Role of Probability Distributions in Signal Processing and Wireless Communication Systems

Role of Probability Distributions in Signal Processing and Wireless Communication Systems

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  SRI RAMAKRISHNA ENGINEERINGCOLLEGE [Educational Service: SNR Sons Charitable Trust] [Autonomous Institution, Reaccredited by NAAC with ‘A+’ Grade] [Approved by AICTE and Permanently Affiliated to Anna University, Chennai] [ISO 9001:2015 Certified and all eligible programmes Accredited by NBA] Vattamalaipalayam, N.G.G.O. Colony Post, Coimbatore – 641 022. DEPARTMENT OF SCIENCE AND HUMANITIES (MATHEMATICS) Dr.R.Kasthuri Associate Professor Department of Mathematics Sri Ramakrishna Engineering College Role of Probability in Signal Processing & Wireless Communication
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  2 •The Core Problem:Real-world signals and transmission channels are inherently corrupted by random, unpredictable variations. •Probability Models: We use probability distributions to capture this randomness, turning unpredictable physical phenomena into quantifiable mathematical models. • Key Definitions: PDF (Probability Density Function): Defines the likelihood of a continuous random variable (e.g., noise voltage, signal phase). PMF (Probability Mass Function): Defines the likelihood of a discrete random variable (e.g., digital bits, number of users). CDF (Cumulative Distribution Function): The probability that a random variable takes a value less than or equal to a specific value. Overview & Core Concepts
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  3 Geometric Distribution- DiscreteTime Failure, Retransmission and Search Dynamics. • Models the number of discrete, independent Bernoulli trials (0 or 1) required to achieve the first success. • Retransmission Mechanics: Forms the exact foundation for ARQ (Automatic Repeat reQuest) protocols by predicting how many packet transmission attempts it takes to bypass channel noise. • Directly calculates the exact battery power depletion of remote IoT sensors by mapping the number of random-access channel attempts needed to establish a connection.
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  4 Gaussian (Normal) Distribution- ModelingThermal Noise & System Interference
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  5 Uniform distribution-Role inSignal Processing and Wireless Communication • Uniform distributions are useful for modeling random signals and errors where all values in a particular range are equally likely.
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  6 Exponential distribution-Role inSignal Processing and Wireless Communication
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