4 Channels: Modeling, Simulating and Mitigating their Effects
4.1 What You Will Learn
4.2 Channel Models
4.2.1 LTI Gaussian channel
4.2.2 Flat-fading channel
4.2.3 Discrete-time scalar AWGN
4.2.4 Discrete-time vector AWGN
4.2.5 Continuous-time AWGN channel
4.2.6 LTI channel with non-white additive noise
4.3 Optimal Receivers for AWGN: Matched Filters or Correlators
4.3.1 Motivation to matched filtering
4.3.2 Relation between matched filtering and correlative decoding
4.3.3 Orthogonal expansion of white Gaussian noise
4.3.4 SNR at the output of a continuous-time matched filter
4.3.5 Discrete-time matched filtering
4.3.6 Characteristics of the matched filter
4.3.7 Simulations with matched filtering
4.3.8 Proof sketch of the optimality of matched filtering for AWGN
4.4 Receivers to Combat ISI and Their Analysis
4.4.1 Intersymbol interference (ISI)
4.4.2 Pulse response
4.4.3 Examples of intersymbol interference (ISI) in PAM
4.4.4 Some practical aspects concerning the “pulse” to study ISI
4.4.5 Nyquist Criterion for Zero ISI
4.4.6 Cursor, precursor ISI and postcursor ISI
4.5 Raised Cosine Shaping Pulses (Filters)
4.6 Matched Filtering and the Square-Root Raised Cosine
4.7 Eye Diagrams
4.8 Distinguishing Nyquist Criterion and Sampling Theorem
4.9 Equalization and System Identification
4.9.1 System identification using least squares (LS)
4.9.2 Zero-forcing (ZF) equalization criterion
4.9.3 Least squares FIR equalizer based on estimated channel
4.9.4 FIR equalizer: LS direct estimation with training sequence
4.9.5 Probabilistic approach to LS FIR system identification
4.10 Channel Capacity
4.10.1 Capacity of AWGN channels
4.10.2 Water filling
4.10.3 Capacity of the frequency-selective LTI Gaussian channel
4.10.4 Revisiting the capacity of flat fading continuous-time AWGN
4.11 Synchronization
4.11.1 Carrier recovery
4.11.2 Carrier recovery using FFT
4.11.3 Phase-locked loop (PLL)
4.11.4 Continuous-time PLL for tracking sinusoids
4.11.5 Discrete-time PLL (DPLL) for tracking sinusoids
4.11.6 Design of PLL and DPLL
4.11.7 Discrete-time PLL (DPLL) for tracking digitally modulated... decision directed...
4.12 Channel Model with Frequency Offset
4.13 Applications
4.14 Comments and Further Reading
4.15 Exercises
4.2 Channel Models
4.2.1 LTI Gaussian channel
4.2.2 Flat-fading channel
4.2.3 Discrete-time scalar AWGN
4.2.4 Discrete-time vector AWGN
4.2.5 Continuous-time AWGN channel
4.2.6 LTI channel with non-white additive noise
4.3 Optimal Receivers for AWGN: Matched Filters or Correlators
4.3.1 Motivation to matched filtering
4.3.2 Relation between matched filtering and correlative decoding
4.3.3 Orthogonal expansion of white Gaussian noise
4.3.4 SNR at the output of a continuous-time matched filter
4.3.5 Discrete-time matched filtering
4.3.6 Characteristics of the matched filter
4.3.7 Simulations with matched filtering
4.3.8 Proof sketch of the optimality of matched filtering for AWGN
4.4 Receivers to Combat ISI and Their Analysis
4.4.1 Intersymbol interference (ISI)
4.4.2 Pulse response
4.4.3 Examples of intersymbol interference (ISI) in PAM
4.4.4 Some practical aspects concerning the “pulse” to study ISI
4.4.5 Nyquist Criterion for Zero ISI
4.4.6 Cursor, precursor ISI and postcursor ISI
4.5 Raised Cosine Shaping Pulses (Filters)
4.6 Matched Filtering and the Square-Root Raised Cosine
4.7 Eye Diagrams
4.8 Distinguishing Nyquist Criterion and Sampling Theorem
4.9 Equalization and System Identification
4.9.1 System identification using least squares (LS)
4.9.2 Zero-forcing (ZF) equalization criterion
4.9.3 Least squares FIR equalizer based on estimated channel
4.9.4 FIR equalizer: LS direct estimation with training sequence
4.9.5 Probabilistic approach to LS FIR system identification
4.10 Channel Capacity
4.10.1 Capacity of AWGN channels
4.10.2 Water filling
4.10.3 Capacity of the frequency-selective LTI Gaussian channel
4.10.4 Revisiting the capacity of flat fading continuous-time AWGN
4.11 Synchronization
4.11.1 Carrier recovery
4.11.2 Carrier recovery using FFT
4.11.3 Phase-locked loop (PLL)
4.11.4 Continuous-time PLL for tracking sinusoids
4.11.5 Discrete-time PLL (DPLL) for tracking sinusoids
4.11.6 Design of PLL and DPLL
4.11.7 Discrete-time PLL (DPLL) for tracking digitally modulated... decision directed...
4.12 Channel Model with Frequency Offset
4.13 Applications
4.14 Comments and Further Reading
4.15 Exercises