# 100204-lecture2 - 19 Example #3 - Rayleigh pdf 20 Rayleigh...

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1 EE522 Communications Theory 2010. 02. 04 Instructor: Hwang Soo Lee Lecture #2 - Review of Probability and Random Processes

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2 Announcements ± Handout: Lecture #2 Notes ± Homework #1 is due Thursday, February 11
3 Why are Random Processes important? ± Random Variables and Processes let us talk about quantities and signals which are unknown in advance: ² The data sent through a communication system is modeled as random. ² The noise, interference, and fading introduced by the channel can all be modeled as random processes. ² Even the measure of performance (Probability of Bit Error) is expressed in terms of a probability.

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4 Random Events
5 Probability

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6 Relationships Between Random Events
7 Random Variables

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8 Probability Distribution Function (PDF)
9 Probability Density Function (pdf )

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10 Expected Values
11 Chebyshev Inequality ± The size of the variance determines how a random variable is to lie close to it’s mean value ± This bound can be used to determine confidence intervals of a simulation.

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12 Chernoff Bound
13 Example #1: Uniform pdf

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14 Example #1 (continued)
15 Example #2: Gaussian pdf

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16 A Communication System with Gaussian Noise
17 The Q-function

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18 The Q-function and its Approximation

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Unformatted text preview: 19 Example #3 - Rayleigh pdf 20 Rayleigh pdf 21 Probability Mass Functions (pmf) 22 Example #1: Binary Distribution 23 Example #2: Binomial Distribution 24 Example #2 (continued) 25 Central Limit Theorem 26 Example of Central Limit Theorem: 27 Random Processes 28 Terminology Describing Random Processes 29 Description of Random Processes ± Knowing the pdf of individual samples of the random process is not sufficient. We also need to know how how individual samples are related to each other. ± Two tools are available to describe this relationship: ² Autocorrelation function ² Power spectral density function 30 Autocorrelation 31 Power Spectral Density 32 Gaussian Random Processes ± Gaussian Random Processes have several special properties: ² If a Gaussian random process is wide-sense stationary, then it is also stationary. ² Any sample point from a Gaussian random process is a Gaussian random variable. ² If the input to a linear system is a Gaussian random process, then the output is also a Gaussian random process. 33 Linear Systems 34 Computing the Output of Linear Systems...
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## This note was uploaded on 11/23/2010 for the course EE EE522 taught by Professor Eeehwangsoo during the Spring '10 term at Korea Advanced Institute of Science and Technology.

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100204-lecture2 - 19 Example #3 - Rayleigh pdf 20 Rayleigh...

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