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.

Probability and Random Variables/ Processes for Wireless Communications.
Basics - Sample Space and Events.
Axioms of Probability.
Conditional Probability - Mary-PAM Example.
Independent Events - Mary-PAM Example.
Independent Events - Block Transmission Example.
Independent Events - Multiantenna Fading Example.
Bayes Theorem and Aposteriori Probabilities.
Maximum Aposteriori Probability (MAP) Receiver.
Random Variables, Probability Density Function (PDF).
Application: Power of Fading Wireless Channel.
Mean, Variance of Random Variables.
Application: Average Delay and RMS Delay Spread of Wireless Channel.
Transformation of Random Variables and Rayleigh Fading Wireless Channel.
Gaussian Random Variable and Linear Transformation.
Special Case: IID Gaussian Random Variables.
Application: Array Processing and Array Gain with Uniform Linear Arrays.
WSS Example Narrowband Wireless Signal with Random Phase.
Random Processes and Wide Sense Stationarity (WSS).
Power Spectral Density (PSD) for WSS Random Process.
PSD Application in Wireless Bandwidth Required for Signal Transmission.
Transmission of WSS Random Process Through LTI System.
Special Random Processes Gaussian Process and White Noise AWGN Communication Channel.
Gaussian Process Through LTI System Example: WGN Through RC Low Pass Fillter Not Started.