Probability and Random Variables/ Processes for Wireless Communications

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

Lecture 16 - Application: Array Processing and Array Gain with Uniform Linear Arrays

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