l09 Phy Simulations

8/3/2019 l09 Phy Simulations

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Simulation hierarchySimulation hierarchy

Networks

Links

DSP Circuits RF

Event driven simulations:

ns2, Opnet

Time driven simulations:

SPW, Cossap, Simulink/Matlab

Algorithm simulations:

TI CodeComposer

Packets, messages, flows

Waveforms

Circuit simulations:

NC-{VHDL/Verilog}, Scirroco,

RF simulations:

PSpice, ADS,XFDTD

Technology


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Waveform Level SimulationsWaveform Level Simulations

Usually used when analytical evaluationUsually used when analytical evaluation

of performance is difficult (of performance is difficult (nonlinearities, ISInonlinearities, ISI

caused by bandlimiting filterscaused by bandlimiting filters))

Typically:Typically:1.1. Generate sampled values of the inputGenerate sampled values of the input

waveforms (process)waveforms (process)

2.2. Process them through system models andProcess them through system models and

generate outputgenerate output

3.3. Estimate the performance by comparing inputsEstimate the performance by comparing inputs

and outputsand outputs


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MethodologyMethodology

Ideally model is a perfect replica ofIdeally model is a perfect replica of

the real system hard to dothe real system hard to do

Instead we introduce approximationsInstead we introduce approximations

to reduce complexity or run-time:to reduce complexity or run-time:

Modeling level simplification of theModeling level simplification of the

specific functionsspecific functions

Performance evaluation level Performance evaluation level

estimation of performance measuresestimation of performance measures


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Methodology (cont.)Methodology (cont.)

Modeling:Modeling: System ModelingSystem Modeling - highest level of- highest level of

description; complexity reductiondescription; complexity reduction

Device ModelingDevice Modeling block or subsystem (e.g. block or subsystem (e.g.transfer function on every clock cycle: "input-transfer function on every clock cycle: "input-transfer-output)transfer-output)

Random Process Modeling:Random Process Modeling:

Source random process (imitated withSource random process (imitated withpseudo random number generator RNG)pseudo random number generator RNG) Time-variant random channelTime-variant random channel Equivalent random process (ERP)Equivalent random process (ERP)


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Monte Carlo simulation as the nameMonte Carlo simulation as the nameimplies relates to game of chanceimplies relates to game of chance

Input signals are assumed to be randomInput signals are assumed to be random

processesprocesses

Objective is to find statistical properties ofObjective is to find statistical properties of

)(tV Model ofCommunication System

)(tU

)(tY

)(tW

)(tY

If we do time evolution of all the waveforms -pure Monte Carlo simulation Generating sampled values of all the input processes


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=

=

N

i

iYgN

tYgE1

^

))((1

))((

Procedure: Generate sampled values of the inputs

(e.g. bit sequence {U(k)}, k=1,2,,N and noise {V(j)}, j=1,2,,mN)

Process samples through the model andgenarate Y(k) (received bits):

Estimate the performance by counting errors

In general find expected value of E{g(Y(t)}

from the simulation according to:


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For our example: whereFor our example: where

If only some input processes areIf only some input processes are

simulated explicitly partial MCsimulated explicitly partial MC(quasianalytical simulation)(quasianalytical simulation)

Random number generation is essentialRandom number generation is essentialfor MC simulationsfor MC simulations

Requires RNG generation methods fromRequires RNG generation methods froma wide variety of distributions and witha wide variety of distributions and witharbitrary autocorrelation (PSD).arbitrary autocorrelation (PSD).

=

=N

k

kYgN

Pe1

^))((1

==

)()(0)()(1))((kUkYkUkYkYg


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RNGRNG

Important properties:Important properties:

AlgebraicAlgebraicStructure (uncorrelated samples)Structure (uncorrelated samples)

PeriodPeriod

StatisticalStatisticalDistributionDistribution

Uniform RNGUniform RNG Congruent or the power residue methodCongruent or the power residue method

MckaXkX mod])1([)( +=


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RNG (cont)RNG (cont)

wherewhere M>0 large (prime) integer - modulusM>0 large (prime) integer - modulus

0


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Few good menFew good men(for 32 bit machines)(for 32 bit machines)

For longer periodsFor longer periods Wichman-Hill Algorithm combines 3 RNGs:Wichman-Hill Algorithm combines 3 RNGs:

periodperiod

)2mod(]1)1(069.69[)(

)12mod()]1(807.16[)(

32

31

+=

=

kXkX

kXkX

1mod30269

)(

30307

)(

30269

)()(

30323mod)]1(170[)(

30307mod)]1(172[)(

30269mod)]1(171[)(

++=

=

=

=

nZnYnXnU

nZnZ

nYnY

nXnX

12107x


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l09 Phy Simulations

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