vanced Signal Processing, Power & Control & Communication

vanced Signal Processing, Power & Control & Communication 2nd Session MAT 14 Department of Electronics & Electrical Engineering I.I.T. Guwahati August 30 2014

Me You Communication • & • MATLAB by : Samdarshi Department of Electronics & Electrical Engineering I.I.T. Guwahati August 30 2014

Plan of Talk • Objective of the Lecture • Randomness in communication • Lets modulate something ! • Limiting factors • BER/Outage : as performance evaluation tool • Simulating a Communication Link….Examples • Interference : a bottle-neck • Extras : f(time) EEE Department, I.I.T. Guwahati

? Why Simulation EEE Department, I.I.T. Guwahati

? Why Simulation In theory, there is no difference between theory and practice. But, in practice, there is. - Jan L.A. van de Snepscheut EEE Department, I.I.T. Guwahati

Communication Toolbox • For the physical layer of communication systems !! • For designing of communications links, including source coding, channel coding, interleaving, modulation, channel models, and equalization • Comparison of your system with a wide variety of proven analytical results EEE Department, I.I.T. Guwahati

Expected Background • The Basic Knowledge of the Communication system Primary components of a communication system Matlab Basics !! Channel , noise, fading Performance evaluation tools : BER, Outage Basic Probability theory EEE Department, I.I.T. Guwahati

Introduction :Wireless networks Wireless Networks With Infrastructure Topology based Without Infrastructure Any practical Example ! Cellular Networks Ad-hoc Networks Wireless Sensor Networks EEE Department, I.I.T. Guwahati Example

Components of Communication system • Analog Communications • Digital Communications EEE Department, I.I.T. Guwahati

Analog Communication System This may be any analog signal such as Sine wave, Cosine Wave, Triangle Wave……………….. EEE Department, I.I.T. Guwahati

Analog Modulation/Demodulation Functions ammodAmplitude modulation amdemodAmplitude demodulation fmmodFrequency modulation fmdemodFrequency demodulation pmmodPhase modulation pmdemodPhase demodulation ssbmodSingle sideband amplitude Mod ssbdemodSingle sideband amplitude DeMod EEE Department, I.I.T. Guwahati

Digital World EEE Department, I.I.T. Guwahati

Digital Communication EEE Department, I.I.T. Guwahati

Source randintGenerate matrix of Uniformly distributed Random integers randsrcGenerate random matrix using prescribed alphabet randerrGenerate bit error patterns EEE Department, I.I.T. Guwahati

Randomness • deterministic • Random ! Prediction in advance is not possible Specified function of time EEE Department, I.I.T. Guwahati

Randomness • deterministic • Random ! Prediction in advance is not possible Specified function of time • Randomness in DoA EEE Department, I.I.T. Guwahati

Randomness • Random variable ! • Introduction to Statistics and Econometrics • By Takeshi Amemiya EEE Department, I.I.T. Guwahati

Randomness • Random variable ! Function • Statistics: An Introduction • By Roger Kirk EEE Department, I.I.T. Guwahati

Randomness • Random process • Random variable ! Obtained by observing a random process @ fixed instant of time Consists of an ensemble (family) of sample functions, each of which varies randomly with time. EEE Department, I.I.T. Guwahati

Random variables : type • Random variables : various distributions • Uniform distribution • Gaussian distribution • Exponential distribution • Rayleigh distribution • …………………………………. EEE Department, I.I.T. Guwahati

RVs with Matlab • Uniformly distributed RVs • rand function • How to verify ? • Draw probability density function (pdf). How ! • Ksdensity function : Histogram EEE Department, I.I.T. Guwahati

RVs with Matlab • Exponentially distributed RVs : exprnd function • Gaussian distributed RVs : randn function • Rayleigh distributed RVs : raylrndfunction EEE Department, I.I.T. Guwahati

A Different Experiment ! • Adding ‘n’ same/different RVs ! • What will be the resultant distribution ? • Central limit theorem EEE Department, I.I.T. Guwahati

Distributions • Unknown distribution ! (not in standard form) • Principles of Communication Systems Simulation with wireless applications • - By W.H. Tranter, K. Sam Shanmugan, T.S. Rappaport • & K.L. Kosbar EEE Department, I.I.T. Guwahati

For Non-standard Distributions • Let say, distribution in hand : • 1st step is to find the CDF : EEE Department, I.I.T. Guwahati

For Non-standard Distributions • Equating the distribution to the uniform RV U • So, Now we have : EEE Department, I.I.T. Guwahati

For Non-standard Distributions • Further, solution for X : • But, we can also write : Why ? EEE Department, I.I.T. Guwahati

This transformation is the initial step in the Box-Muller algorithm, which is one of the basic algorithms for Gaussian number generation. For Non-standard Distributions • Now, all is set to go for the Matlab code EEE Department, I.I.T. Guwahati

This function uses, by default, the Mersenne Twister algorithm • by Nishimura and Matsumoto. Source randintGenerate matrix of Uniformly distributed Random integers randsrcGenerate random matrix using prescribed alphabet randerrGenerate bit error patterns EEE Department, I.I.T. Guwahati

randintRandom Integer Syntax out = randint%generates a random scalar that is either 0 or 1, with equal probability out = randint(m) %generates an m-by-m binary matrix, each of whose entries independently takes the value 0 with probability ½ out = randint(m,n) %generates an m-by-n binary matrix, each of whose entries takes the value 0 with probability ½ EEE Department, I.I.T. Guwahati

Example Statement :To generate a 10-by-10 matrix whose elements are uniformly distributed in the range from 0 to 7 out = randint(10,10,[0,7]) or out = randint(10,10,8); Results

Example Statement :How to generate 0s and1s…. Randi out = randint(1,7,[0,1]) Results EEE Department, I.I.T. Guwahati

Digital Modulation/Demodulation pskmod Phase shift keying modulation pskdemod Phase shift keying demodulation fskmod Frequency shift keying modulation fskdemod Frequency shift keying demodulation mskmod Minimum shift keying modulation mskdemod Minimum shift keying demodulation qammodQuadrature amplitude modulation qamdemodQuadrature amplitude demodulation EEE Department, I.I.T. Guwahati

Lets modulate something ! EEE Department, I.I.T. Guwahati

Example • Modulation !! • Binary phase shift keying : BPSK • Matlab code EEE Department, I.I.T. Guwahati

Channels awgnAdd white Gaussian noise channel rayleighchanConstruct Rayleigh fading channel object ricianchanConstruct Rician fading channel object bscModel binary symmetric channel And many More………………………. awgnAdd white Gaussian noise channel EEE Department, I.I.T. Guwahati

vanced Signal Processing, Power & Control & Communication