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Last updated:

September 25, 2023


Unlimited Duration


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Unlimited Duration

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Concepts in probability and random variables/ processes play a fundamental role in understanding various aspects of wireless communication systems.

Characterizing several components of wireless systems such as the average transmit power, bit-error rate and behavior of the fading channel coefficient requires knowledge of principles of random variables and processes. This course is designed to serve as a basic course towards introducing the students to various aspects of probability from the perspective of modern digital and wireless communications. Thus, it will focus on basic concepts in probability, random variables and random processes, while also illustrating digital/ wireless communication specific examples to better bridge the gap between theory and application (from nptel.ac.in)

Course Curriculum

    • Lecture 01 – Basics – Sample Space and Events Unlimited
    • Lecture 02 – Axioms of Probability Unlimited
    • Lecture 03 – Conditional Probability – M-ary PAM Example Unlimited
    • Lecture 04 – Independent Events – M-ary PAM Example Unlimited
    • Lecture 05 – Independent Events – Block Transmission Example Unlimited
    • Lecture 06 – Independent Events – Multiantenna Fading Example Unlimited
    • Lecture 07 – Bayes Theorem and A Posteriori Probability Unlimited
    • Lecture 08 – Maximum A Posteriori Probability (MAP) Receiver Unlimited
    • Lecture 09 – Random Variables, Probability Density Function (PDF) Unlimited
    • Lecture 10 – Application: Power of Fading Wireless Channel Unlimited
    • Lecture 11 – Mean, Variance of Random Variables Unlimited
    • Lecture 12 – Application: Average Delay and RMS Delay Spread of Wireless Channel Unlimited
    • Lecture 13 – Transformation of Random Variables and Rayleigh Fading Wireless Channel Unlimited
    • Lecture 14 – Gaussian Random Variable and Linear Transform Unlimited
    • Lecture 15 – Special Case: IID Gaussian Random Variables Unlimited
    • Lecture 16 – Application: Array Processing and Array Gain with Uniform Linear Arrays Unlimited
    • Lecture 17 – Random Processes and Wide Sense Stationary (WSS) Unlimited
    • Lecture 18 – WSS Example – Narrowband Wireless Signal with Random Phase Unlimited
    • Lecture 19 – Power Spectral Density (PSD) for WSS Random Process Unlimited
    • Lecture 20 – PSD Application in Wireless Bandwidth Required for Signal Transmission Unlimited
    • Lecture 21 – Transmission of WSS Random Process through LTI System Unlimited
    • Lecture 22 – Special Random Processes – Gaussian Process and White Noise Unlimited
    • Lecture 23 – Gaussian Process through LTI System Example Unlimited

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