Understanding Cell Phone Technology: Frequency Bands and Modulation

Several weeks ago, we talked about the different bands of the electromagnetic spectrum. Each band corresponds to a range of frequencies, measured in cycles/second or Hertz (Hz). One of those bands is the Radio Frequency (RF) band. In the United States, the Federal Communications Commission (FCC) is responsible for regulating the use of this radio spectrum. Why is this important?

We’ve all had the experience of one signal interfering with another. Perhaps we were talking on our cell phone, and suddenly we started getting a lot of unwanted noise on the channel. Remember all the work we did to understand noise. When two nearby signals are transmitting at the same frequency, they interfere with one another. That interference or noise makes it difficult, if not impossible, for the message of either signal to get through. The FCC issues licenses to different entities – like radio stations and cell phone providers – so that RF transmitters don’t interfere with one another.

The FCC has allocated radio frequencies in the bands 9 kHz to 275 GHz. The chart of the allocated frequencies is a big, complicated thing. If you want to see it in all its glory, go to https://transition.fcc.gov/oet/spectrum/table/fcctable.pdf

Now let’s go back to our cell phone. Suppose we want to transmit some information, which might be analog (like voice) or digital (like bits in a computer file). All the coding methods used for cell phone communications, including data compression and error control, use a digitized version of the information. So if the message we start with is analog, we have to convert it to a digital representation before doing any encoding, something we talked about in a previous blog.

The company which provides your cellular service has an FCC license to operate at specified radio frequencies. To avoid substantial fines and other FCC penalties, your provider only allows your cell phone to transmit at those authorized frequencies, known as the carrier frequencies. We can see the carrier frequency of a signal by applying the Fast Fourier Transform (FFT) to the time domain signal. We talked about the FFT in a previous blog.

The information gets onto the carrier frequency through modulation. Modulation is defined as “the process by which some characteristic of a carrier [frequency] is varied in accordance with the modulating wave.” The process of adding information to a radio signal by varying its amplitude is called amplitude modulation or AM.

Wow, that’s a lot of fancy words! What does it mean?

Let’s consider a cell phone example. We start with a cosine wave that will be the carrier frequency. It is given by

c(t) = Ac cos (2πfct)

Ac is called the carrier amplitude, and fis the carrier frequency authorized by the FCC. Suppose we denote the baseband message as m(t). If we vary the carrier’s amplitude by the baseband signal, we call that AM. We can then write the transmitted signal as

s(t) = Ac[1 + kam(t)] cos (2πfct)

where ka is a constant such that |kam(t)| < 1 to avoid signal distortion. If you want to see what AM signals look like when you vary the baseband signal and the carrier frequency, go to https://academo.org/demos/amplitude-modulation/

There are many other types of modulation. Just like there is AM radio, there is also FM radio, which uses frequency modulation. The basic approach remains the same – to use the original signal (message) is to modulate the carrier wave in amplitude, frequency, and so on.

The antenna at the receiving cell phone receives the signal. This signal is then transferred to other components inside the phone. These components perform demodulation, error-correction, and decompression to recover the message. If the information was originally analog, then there is one additional step, which converts the recovered digital message into the expected analog format, like voice.

We’ve now talked about all the significant elements of a communications system pictured in the model below. Having finished discussing the amazing technology packed into your pocket-sized smartphone, we will move on to other topics next week.