{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

ece4305_lab1 - ECE4305 Software-Dened Radio Systems and...

Info iconThis preview shows pages 1–4. Sign up to view the full content.

View Full Document Right Arrow Icon
ECE4305: Software-Defined Radio Systems and Analysis Lab 1: Understanding the Tools for SDR Design and Analysis Objective This laboratory will introduce some of the theory behind several digital communications concepts. It will also introduce MATLAB TM and Simulink TM as a development tool for digital communication systems design and implementation. Contents 1 Theoretical Preparation 2 1.1 Random Variables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 1.2 Central Limit Theorem . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 1.3 Gaussian Processes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 1.4 The Q Function . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 1.5 Power Spectral Density . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 1.6 Complex Baseband & Signal Representation . . . . . . . . . . . . . . . . . . . . . . . 4 1.7 Problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6 2 Simulation 7 2.1 Random Number Generators . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7 2.1.1 Step 1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7 2.1.2 Step 2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7 2.1.3 Step 3 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7 2.1.4 Step 4 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7 2.2 AM Transmission in MATLAB . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8 2.3 An Introduction to Simulink . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9 2.3.1 Data Sequence Generators . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9 2.3.2 AM Transmission in Simulink . . . . . . . . . . . . . . . . . . . . . . . . . . . 11 3 GNU Radio Implementation 11 3.1 Basic Setup . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12 3.2 Frequency Offset . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12 3.3 Digital Communication . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13 3.4 IEEE 802.11 Wireless . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14 4 Analysis & Synthesis 14 5 Lab Report Instructions 14 1
Background image of page 1

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon
1 Theoretical Preparation These fundamental concepts of digital communication systems will serve as a basis for the implemen- tation and design of systems later on in this course. 1.1 Random Variables A random variable (rv) is a mapping function whose domain is a sample space and whose range is some set of real numbers: X = X ( s ) (1) where X is the rv and X ( s ) is the outcome of an experiment. The cumulative distribution function (CDF) describes how the rv behaves probabilistically, and is defined as: F x ( x ) = P ( X x ) . (2) Consequently, this means the probability that the outcome of an experiment described by the rv X is less than or equal to the dummy variable x . Several properties of the CDF include the following: F x ( x ) is bounded between zero and one. F x ( x ) is a non-decreasing function, i.e., F x ( x 1 ) F x ( x 2 ) if x 1 x 2 . The probability density function (pdf) is given as the derivative of the CDF in terms of the dummy variable x , namely: f x ( x ) = d dx F x ( x ) . (3) For more information about random variables, please refer to Section 4.1 of the course textbook [3]. 1.2 Central Limit Theorem The central limit theorem (CLT) states that if you have a set of random variables { X i } i = N i - 1 such that X i is independently and identically distributed (i.i.d.), i.e.: 1. X i are statistically independent, and 2. X i have the same pdf with mean μ x and variance σ 2 x , Then as N → ∞ , the distribution of the sample expectation will be Gaussian regardless of the original distribution. 1.3 Gaussian Processes Given the following expression: y = integraldisplay T 0 g ( t ) X ( t ) dt (4) we can say that X ( t ) is a Gaussian process if: 1. E ( y 2 ) is finite, i.e., does not blow up, and 2
Background image of page 2
2. Y is Gaussian-distributed for every g ( t ). Note that the rv y has a Gaussian distribution, where its PDF is defined as: f y ( y ) = 1 radicalbig 2 πσ 2 y e - ( y - μy ) 2 2 σy 2 , (5) where μ y is the mean and σ y 2 is the variance. Such processes are important because they closely match the behavior of numerous physical phenomena, such as additive white Gaussian noise.
Background image of page 3

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon
Image of page 4
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}