencies go to http://www.fearofphysics.com/Sound/sounds.html A nice example is the  combinations of tones to signal that you have pressed a key on your touch tone phone.

"A normal human can hear between 20 Hz and 20,000 Hz. That is quite a range. 20 Hz is a very low pitch sound or very deep tones. 20,000 Hz is a high pitch sound. Besides hearing low frequencies, you can often feel them. An example of that is when you can feel the bass from a loudspeaker." (See the URL http://www.school-for-champions.com/senses/hearpitch.htm )

In the US there are two common types of cell phones, regular cell phones which operate at frequencies of 800-900 MHz and Personal Communications Service (PCS) at 1850-1990 MHz. There are only so many frequencies that are available, hence there are regulations for using "bands" (or sets of frequencies) of carrier waves for specific purposes. (See Figure 1.) These regulations vary from country to country, hence a cell phone from the US may not be compatible with cellular networks in Europe.

With so few frequencies available for cell phones and so many people wanting to use this form of communication a plan was implemented for cellular networks which made this type of communication feasible. In the US a cell phone company gets about 800 frequencies to use in a city. (For voice communication two frequencies are used; one for each party to the conversation. These are called duplex channels. Hence there are fewer than 400 channels available since some frequencies are needed for company use.) The company divides the city into cells. Each cell is about 10 square miles. These cells are often thought of as hexagons which appear as in Figure 2. Each cell contains a base station consisting of a tower or building outfitted with radio equipment. A single cell is allocated about 1/7th of the duplex channels. The configuration is designed so that one cell and the six cells surrounding it on the hexagonal grid are using a different 1/7th of the duplex channels. Thus each cell has a unique set of channels, typically about 56, and there are no customers assigned the same frequency in neighboring cells. Note the description accompanying Figure 2. With digital transmission methods, the number of available channels increases dramatically.

Figure 2.

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In a city of reasonable size this cellular approach requires a large number of base stations. A company in a city also has a central office that handles switching connections to land based lines and also controls the base stations.

Once you initiate a call the network determines which cell you are in, assigns you a duplex channel, and monitors the strength of your signal using the cell base station. As you approach the boundary of your cell the neighboring cell's base station, which has also been monitoring your signal, readies itself to switch your channel to one in that cell. (This is sometimes called "handing off" the call.) Figure 3 illustrates this situation. (Naturally for safety reasons, it is the passenger in the car using the cell phone rather than the driver in Figure 3.)

Figure 3.
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