Probability

White noise in Matlab — generate, analyze, and measure power

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How to simulate white noise in Matlab, check spectrum and power, and relate AWGN variance to SNR — with links to AWGN generation and BER tools.

Introduction to concepts in probability

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What is Probability? Probability is a branch of mathematics that deals with uncertainty. The term “probability” is used to quantify the degree of belief or confidence that something is true (or false). It gives us the likelihood of occurrence of a given event. It is expressed as a number that could take any value in … Read more

Derive BPSK BER – optimum receiver in AWGN channel

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BPSK Lab path:Derive BER (theory) → AWGN noise model → BER simulation (Python & Matlab)Tools: BER vs Eb/N0 calculator · Shannon capacity Key focus: Derive BPSK BER (bit error rate) for optimum receiver in AWGN channel. Explained intuitively step by step. BPSK modulation is the simplest of all the M-PSK techniques. An insight into the … Read more

Clarke’s Rayleigh fading model — sum-of-sinusoids simulation

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Fading & Diversity — 6 lessons (same on every page in this path) 1. Rayleigh BER → 2. Clarke’s model (you are here) → 3. Young’s model → 4. SIMO models → 5. Selection combining → 6. MRC Tools: BER vs Eb/N0 · 3GPP TDL · CDL / Doppler Lesson 2 of 6. You saw … Read more

Fading channel – complex baseband equivalent models

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Fading Lab path: Fading models → Young → Clarke SOS → BPSK BER Rayleigh → MRC  Keyfocus: Fading channel models for simulation. Learn how fading channels can be modeled as FIR filters for simplified modulation & detection. Rayleigh/Rician fading. Introduction A fading channel is a wireless communication channel in which the quality of the … Read more

Central Limit Theorem – a demonstration

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 This post contains interactive python code which you can execute in the browser itself. Central Limit Theorem – What is it ? The central limit theorem (CLT) is a fundamental concept in statistics and probability theory that explains how the sum of independent and identically distributed random variables behaves. The theorem states that as … Read more

Maximum Likelihood estimation

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 Keywords: maximum likelihood estimation, statistical method, probability distribution, MLE, models, practical applications, finance, economics, natural sciences. Introduction Maximum Likelihood Estimation (MLE) is a statistical method used to estimate the parameters of a probability distribution by finding the set of values that maximize the likelihood function of the observed data. In other words, MLE is … Read more

Maximum likelihood decoding — BSC Hamming metric and AWGN Euclidean metric

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Detection path: ML estimation → ML decoding → Hard vs soft decision → Hamming codes In one sentence: Maximum-likelihood decoding picks the codeword that maximizes the channel likelihood of the received word — on a BSC that reduces to nearest Hamming neighbor when the crossover probability is below one half.  Introduction Maximum likelihood decoding … Read more

Random Variables, CDF and PDF

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 Introduction to Probability: The Foundation of Random Signals In the world of communication engineering, “certainty” is a luxury we don’t have. From the thermal noise in your smartphone’s receiver to the fading of a satellite signal, every process we analyze is governed by uncertainty. Probability is the mathematical language that allows us to model … Read more