### Channel Coding

- Block Interleaver Design for RS codes
- Viterbi Decoding of Convolutional codes
- Convolutional Coding
- Maximum Likelihood estimation
- Maximum Likelihood Decoding
- Hard and Soft decision decoding
- Distance - Hamming Vs Euclidean
- More on Shannon's limit
- Relation between Eb/N0 and SNR
- Matlab code for RS codes
- Reed Solomon Codes - Introduction
- Construction of Hamming codes using Matrix
- Hamming Codes - How it works
- Types of Channel Codes
- Performance of Channel Codes
- Channel Capacity & Shannon's theorem - demystified
- Channel Coding

### Pulse Shaping

- Symbol Timing Recovery for QPSK (digital modulations)
- Derivation of expression for a Gaussian Filter with 3 dB bandwidth
- Correlative coding - Duobinary Signaling
- Introduction to controlled ISI (Inter Symbol Interference)
- Square Root Raised Cosine Filter (Matched/split filter implementation)
- Raised Cosine Filter
- Nyquist and Shannon Theorem

### Probability

- How to use Histogram function in Matlab to plot the estimated PDF curve
- Simulation and Analysis of White Noise in Matlab
- Bayes’ Theorem
- Introduction to concepts in probability
- Non-central Chi-squared Distribution
- Chi-Squared Distribution
- Uniform Random Variables and Uniform Distribution
- Intuitive derivation of Performance of an optimum BPSK receiver in AWGN channel
- Q function and Error functions
- Simulation of Rayleigh Fading ( Clarke's Model - sum of sinusoids method)
- Fading channels - Rayleigh Fading
- Central Limit Theorem
- Maximum Likelihood estimation
- Maximum Likelihood Decoding
- Procedure for plotting any PDF in Matlab
- Random Variables, CDF and PDF

### Matlab Codes

- Modeling a Frequency Selective Multipath Fading channel using TDL filters
- How to use Histogram function in Matlab to plot the estimated PDF curve
- OFDM and Cyclic Prefix - a handson demonstration using Matlab
- How to interpret FFT results - obtaining magnitude and phase information
- How to generate AWGN noise in Matlab/Octave (without using in-built awgn function)
- Chirp Signal - Frequency Sweeping - FFT and power spectral density
- Generating Basic Signals - Gaussian Pulse and Power Spectral Density using FFT
- Generating Basic signals – Rectangular Pulse and Power Spectral Density using FFT
- Generating Basic signals - Square Wave and Power Spectral Density using FFT
- How to plot FFT using Matlab - FFT of basic signals : Sine and Cosine waves
- Generating Multiple Sequences of correlated random variables
- Generating correlated random numbers
- Sampling a Signal in Matlab
- AutoCorrelation (Correlogram) and persistence - Time series analysis
- Yule Walker Estimation and simulation in Matlab
- Simulation and Analysis of White Noise in Matlab
- Symbol Timing Recovery for QPSK (digital modulations)
- Theoretical BER using Matlab - BERTOOL
- Tips & Tricks - Indexing in Matlab
- Natural Binary Codes and Gray Codes
- Simulation of M-PSK modulation techniques in AWGN channel
- Eb/N0 Vs BER for BPSK over Rician Fading Channel
- Eb/N0 Vs BER for BPSK over Rayleigh Channel and AWGN Channel
- Simulation of Rayleigh Fading ( Clarke's Model - sum of sinusoids method)
- Correlative Coding - Modified Duobinary Signaling
- Correlative coding - Duobinary Signaling
- Introduction to controlled ISI (Inter Symbol Interference)
- Square Root Raised Cosine Filter (Matched/split filter implementation)
- Oversampling, ADC - DAC Conversion,pulse shaping and Matched Filter
- BER Vs Eb/N0 for 8-PSK modulation over AWGN
- Walsh Hadamard Code - Matlab Simulation
- Window Functions - An Analysis
- FFT and Spectral Leakage
- Raised Cosine Filter
- An utility for plotting eyediagram in matlab (without using Communication toolbox)
- Moving Average Filter ( MA filter )
- Random Interleaver
- BER Vs Eb/N0 for QPSK modulation over AWGN
- QPSK modulation and Demodulation
- Generation of Gold Codes and their cross-correlation
- Preferred Pairs m-sequences generation for Gold Codes
- Maximum Length Sequences (m-sequences)
- Estimation of Impulse Response of a LTI System
- Performance comparison of Digital Modulation techniques
- BER Vs Eb/N0 for BPSK modulation over AWGN
- BPSK modulation and Demodulation
- Gibbs Phenomena - A demonstration
- Colored Noise Generation in Matlab
- Rayleigh Fading Simulation - Young's model
- Fading channels - Rayleigh Fading
- Generating a signal waveform with required SNR in Matlab
- Central Limit Theorem
- Calculating power and energy content of a signal in MATLAB
- Matlab Simulation - PSD of Line Codes
- Procedure for plotting any PDF in Matlab
- Matlab code for RS codes

### Random Process

- Modeling a Frequency Selective Multipath Fading channel using TDL filters
- How to use Histogram function in Matlab to plot the estimated PDF curve
- Significance of RMS (Root Mean Square) value
- Constructing the Auto Correlation Matrix in Matlab
- Generating Multiple Sequences of correlated random variables
- Generating correlated random numbers
- Simulation and Analysis of White Noise in Matlab
- Characteristics of Noise Received by Software Defined Radio - Part 2
- Characteristics of Noise Received by Software Defined Radio - Part 1
- Non-central Chi-squared Distribution
- Chi-Squared Distribution
- Intuitive derivation of Performance of an optimum BPSK receiver in AWGN channel
- Q function and Error functions
- Procedure for plotting any PDF in Matlab
- Random Variables, CDF and PDF

### Signal Processing

- Choosing a filter - FIR or IIR - Understanding the design perspective
- Modeling a Frequency Selective Multipath Fading channel using TDL filters
- OFDM and Cyclic Prefix - a handson demonstration using Matlab
- How to interpret FFT results - obtaining magnitude and phase information
- How to Interpret FFT results - complex DFT, frequency bins and FFTShift
- Significance of RMS (Root Mean Square) value
- Physical Telepresence: Say goodbye to Skype, Facetime: This is the future of communication.
- How to generate AWGN noise in Matlab/Octave (without using in-built awgn function)
- Hardware Implementation of Gold code generator
- Constructing the Auto Correlation Matrix in Matlab
- Chirp Signal - Frequency Sweeping - FFT and power spectral density
- Generating Basic Signals - Gaussian Pulse and Power Spectral Density using FFT
- Generating Basic signals – Rectangular Pulse and Power Spectral Density using FFT
- Generating Basic signals - Square Wave and Power Spectral Density using FFT
- How to plot FFT using Matlab - FFT of basic signals : Sine and Cosine waves
- Sampling a Signal in Matlab
- Survey of Methods to Compute Linear Convolution
- Polynomials, Convolution and Toeplitz matrices - Connecting the dots
- Computation of Power of a Signal in Matlab - Simulation and Verification
- Power and Energy of a signal
- Breaking the Bandwidth Barrier - Li-Fi turns LED bulbs into High Speed Internet Hotspots
- Symbol Timing Recovery for QPSK (digital modulations)
- A tutorial on Fourier Analysis - Fourier Series
- Sampling Theorem - Bandpass or Intermediate or Under Sampling
- Sampling Theorem - Baseband Sampling
- Correlative Coding - Modified Duobinary Signaling
- Introduction to controlled ISI (Inter Symbol Interference)
- Square Root Raised Cosine Filter (Matched/split filter implementation)
- Oversampling, ADC - DAC Conversion,pulse shaping and Matched Filter
- Window Functions - An Analysis
- FFT and Spectral Leakage
- Raised Cosine Filter
- An utility for plotting eyediagram in matlab (without using Communication toolbox)
- Moving Average Filter ( MA filter )
- BER Vs Eb/N0 for QPSK modulation over AWGN
- Estimation of Impulse Response of a LTI System
- BER Vs Eb/N0 for BPSK modulation over AWGN
- BPSK modulation and Demodulation
- Gibbs Phenomena - A demonstration
- Colored Noise Generation in Matlab
- Generating a signal waveform with required SNR in Matlab
- Calculating power and energy content of a signal in MATLAB

### Channel Modelling

- Modeling a Frequency Selective Multipath Fading channel using TDL filters
- How to use Histogram function in Matlab to plot the estimated PDF curve
- Significance of RMS (Root Mean Square) value
- How to generate AWGN noise in Matlab/Octave (without using in-built awgn function)
- Power Delay Profile
- Statistical Characteristics of Multipath Channels - Scattering Function
- Extended BER Tool
- Simulation and Analysis of White Noise in Matlab
- Symbol Timing Recovery for QPSK (digital modulations)
- Log Distance Path Loss or Log Normal Shadowing Model
- Friis Free Space Propagation Model
- Channel modeling - an Introduction
- Eb/N0 Vs BER for BPSK over Rician Fading Channel
- Eb/N0 Vs BER for BPSK over Rayleigh Channel and AWGN Channel
- Simulation of Rayleigh Fading ( Clarke's Model - sum of sinusoids method)
- Correlative Coding - Modified Duobinary Signaling
- Correlative coding - Duobinary Signaling
- Introduction to controlled ISI (Inter Symbol Interference)
- Square Root Raised Cosine Filter (Matched/split filter implementation)
- Oversampling, ADC - DAC Conversion,pulse shaping and Matched Filter
- An utility for plotting eyediagram in matlab (without using Communication toolbox)
- Estimation of Impulse Response of a LTI System
- Colored Noise Generation in Matlab
- Rayleigh Fading Simulation - Young's model
- Fading channels - Rayleigh Fading

### Digital Modulations

- Constructing a rectangular constellation for M-QAM using Karnaugh Map walks
- Extended BER Tool
- Simulation of DPSK performance curves in Matlab
- Symbol Timing Recovery for QPSK (digital modulations)
- Simulation of Symbol Error Rate Vs SNR performance curve for 64-QAM in AWGN
- Simulation of Symbol Error Rate Vs SNR performance curve for 16-QAM in AWGN
- Constructing a rectangular constellation for 16-QAM
- Simulation of M-PSK modulation techniques in AWGN channel
- Intuitive derivation of Performance of an optimum BPSK receiver in AWGN channel
- Eb/N0 Vs BER for BPSK over Rician Fading Channel
- Derivation of expression for a Gaussian Filter with 3 dB bandwidth
- Eb/N0 Vs BER for BPSK over Rayleigh Channel and AWGN Channel
- BER Vs Eb/N0 for 8-PSK modulation over AWGN
- BER Vs Eb/N0 for QPSK modulation over AWGN
- QPSK modulation and Demodulation
- Performance comparison of Digital Modulation techniques
- BER Vs Eb/N0 for BPSK modulation over AWGN
- BPSK modulation and Demodulation

### Estimation Theory

- Best Linear Unbiased Estimator (BLUE)
- Linear Models - Least Squares Estimator (LSE)
- AutoCorrelation (Correlogram) and persistence - Time series analysis
- Yule Walker Estimation and simulation in Matlab
- Comparing AR and ARMA model - minimization of squared error
- LTI system models for random signals - AR, MA and ARMA models
- Cramer Rao Lower Bound (CRLB) for Vector Parameter Estimation
- Introducing The Kalman Filter
- Cholesky Factorization and Matlab code
- Check Positive Definite Matrix in Matlab
- Solving a Triangular Matrix using Forward & Backward Substitution
- Tests for Positive Definiteness of a Matrix
- Why Cholesky Decomposition ? A sample case:
- Essential Preliminary Matrix Algebra for Signal Processing
- How to estimate unknown parameters using Ordinary Least Squares (OLS)
- The Mean Square Error - Why do we use it for estimation problems
- Normalized CRLB - an alternate form of CRLB and its relation to estimator sensitivity
- Cramer Rao Lower Bound for Phase Estimation
- Efficient Estimators and CRLB
- Applying Cramer Rao Lower Bound (CRLB) to find a Minimum Variance Unbiased Estimator (MVUE)
- Cramer Rao Lower Bound for Scalar Parameter Estimation
- Introduction to Cramer Rao Lower Bound (CRLB)
- Score, Fisher Information and Estimator Sensitivity
- Theoretical derivation of MLE for Gaussian Distribution:
- Theoretical derivation of MLE for Exponential Distribution:
- Theoretical derivation of Maximum Likelihood Estimator for Poisson PDF:
- Likelihood Function and Maximum Likelihood Estimation (MLE)
- Bias of an Estimator
- Minimum Variance Unbiased Estimators (MVUE)
- An Introduction to Estimation Theory

### OFDM

- OFDM and Cyclic Prefix - a handson demonstration using Matlab
- Breaking the Bandwidth Barrier - Li-Fi turns LED bulbs into High Speed Internet Hotspots
- Simulation of OFDM system in Matlab - BER Vs Eb/N0 for OFDM in AWGN channel
- Introduction to OFDM - orthogonal Frequency division multiplexing - part 4 - Cyclic Prefix
- Introduction to OFDM - orthogonal Frequency division multiplexing - part 3
- Introduction to OFDM - orthogonal Frequency division multiplexing - part 2
- Introduction to OFDM - orthogonal Frequency division multiplexing

### Tutorials

- How to interpret FFT results - obtaining magnitude and phase information
- How to Interpret FFT results - complex DFT, frequency bins and FFTShift
- Lauched : New Q&A forum for discussions
- How to generate AWGN noise in Matlab/Octave (without using in-built awgn function)
- Introducing The Kalman Filter
- Computation of Power of a Signal in Matlab - Simulation and Verification
- Power and Energy of a signal
- FFT and Spectral Leakage
- CDMA - IS95 - a tutorial
- GSM and CDMA IS-95
- WiMAX :Taking Wireless To The Max!
- OFDM Basics

### Tips & Tricks

- Choosing a filter - FIR or IIR - Understanding the design perspective
- How to use Histogram function in Matlab to plot the estimated PDF curve
- OFDM and Cyclic Prefix - a handson demonstration using Matlab
- How to interpret FFT results - obtaining magnitude and phase information
- How to Interpret FFT results - complex DFT, frequency bins and FFTShift
- Significance of RMS (Root Mean Square) value
- How to generate AWGN noise in Matlab/Octave (without using in-built awgn function)
- Constructing the Auto Correlation Matrix in Matlab
- Constructing a rectangular constellation for M-QAM using Karnaugh Map walks
- Chirp Signal - Frequency Sweeping - FFT and power spectral density
- Generating Basic Signals - Gaussian Pulse and Power Spectral Density using FFT
- Generating Basic signals – Rectangular Pulse and Power Spectral Density using FFT
- Generating Basic signals - Square Wave and Power Spectral Density using FFT
- How to plot FFT using Matlab - FFT of basic signals : Sine and Cosine waves
- Generating Multiple Sequences of correlated random variables
- Generating correlated random numbers
- Survey of Methods to Compute Linear Convolution
- Polynomials, Convolution and Toeplitz matrices - Connecting the dots
- Computation of Power of a Signal in Matlab - Simulation and Verification
- Power and Energy of a signal
- Simulation and Analysis of White Noise in Matlab
- Theoretical BER using Matlab - BERTOOL
- Tips & Tricks - Indexing in Matlab
- FFT and Spectral Leakage

### Latest Articles

- Choosing a filter - FIR or IIR - Understanding the design perspective
- [Quiz] Signal Processing for Communication systems - part 1
- Logical Effort
- [Quiz] Combinational Circuits
- Quiz on Logic gates
- How to interpret FFT results - obtaining magnitude and phase information
- How to Interpret FFT results - complex DFT, frequency bins and FFTShift
- Lauched : New Q&A forum for discussions
- Significance of RMS (Root Mean Square) value
- Invitation to Submit your work for publication at gaussianwaves.com
- Physical Telepresence: Say goodbye to Skype, Facetime: This is the future of communication.
- How to generate AWGN noise in Matlab/Octave (without using in-built awgn function)
- Hardware Implementation of Gold code generator
- Constructing the Auto Correlation Matrix in Matlab
- Constructing a rectangular constellation for M-QAM using Karnaugh Map walks
- Capacity of a MIMO system over Fading Channels
- Ergodic Capacity of a SISO system over a Rayleigh Fading channel - Simulation in Matlab
- Capacity of a SISO system over a fading channel
- Characterizing a MIMO channel - Channel State Information (CSI) and Condition number
- MIMO - Diversity and Spatial Multiplexing
- Introduction to Multiple Antenna Systems
- Chirp Signal - Frequency Sweeping - FFT and power spectral density
- Generating Basic Signals - Gaussian Pulse and Power Spectral Density using FFT
- Generating Basic signals – Rectangular Pulse and Power Spectral Density using FFT
- Generating Basic signals - Square Wave and Power Spectral Density using FFT
- How to plot FFT using Matlab - FFT of basic signals : Sine and Cosine waves
- Generating Multiple Sequences of correlated random variables
- Generating correlated random numbers
- Sampling a Signal in Matlab
- Power Delay Profile
- Statistical Characteristics of Multipath Channels - Scattering Function
- Best Linear Unbiased Estimator (BLUE)
- Linear Models - Least Squares Estimator (LSE)
- AutoCorrelation (Correlogram) and persistence - Time series analysis
- Yule Walker Estimation and simulation in Matlab
- Comparing AR and ARMA model - minimization of squared error
- LTI system models for random signals - AR, MA and ARMA models
- Cramer Rao Lower Bound (CRLB) for Vector Parameter Estimation
- Introducing The Kalman Filter
- Survey of Methods to Compute Linear Convolution
- Polynomials, Convolution and Toeplitz matrices - Connecting the dots
- Extended BER Tool
- Computation of Power of a Signal in Matlab - Simulation and Verification
- Power and Energy of a signal
- Simulation of DPSK performance curves in Matlab
- Simulation and Analysis of White Noise in Matlab
- Breaking the Bandwidth Barrier - Li-Fi turns LED bulbs into High Speed Internet Hotspots
- Symbol Timing Recovery for QPSK (digital modulations)
- Bayes’ Theorem
- Introduction to concepts in probability
- Theoretical BER using Matlab - BERTOOL
- Log Distance Path Loss or Log Normal Shadowing Model
- Friis Free Space Propagation Model
- Announcement of Release of 2nd Edition of eBook- Simulation of Digital Communication Systems Using Matlab
- Channel modeling - an Introduction
- Tips & Tricks - Indexing in Matlab
- Cholesky Factorization and Matlab code
- Check Positive Definite Matrix in Matlab
- Solving a Triangular Matrix using Forward & Backward Substitution
- A tutorial on Fourier Analysis - Fourier Series
- Top books on basics of Communication Systems
- Tests for Positive Definiteness of a Matrix
- Why Cholesky Decomposition ? A sample case:
- Essential Preliminary Matrix Algebra for Signal Processing
- How to estimate unknown parameters using Ordinary Least Squares (OLS)
- The Mean Square Error - Why do we use it for estimation problems
- Characteristics of Noise Received by Software Defined Radio - Part 2
- Characteristics of Noise Received by Software Defined Radio - Part 1
- Normalized CRLB - an alternate form of CRLB and its relation to estimator sensitivity
- Cramer Rao Lower Bound for Phase Estimation
- Efficient Estimators and CRLB
- Applying Cramer Rao Lower Bound (CRLB) to find a Minimum Variance Unbiased Estimator (MVUE)
- Cramer Rao Lower Bound for Scalar Parameter Estimation
- Introduction to Cramer Rao Lower Bound (CRLB)
- Score, Fisher Information and Estimator Sensitivity
- Theoretical derivation of MLE for Gaussian Distribution:
- Theoretical derivation of MLE for Exponential Distribution:
- Theoretical derivation of Maximum Likelihood Estimator for Poisson PDF:
- Likelihood Function and Maximum Likelihood Estimation (MLE)
- Bias of an Estimator
- Simulation of Symbol Error Rate Vs SNR performance curve for 64-QAM in AWGN
- Simulation of Symbol Error Rate Vs SNR performance curve for 16-QAM in AWGN
- Constructing a rectangular constellation for 16-QAM
- Natural Binary Codes and Gray Codes
- Non-central Chi-squared Distribution
- Chi-Squared Distribution
- Uniform Random Variables and Uniform Distribution
- Minimum Variance Unbiased Estimators (MVUE)
- Simulation of M-PSK modulation techniques in AWGN channel
- Intuitive derivation of Performance of an optimum BPSK receiver in AWGN channel
- Q function and Error functions
- Eb/N0 Vs BER for BPSK over Rician Fading Channel
- An Introduction to Estimation Theory
- Derivation of expression for a Gaussian Filter with 3 dB bandwidth
- Sampling Theorem - Bandpass or Intermediate or Under Sampling
- Sampling Theorem - Baseband Sampling
- Simulation of OFDM system in Matlab - BER Vs Eb/N0 for OFDM in AWGN channel
- Introduction to OFDM - orthogonal Frequency division multiplexing - part 4 - Cyclic Prefix
- Introduction to OFDM - orthogonal Frequency division multiplexing - part 3
- Introduction to OFDM - orthogonal Frequency division multiplexing - part 2
- Introduction to OFDM - orthogonal Frequency division multiplexing
- Eb/N0 Vs BER for BPSK over Rayleigh Channel and AWGN Channel
- Simulation of Rayleigh Fading ( Clarke's Model - sum of sinusoids method)
- Correlative Coding - Modified Duobinary Signaling
- Correlative coding - Duobinary Signaling
- Introduction to controlled ISI (Inter Symbol Interference)
- Square Root Raised Cosine Filter (Matched/split filter implementation)
- Oversampling, ADC - DAC Conversion,pulse shaping and Matched Filter
- BER Vs Eb/N0 for 8-PSK modulation over AWGN
- Walsh Hadamard Code - Matlab Simulation
- Codes used in CDMA
- Window Functions - An Analysis
- FFT and Spectral Leakage
- Raised Cosine Filter
- An utility for plotting eyediagram in matlab (without using Communication toolbox)
- Moving Average Filter ( MA filter )
- Random Interleaver
- Block Interleaver Design for RS codes
- Interleavers and deinterleavers
- BER Vs Eb/N0 for QPSK modulation over AWGN
- QPSK modulation and Demodulation
- Generation of Gold Codes and their cross-correlation
- Preferred Pairs m-sequences generation for Gold Codes
- Maximum Length Sequences (m-sequences)
- Spread Spectrum Communications - Intro
- Viterbi Decoding of Convolutional codes
- Convolutional Coding
- Estimation of Impulse Response of a LTI System
- Performance comparison of Digital Modulation techniques
- BER Vs Eb/N0 for BPSK modulation over AWGN
- BPSK modulation and Demodulation
- Gibbs Phenomena - A demonstration
- Colored Noise Generation in Matlab
- Rayleigh Fading Simulation - Young's model
- Fading channels - Rayleigh Fading
- Generating a signal waveform with required SNR in Matlab
- Central Limit Theorem
- Calculating power and energy content of a signal in MATLAB
- Matlab Simulation - PSD of Line Codes
- Maximum Likelihood estimation
- Maximum Likelihood Decoding
- Hard and Soft decision decoding
- Distance - Hamming Vs Euclidean
- More on Shannon's limit
- Relation between Eb/N0 and SNR
- Procedure for plotting any PDF in Matlab
- Matlab code for RS codes
- Reed Solomon Codes - Introduction
- Construction of Hamming codes using Matrix
- Hamming Codes - How it works
- Types of Channel Codes
- Performance of Channel Codes
- Nyquist and Shannon Theorem
- Channel Capacity & Shannon's theorem - demystified
- Channel Coding
- Source Coding
- Random Variables, CDF and PDF
- Introduction to Digital Communication
- CDMA - IS95 - a tutorial
- GSM and CDMA IS-95
- WiMAX :Taking Wireless To The Max!
- OFDM Basics

### MIMO systems

- Capacity of a MIMO system over Fading Channels
- Ergodic Capacity of a SISO system over a Rayleigh Fading channel - Simulation in Matlab
- Capacity of a SISO system over a fading channel
- Characterizing a MIMO channel - Channel State Information (CSI) and Condition number
- MIMO - Diversity and Spatial Multiplexing
- Introduction to Multiple Antenna Systems