Section Overview

  Using Simulated Data to Compute Bit and Symbol Error Rates

  Example: Computing Error Rates

  Comparing Symbol Error Rate and Bit Error Rate

  Section Overview

  When to Use the Semianalytic Technique

  Procedure for the Semianalytic Technique

  Example: Using the Semianalytic Technique

  Computing Theoretical Error Statistics

  Plotting Theoretical Error Rates

  Comparing Theoretical and Empirical Error Rates

  Section Overview

  Creating Error Rate Plots Using semilogy

  Curve Fitting for Error Rate Plots

  Example: Curve Fitting for an Error Rate Plot

  Section Overview

  EyeScope

  Section Overview

  Viewing Signals Using Scatter Plots

  Overview of ACPR Measurement Tutorial

  Section Overview

  Section Overview

  Writing A Register Method

  Writing a Setup Method

  Writing a Reset Method

  Writing a Run Method

  Getting Test Inputs From the Error Rate Test Console

  Getting the Current Simulation Sweep Value of a Registered Test Parameter

  Logging Test Data to a Registered Test Probe

  Logging User-Defined Data To The Test Console

  Implementing A Default Input Generator Function For Debug Mode

  Attaching a System to the Error Rate Test Console

  Defining Simulation Conditions

  Registering a Test Point

  Getting Test Information

  Running a simulation

  Getting Results and Plotting Data

  Components of BERTool

  Interaction Among BERTool Components

  Section Overview

  Example: Using the Theoretical Tab in BERTool

  Available Sets of Theoretical BER Data

  Section Overview

  Example: Using the Semianalytic Tab in BERTool

  Procedure for Using the Semianalytic Tab in BERTool

  Section Overview

  Example: Using a MATLAB Simulation with BERTool

  Varying the Stopping Criteria

  Plotting Confidence Intervals

  Fitting BER Points to a Curve

  Requirements for Functions

  Template for a Simulation Function

  Example: Preparing a Simulation Function for Use with BERTool

  Section Overview

  Example: Using a Simulink Model with BERTool

  Varying the Stopping Criteria

  Requirements for Models

  Tips for Preparing Models

  Example: Preparing a Model for Use with BERTool

  Exporting Data Sets or BERTool Sessions

  Importing Data Sets or BERTool Sessions

  Managing Data in the Data Viewer

  Section Overview

  Representing Partitions

  Representing Codebooks

  Scalar Quantization Example 1

  Scalar Quantization Example 2

  Determining Which Interval Each Input Is In

  Section Overview

  Example: Optimizing Quantization Parameters

  Section Overview

  DPCM Terminology

  Representing Predictors

  Example: DPCM Encoding and Decoding

  Section Overview

  Example: Comparing Optimized and Nonoptimized DPCM Parameters

  Section Overview

  Example: µ-Law Compander

  Section Overview

  Creating a Huffman Code Dictionary

  Example: Creating and Decoding a Huffman Code

  Section Overview

  Representing Arithmetic Coding Parameters

  Example: Creating and Decoding an Arithmetic Code

  Section Overview

  Block Coding Features of the Toolbox

  Block Coding Terminology

  Representing Words for Reed-Solomon Codes

  Parameters for Reed-Solomon Codes

  Creating and Decoding Reed-Solomon Codes

  Representing Words for BCH Codes

  Parameters for BCH Codes

  Creating and Decoding BCH Codes

  LDPC Codes

  Representing Words for Linear Block Codes

  Parameters for Linear Block Codes

  Creating and Decoding Linear Block Codes

  Performing Other Block Code Tasks

  Selected Bibliography for Block Coding

  Section Overview

  Convolutional Coding Features of the Toolbox

  Polynomial Description of a Convolutional Encoder

  Trellis Description of a Convolutional Encoder

  Creating and Decoding Convolutional Codes

  Examples of Convolutional Coding

  Selected Bibliography for Convolutional Coding

  Overview

  CRC Algorithm

  Selected Bibliography for CRC Coding

  Section Overview

  Block Interleaving Features of the Toolbox

  Example: Block Interleavers

  Section Overview

  Convolutional Interleaving Features of the Toolbox

  Example: Convolutional Interleavers

  Delays of Convolutional Interleavers

  Modulation Techniques

  Baseband vs. Passband Simulation

  Representing Analog Signals

  Analog Modulation Example

  Section Overview

  Representing Digital Signals

  Baseband Modulated Signals Defined

  Gray Encoding a Modulated Signal

  Examples of Digital Modulation and Demodulation

  Plotting Signal Constellations

  Section Overview

  Constructing a Modem Object

  Managing Object Properties

  Copying a Modem Object

  Displaying a Modem Object

  Resetting a Modem Object

  Modulating a Signal

  Demodulating a Signal

  Example of Basic Modulation and Demodulation

  Exact LLR Algorithm

  Approximate LLR Algorithm

  Section Overview

  Example: Compensating for Group Delays in Data Analysis

  Section Overview

  Example with Default Parameters

  Section Overview

  Sampling Rates

  Designing Filters Automatically

  Specifying Filters Using Input Arguments

  Controlling the Rolloff Factor

  Controlling the Group Delay

  Combining Two Square-Root Raised Cosine Filters

  Section Overview

  Sampling Rates

  Example Designing a Square-Root Raised Cosine Filter

  Other Options in Filter Design

  Section Overview

  Describing the Noise Level of an AWGN Channel

  Section Overview

  Overview of Fading Channels

  Simulation of Multipath Fading Channels: Methodology

  Specifying Fading Channels

  Specifying the Doppler Spectrum of a Fading Channel

  Configuring Channel Objects

  Using Fading Channels

  Examples Using Fading Channels

  Using the Channel Visualization Tool

  Section Overview

  Example: Introducing Noise in a Convolutional Code

  Section Overview

  Symbol-Spaced Equalizers

  Fractionally Spaced Equalizers

  Decision-Feedback Equalizers

  Section Overview

  Basic Procedure for Equalizing a Signal

  Example Illustrating the Basic Procedure

  Learning More About Adaptive Equalizer Functions

  Choosing an Adaptive Algorithm

  Indicating a Choice of Adaptive Algorithm

  Accessing Properties of an Adaptive Algorithm

  Defining an Equalizer Object

  Accessing Properties of an Equalizer

  Section Overview

  Equalizing Using a Training Sequence

  Equalizing in Decision-Directed Mode

  Delays from Equalization

  Equalizing Using a Loop

  Section Overview

  Equalizing a Vector Signal

  Equalizing in Continuous Operation Mode

  Using a Preamble or Postamble

  Section Overview

  Creating a Galois Array

  Example: Creating Galois Field Variables

  Example: Representing Elements of GF(8)

  How Integers Correspond to Galois Field Elements

  Example: Representing a Primitive Element

  Primitive Polynomials and Element Representations

  Section Overview

  Example: Addition and Subtraction

  Example: Multiplication

  Example: Division

  Example: Exponentiation

  Example: Elementwise Logarithm

  Section Overview

  Testing for Equality

  Testing for Nonzero Values

  Basic Manipulations of Galois Arrays

  Basic Information About Galois Arrays

  Inverting Matrices and Computing Determinants

  Computing Ranks

  Factoring Square Matrices

  Solving Linear Equations

  Section Overview

  Filtering

  Convolution

  Discrete Fourier Transform

  Section Overview

  Addition and Subtraction of Polynomials

  Multiplication and Division of Polynomials

  Evaluating Polynomials

  Roots of Polynomials

  Roots of Binary Polynomials

  Minimal Polynomials

  Section Overview

  Determining Whether a Variable Is a Galois Array

  Extracting Information from a Galois Array

  Section Overview

  Exponential Format

  Polynomial Format

  List of All Elements of a Galois Field

  Nonuniqueness of Representations

  Converting to Simplest Polynomial Format

  Example: Generating a List of Galois Field Elements

  Converting to Simplest Exponential Format

  Section Overview

  Arithmetic in Prime Fields

  Arithmetic in Extension Fields

  Section Overview

  Cosmetic Changes of Polynomials

  Polynomial Arithmetic

  Characterization of Polynomials

  Roots of Polynomials

  M-PSK

  DE-M-PSK

  OQPSK

  DE-OQPSK

  M-DPSK

  M-PAM

  M-QAM

  Orthogonal M-FSK with Coherent Detection

  Nonorthogonal 2-FSK with Coherent Detection

  Orthogonal M-FSK with Noncoherent Detection

  Nonorthogonal 2-FSK with Noncoherent Detection

  Precoded MSK with Coherent Detection

  Differentially Encoded MSK with Coherent Detection

  MSK with Noncoherent Detection (Optimum Block-by-Block)

  CPFSK Coherent Detection (Optimum Block-by-Block)

  Notation

  M-PSK with MRC

  DE-M-PSK with MRC

  M-PAM with MRC

  M-QAM with MRC

  M-DPSK with Postdetection EGC

  Orthogonal 2-FSK, Coherent Detection with MRC

  Nonorthogonal 2-FSK, Coherent Detection with MRC

  Orthogonal M-FSK, Noncoherent Detection with EGC

  Nonorthogonal 2-FSK, Noncoherent Detection with No Diversity

  Common Notation for This Section

  Block Coding

  Convolutional Coding

  Errors-only Decoding