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L14-15 - MIT 6.02 DRAFT Lecture Notes Fall 2010(Last update...

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MIT 6.02 DRAFT Lecture Notes Fall 2010 (Last update: November 9, 2010) Comments, questions or bug reports? Please contact [email protected] L ECTURE 14 Frequency-Domain Sharing and Fourier Series In earlier lectures, we learned about medium access (MAC) protocols for allowing a set of users to share a single communication medium by well-controlled turn-taking, a form of time-domain sharing (we used the term “time sharing” earlier). In these three lectures, we will focus on using P sinusoids of P different frequencies to simultaneously “carry” P dif- ferent messages (from one or more transmitters) over a common, shared communication medium. This form of sharing is termed frequency-domain sharing (aka “frequency shar- ing”) or spectral-domain sharing . 1 Frequency sharing eliminates contention, so there are no collisions, but at the same time, dedicates frequencies to different transmissions whether or not they are used, so when traf±c loads are skewed, the peak data transfer rate is generally lower than with contention protocols. In practice, wireless networks use a combination of time and frequency sharing, as we will see in a case study on 802.11 (WiFi) networks later in the course. To understand these trade-offs, we will need a new mathematical tool, the Fourier se- ries . Even though we will focus on using the Fourier series to analyze only frequency- domain sharing, Fourier series appear in an enormous variety of applications including quantum mechanics, electromagnetics, video, audio, and image compression, semicon- ductor transport, magnetic-resonance imaging (MRIs), and crystallography, to name just a few. ° 14.1 Spectral-Domain Channel Sharing, Once over “Lightly” A good way to understand some of the issues in spectral-domain sharing is to consider the visible spectrum, colors from red to violet, corresponding to frequencies roughly in the 4 × 10 14 to 8 × 10 14 hertz ( 400 to 800 terahertz ) range. If two users want to simultaneously send different messages over some distance using high powered lamps, they can use different colors. The ±rst transmitter could send a message by turning on and off a red lamp, and the second transmitter could send a message by turning on an off a green lamp. Over 1 We will use the two terms interchangeably. 1
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2 LECTURE 14. FREQUENCY-DOMAIN SHARING AND FOURIER SERIES Figure 14-1: A Diagram of frequency-domain sharing. time, a distant receiver will see a changing mixture of red, green, and yellow, but will be able to untangle the messages from the two transmitters by “pulling out” the frequency of interest. If there are many transmitters, all using different colors, then the receiver may see what looks like white light, but with the aid of a simple glass prism, the receiver will be able to separate out each of the colors and determine each of the messages.
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L14-15 - MIT 6.02 DRAFT Lecture Notes Fall 2010(Last update...

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