1.2  An Illustrative Design
1.3  The Complete Onion
2  A TELECOMMUNICATION SYSTEM
2.1  Electromagnetic Transmission of Analog Waveforms
2.2  Bandwidth
2.3  Upconversion at the Transmitter
2.4  Frequency Division Multiplexing
2.5  Filters that Remove Frequencies
2.6  Analog Downconversion
2.7  Analog Core of Digital Communication System
2.9  Digital Communications Around an Analog Core
2.10  Pulse Shaping
2.11  Synchronization
2.12  Equalization
2.13  Decisions and Error Measures
2.14  Coding and Decoding
2.15  A Telecommunication System
3  THE FIVE ELEMENTS
3.1  Finding the Spectrum of a Signal
3.2  The First Element: Oscillators
3.3  The Second Element: Linear Filters
3.4  The Third Element: Samplers
3.5  The Fourth Element: Static Nonlinearities
3.7  Summary
4  MODELLING CORRUPTION
4.1  When Bad Things Happen to Good Signals
4.1.1  Other Users
4.1.3  Narrowband Noise
4.1.4  Multipath Interference
4.2  Linear Systems: Linear Filters
4.3  The Delta "Function"
4.4  Convolution in Time: It's What Linear Systems Do
4.5  Convolution ’Ç¨ Multiplication
4.6  Improving SNR
5  ANALOG (DE)MODULATION
5.1  Amplitude Modulation with Large Carrier
5.2  Amplitude Modulation with Suppressed Carrier
5.4  Injection to Intermediate Frequency
6  SAMPLING with AUTOMATIC GAIN CONTROL
6.1  Sampling and Aliasing
6.2  Downconversion via Sampling
6.3  Exploring Sampling in MATLAB
6.4  Interpolation and Reconstruction
6.5  Iteration and Optimization
6.6  An Example of Optimization: Polynomial Minimization
6.7  Automatic Gain Control
6.8  Using an AGC to Combat Fading
6.9  Summary
7  DIGITAL FILTERING AND THE DFT
7.1  Discrete Time and Discrete Frequency
7.1.1  Understanding the DFT
7.1.2  Using the DFT
7.2  Practical Filtering
7.2.1  Implementing Filters
7.2.2  Filter Design
8  BITS TO SYMBOLS TO SIGNALS
8.1  Bits to Symbols
8.2  Symbols to Signals
8.3  Correlation
8.4  Receive Filtering: From Signals to Symbols
8.5  Frame Synchronization: From Symbols to Bits
9  STUFF HAPPENS
9.1  An Ideal Digital Communication System
9.2  Simulating the Ideal System
9.3  Flat Fading: A Simple Impairment and a Simple Fix
9.4  Other Impairments: More "What Ifs"
9.4.2  Multipath Interference
9.4.3  Carrier Phase Offset
9.4.4  Carrier Frequency Offset
9.4.5  Downsampler Timing Offset
9.4.6  Downsampler Period Offset
9.4.7  Repairing Impairments
10  CARRIER RECOVERY
10.1  Phase and Frequency Estimation via an FFT
10.2  Squared Difference Loop
10.3  The Phase Locked Loop
10.4  The Costas Loop
10.5  Decision Directed Phase Tracking
10.6  Frequency Tracking
10.6.1  Direct Frequency Estimation
10.6.2  Indirect Frequency Estimation
11  PULSE SHAPING AND RECEIVE FILTERING
11.1  Spectrum of the Pulse: Spectrum of the Signal
11.2  Intersymbol Interference
11.3  Eye Diagrams
11.4  Nyquist Pulses
11.5  Matched Filtering
11.6  Matched Transmit and Receive Filters
12  TIMING RECOVERY
12.1  The Problem of Timing Recovery
12.2  An Example
12.3  Decision Directed Timing Recovery
12.4  Timing Recovery via Output Power Maximization
12.5  Two Examples
14  LINEAR EQUALIZATION
14.1  Multipath Interference
14.2  Trained Least-Squares Linear Equalization
14.2.1  A Matrix Description
14.2.2  Source Recovery Error
14.2.3  The Least-Squares Solution
14.2.4  Summary of Least-squares Equalizer Design
14.2.5  Complex Signals and Parameters
14.2.6  Fractionally-Spaced Equalization
14.3  An Adaptive Approach to Trained Equalization
14.4  Decision-Directed Linear Equalization
14.5  Dispersion-Minimizing Linear Equalization
14.6  Examples and Observations
15  CODING
15.1  What is Information?
15.2  Redundancy
15.3  Entropy
15.4  Channel Capacity
15.5  Source Coding
15.6  Channel Coding
15.7  Encoding a Compact Disc
16.1  How the Received Signal is Constructed
16.2  A Design Methodology for the M6 Receiver
16.2.1  Stage One: Ordering the Pieces
16.2.2  Stage Two: Selecting Components
16.2.3  Stage Three: Anticipating Impairments
16.2.4  Sources of Error and Trade-Offs
16.2.5  Tuning and Testing
16.3  The M6 Receiver Design Challenge
A  TRANSFORMS, IDENTITIES AND FORMULAS
A.1  Trigonometric Identities
A.2  Fourier Transforms and Properties
A.3  Energy and Power
A.4  Z-Transforms and Properties
A.5  Integral and Derivative Formulas
A.6  Matrix Algebra
B  SIMULATING NOISE
C  ENVELOPE OF A BANDPASS SIGNAL
D  RELATING THE FOURIER TRANSFORM AND THE DFT
D.1  The Fourier Transform and its Inverse
D.2  The DFT and the Fourier Transform
E  POWER SPECTRAL DENSITY
F  RELATING DIFFERENCE EQUATIONS TO FREQUENCY RESPONSE AND INTERSYMBOL INTERFERENCE
F.1  Z-Transforms
F.2  Sketching the Frequency Response From the Z-Transform
F.3  Measuring Intersymbol Interference
G  AVERAGES and AVERAGING
G.1  Averages and Filters
G.2  Derivatives and Filters
G.3  Differentiation is a Technique: Approximation is an Art