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Communication Systems Simulation - I

Harri SaarnisaariPart of Simulations and Tools for Telecommunication

Course

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Introduction

• First we study what simulation methods are available

– Use of the Monte Carlo method is investigated more thoroughly

• Then we study the structure of communication systems and discuss their simulations

– What parts can be found in communication systems?

– What is simulated in different parts?

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Simulation methods

• Monte Carlo (MC) method

– Repeated random trials

• Quasianalytical (QA) method (or semianalytical)

– Average signal (e.g., bit/symbol decisions) is obtained by passing a noiseless signal through the system• Simulation part of QA

– Average is then used to obtain the result via analytical tools• Assumed noise statistics is used

• Analytical part of QA

– May be also mixed with the MC method

• Also other less used techniques exits

• Only the MC method will be discussed hereafter

– Although QA is also useful

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Monte Carlo method

• Communication signals are random, – Random data, random channel coefficient, random noise (thermal noise, environmental noise), random delay, random frequency error, …

• Therefore, a single realization does not explain the whole story – It may even yield to misleading conclusions

• E.g., you send (in a simulator) a bit through a bad channel and receive it correctly and then claim that BER is 0 although it really is 0.4 after serious simulations

• Several realizations are needed to see the average behavior• In the MC method the same experimental is repeated several times such that random phenomena in the process are modeled as random variables and generated again and again using random number generators (RNGs)

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Monte Carlo method

• Basically, one measures how many times the trial succeeds and how many times not

– i.e., the probability of success is calculated

• One is also interested to know how reliable the obtained results are

– Confidence interval

• Simulations should be made in such a fashion that the results have a desired error margin or result can be expressed asresult = value ± desired conf. interval

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Monte Carlo methods

• How many trials are needed for reliable results?

– In order that statistical measures are reliable, a certain amount of experiments have to be made

– The larger the number of trials N is, the reliable the results are since• Average often converges to the actual value

• Confidence intervals tend to zero at rate (1/N)1/2

• i.e., as N increases – The average of trials becomes closer the actual value

– Interval at which the actual value is within certain limits of the average becomes smaller

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Monte Carlo methods, BER case

10 expected errors

100 expected errors

Number of simulated symbols

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Monte Carlo methods, BER case

• From the previous fig one can draw the following results

• If we consider 95 % conf. limit

– And have 10 expected errors the conf. limit is4×10-(v-1) – 2,8 ×10-v

– And have 100 expected error the conf. limit is9×10-(v+1) – 1,8 ×10-v

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Monte Carlo methods

• BER analysis

– 10-100 successful experiments (i.e., bit errors) have to be made in order that BER analyses are reliable• The larger value is better

• This means that if we want to reliably simulate results down to BER 10-5 we have to send at least 106 bits or (preferably) 107 bits, both very large numbers

– At very low BER simulation time may become very long

– Usually simulations are stopped somewhere BER > 10-5

• Simulations may be arranged such that you have a maximum number of iterations Nmax and a minimum number of errors Nerr– Simulation is stopped whichever limit is first reached

– This fastens simulations at low SNR/SINR since Nerr is usually achieved much faster than Nmax

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Monte Carlo methods, estimation

• Communication signals have to be synchronized before data communication is possible

– Time, frequency, phase, amplitude are possible synchronization/channel estimation targets

• The receiver has estimators for this purpose

• The performance of these estimators has to be simulated (or analyzed if possible)

• The MC method is used also herein

– The random phenomena are modelled by RNGs as in BER analysis

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Monte Carlo methods, estimation

• In estimation algorithm studies simulations may concern

– the mean and variance of the estimator and/or

– the probability that the estimator finds and/or does not find the correct value

• For the latter case previous BER rules can be used, i.e., 10-100 successful measurements

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Monte Carlo methods, estimation

• Estimator is unbiased if its average value is equal to the actual value

– Otherwise it is biased, i.e., there is a bias between estimated and actual value

• The estimator is said to be efficient if the variance attains the theoretical lower bound known as the Cramer-Rao bound

• Estimator analysis usually contain comparison of simulated results to this bound

– Often as a function of SNR

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Monte Carlo methods, estimation

• The estimated variance σ2 is often used to set the confidence limit as follows

– It is assumed that the estimator has Gaussian distribution • this is often valid, at least approximately due to Central limit theorem

– It is well known that in Gaussian case • 65% of samples are within ±σ of the mean and • 95% of samples are within ±2σ of the mean

– 95 % accuracy or 2σ accuracy are often used terms in system design

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Monte Carlo methods, estimation

• How many MC iterations are needed?

– The book explains that this is a difficult question

• The rule of thumb is that the larger the SNR the easier the estimation and the less iterations are needed for reliable results

• If scientific papers are considered 100 even 1000 iterations are often used, but values outside this interval are also common

• Accuracy usually increases at rate (1/N)1/2

• As a rule of thumb, the result curves should be smooth, not fluctuating

yes

no

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Monte Carlo methods, estimation

• One way to solve the problem of number of iterations is as follow

– Let a successful trial be such that the estimator gives a result B that is within certain interval around ±δ the true value A, i.e., A-δ < B < A+δ

– If the number of successful trials is 10-100, the iterations can be stopped (large value is better, even larger than 100)

• Some even use conditioned estimation results

– they take into account for the mean and variance calculation only the successful trials

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Communication simulations

• A communication system designer has requirements the system has to satisfy and also limitations that have to be taken in the account

• Simulations (in addition to analysis and prototyping) are used to verify are the requirements and limitations possible to satisfy with the selected elements or to find which elements satisfy the requirements and limitations

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Communication simulations

• A communication network consist of set of nodes

• The target

– of a node is to send information to some other node or nodes

– and of a network is to allow these connections

• The nodes are devices that consist of

– Hardware

– Software

• The totality therefore consists of different (sub)systems

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Communication simulations

• Thus, we have

– System level requirements

• The overall system has to satisfy the requirements

– Subsystem level requirements

• The subsystems have to satisfy their requirements

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Some possible requirements

– Bit rates the system has to support• May be different for different services

– voice, data, video,…

– BER targets• May be different for different services:

– voice, data, video,…

– Number of nodes the (sub)system has to support– Nodes should be networked possibly in different ways– Level and type of interference the system has to tolerate

• Interference from other systems at nearby frequency bands• Intentional interference in military systems

– The system possibly has to operate in different environments

– The system has to have connections to other systems– …

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Some possible requirements/limitations

– Costs

– Size of equipments

– Power consumption

– Interference to other systems

– …

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Communication simulations

• Communication systems can be considered at different levels– higher and lower levels contain different parts of the systems

• Nodes jointly form (communication) networks (higher level)• Different (kind of) networks jointly form larger networks• Nodes are connected through (communication) links (lower level)– Links consists of

• Transmitter• Propagation medium (optic, wired, wireless) • Receiver

• At different levels the simulations concern different things

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Satellite dish

Radio tower

Radio tower

Radio tower

Public switch

Satellite

Cell phone

Cell phone

Cell phone

Cell phone

Cell phone

Cell phone

Satellite dish

Base stationnetwork

Semi Ad-hoc

network

Link between nodes

Multiple networks

communicate

Satellite network

Another network

Networks are usuallylinked somehow sincethe goal in communicationsis to send informationfrom a place to another (not just inside a network)

Networks and links are justmeans to attain the goal

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Communication simulations

• Transmitters and receivers (transceivers) are indented to execute some functions such that data can be communicated

• Transceivers consist of different elementary parts

– Hardware (HW)

– Software (SW)

• Both parts do some functions and consist of several building blocks

– Each block and their entity has to satisfy given requirements

• The overall transceiver (HW+SW) has to satisfy the requirements

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Communication simulations

• Communication simulations can be divided into several parts

– Network level simulations

– Link level simulations

– Algorithm level simulations

• Performance of algorithms in a link are investigated separately

– Platform level SW simulations

– Platform level HW simulations

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Network level simulations

• Data throughput as a function of the number of nodes or some other variable

• Latency (delay) and jitter (change of delay) of messages• Usability and effects of – Routing protocols, – Access protocols, MAC (like Carrier Sensing), – Packet addressing protocols (like IPv6), – QoS (quality of service) protocols (like packet priority), ….

• Scalability of protocols – Does them work with different number of nodes?

• Mobility of nodes– How this affects the performance?

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Network level simulations

• One has to think what are relevant features the network simulator has to have

• Usually links are modeled using a high level model

– Link budget is calculated for the desired and interfering signals

• Gives SINR (signal-to-interference-plus-noise ratio)

– BER is calculated analytically based on SINR,

• i.e., transceivers are not actually simulated

– This saves efforts, time and costs

– This is QA method

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Network level simulations

• Random features in network simulations may be

– Packet length

– Packet transmission/arrival times

– Packet transmission/arrival rate

– Number of active nodes (users)

– Number of connections

– Length of connections

• Transmission medium may vary

• Static (AWGN) vs time varying (fading) channels

• Different median propagation loss models

– Different high level link models

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Link level simulations

• Obtained BER at different channels using different modulations and receiver algorithms

• Supported bit rates at different channels (BER goals in mind)

• RF and antenna effects

• Effects of uncertainties in synchronization/channel estimation to BER

• Performance of different synchronization and channel estimators (algorithms) in different environments

• Performance of different detection and demodulation algorithms, channel coding schemes, …

• We consider the link level hereafter (since the book does it too)

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Link simulations

• Random elements are

– Data symbols (bits)

– Additive (thermal) noise

– Amplitude and phase of multipath components (in fading channels)

– Number of multipath components

– Frequency error in some channels

– Delay (time-of-arrival)

– Delay and frequency spread

– Direction-of-arrival (in multiantenna channels)

– External interference usually contains random features

– …

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Othersignals

Typical elements of a link

Thermalnoise

Effects ofRF/AD

Effects of RF/DA

channel

estimation

Coding part

Digital signalformation

To RF frequency,power amplification

Radio

channel

From RF to IF/baseband

Digital signal processing for demodulation/synchronization/channel estimation

Decoding part

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RF Simulations

• RF simulations and corresponding tools are used for RF design

• These are used to design, e.g.,

– RF filters

– Power amplifiers

– Mixers (up and downconversion)

– Combinations of these

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RF Simulations

• Different RF building blocks may have existing models (e.g., from manufacturers)

• Blocks are combined to form a complete RF block

• Simulation shows does the RF part perform as it should or are changes needed

• Note:

– RF simulations give also the transfer function of the RF part

– Can be used in link level simulations to model the RF part

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Platform Simulations

• Platform is a device or set of devices on which the transceiver is implemented

• There are several topics that have to be considered– AD/DA conversion

• Sufficient word length• Effects of limiting is reception (insufficient AGC)

– Finite word length effects• Fixed point vs floating point• How algorithms perform with these

– How many bits are needed for satisfactory performance» Input word length, internal word length» E.g., how many internal bits are needed for sufficient performance for given input word length

• How to scale signal to prevent overflow?• How overflow affects?

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Platform Simulations

• How signal flows between different blocks

• Simulation of different finite word length algorithms

– Filters

– Matrix inversions

– (I)FFT

– ...

• Etc.