Lesson Communication systems simulation - I

Lesson present content: 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.

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Communication Systems

Simulation - I

Harri Saarnisaari Part 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 carrier 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

– 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 as

result= 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

Monte Carlo methods, BER case

10 expected

errors

100 expected errors

Number of simulated symbols

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 is

4 × 10-(v-1)– 2,8 × 10-v

– And have 100 expected error the conf limit is

9 × 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 10-5we have to send at least 106bits or (preferably) 107bits,

both very large numbers

– At very low BER simulation time may become very long

– Desired BER level depends on application

• For uncoded BER > 10 -5 is usually sufficient

• For coded BER ≤ 10 -6 is usually required

• For voice 10 -2 -10 -3 is often sufficient whereas data requires 10 -6

• Simulations may be arranged such that you have a maximum

number of iterations Nmaxand a minimum number of errors Nerr

– Simulation is stopped whichever limit is first reached

– This fastens simulations at low SNR/SINR since Nerris usually

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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• 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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• 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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• The estimated variance σ2is 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 the

central limit theorem

– It is well known that in Gaussian case

• 65% of samples are within ±σof the mean and

• 95% of samples are within ±2σof the mean

– 95 % accuracy or 2 σ (2sigma) accuracy are

often used terms in system design

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• 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

• 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 ±δthe 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

– Depending on application this may be a valid way to do

it

• Use of limits is often sensible since – In order that data system works at all, the synchronization errors should be inside certain margins – Synchronizers often have a coarse phase (acquisition) and a fine tuning phase (tracking) and the latter usually assumes that errors are within its pull in range

• NOTE – Sometimes also maximum errors, maximum and minimum BER, etc are recorded and these are reported together with means,

– Or, 95% (or X %) results are calculated in simulations instead assumed to be approximated from theory (look the figure)

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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

– These may be given in a requirements

definition document by the “customer”

• 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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• 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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• 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,…

• Also frame or packet error rate may be of interest – 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 and weight of equipments

– Power consumption

• E.g., effect to operation time without battery

recharge

– Interference to other systems

• E.g., adjacent band interference

– …

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• 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

Networks are usually

linked somehow since

the goal in communications

is to send information

from a place to another (not

just inside a network)

Networks and links are just

means to attain the goal

• 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 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

• Network level simulations are used to see – How information flows inside a network and/or between networks

– How applications and devices are able to send and receive information

– How networking functions (algorithms) affect to this capability

– Which networking algorithms satisfy requirements – Where, in which situations, certain networking algorithm

is useful

• Networking – Routing (NET) – Medium access control (MAC)

• often MAC and NET investigated separately – Link control

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• Possible variables

– Number of nodes

– Density of nodes in certain area

– Propagation loss and range between nodes

– Mobility of nodes

– Interference,

• e.g., co-channel interference effects

– Information packet size and birth rate

• E.g., follow certain statistical distributions (that are

obtained as approximation based on real measurements)

• It is obvious that voice and data (e.g video) packet sizes

are different

– Possible communications data rates for a link

(models modulation level, channel coding, etc)

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• What is simulated – Data throughput as a function of the number of nodes or some other variable

• Maximum (capacity of the network), average – Latency (end-to-end delay) and jitter (change of delay)

of messages

• Important e.g for voice and other (near) real time services – Usability and effects of

• Routing protocols,

– Proactive, reactive

• Access protocols, MAC

– Carrier Sensing (CSMA), TDMA, FDMA, CDMA, ALOHA

• Packet addressing protocols (like IPv6),

• QoS (quality of service) protocols (like packet priority), ….

– voice (low latency), real time video vs non-real time, etc

– How much capacity networking commands require?

• What is networking overhead?

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• What is simulated

– Scalability of protocols

• Does them work with different number of nodes? E.g., with 10

nodes and also with 200 nodes

– Mobility of nodes

• How this affects the performance?

– How interference or for some other reason lost

connections (links) affect to the system

• Robustness of the network

– How packets are distributed inside network

– How network recovers from problematic situations

• E.g., lost connections (auto-recover, self-fixing)

• Rush hours

– What is the utilization rate of the network

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• 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 like BER=f(SINR)

• In AWGN f() is well known Q-function

• i.e., transceivers are not actually simulated – This saves efforts, time and costs – This is a QA method

• Sensor networks

– Cheap simple sensors are deployed in an area Collected

information is used to make decisions

– Hundreds or thousands of nodes

• Simulation only meaningful way to test

– Must be energy efficient

• Stand-alone nodes must be operable as long as possible

– Energy efficient simple routing protocols are needed

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 cases the direction matters like

multiantenna, directional antenna)

– External interference usually contains random features

– …

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Other signals

Thermal noise Effects of RF/AD

Effects of RF/DA Coding part

Digital signal formation

To RF frequency, power amplification

R a d i

o c h a n e l

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.,

– Antennae and antenna groups

(e.g., mutual coupling)

– 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 in 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

Other Simulation Examples

• Simulations are also used to design base station

locations

– Propagation models in addition with map and

geographical information (hills, vegetation,

streets, buildings) are used to estimate base

station coverage areas

• Network time synchronization

– How clocks are kept to show equal time

– Needed, e.g., in time stamping of events

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