Transcript At different levels the simulations concern different things

Communication Systems
Simulation - I
Harri Saarnisaari
Part of Simulations and Tools for Telecommunication
Course
Introduction
• First we study what simulation methods are
available
• Then we study the structure of communication
systems and discuss their simulations
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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
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Monte Carlo method
• Since the communication signals are random, 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
– convergence to the average value: consistency
• 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 methods
• How many trials are needed?
– 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
P % confidence limit
Actual value
N
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Monte Carlo methods
• BER analysis
– The theory of sequence of Bernoulli trials (which MC method
essentially is) says that
– 10-100 successful experiments (i.e., bit errors) have to be
made in order that BER analyses are reliable
• This means that for BER 10-5 we have to send at least 106 bits or
107 bits for more reliable results, 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 algorithms are needed, e.g., in channel
estimation and synchronization
• In estimation algorithm studies simulations 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., 10100 successful measurements
• For the former the used minimum number of trials is
usually 100 although 1000 is better
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General
• A communication system designer has
requirements the system has to satisfy and also
limitations that has to be taken in the account
• Simulations (in addition to analysis and
prototyping) are used to verify are requirements
and limitations possible to satisfy
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Some possible requirements
– Bit error 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 users
– Users 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 limitations
–
–
–
–
–
Costs
Size of equipments
Power consumption
Interference to other systems
…
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General
• Communication systems can be considered at different
levels
– higher and lower levels contain different parts of the
systems
• Communication 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
Satellite network
Satellite dish
Satellite dish
Public switch
Multiple networks
communicate
Radio tower
Another network
Networks are usually
linked somehow since
the goal in communications
is to send information
from a place to another (not
just inside a network)
Base station
network
Cell phone
Cell phone
Networks and links are just
means to attain the goal
Radio tower
Link between nodes
Radio tower
Semi Ad-hoc
network
Cell phone
Cell phone
Cell phone
Cell phone
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Network level simulations
• 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 (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?
• …
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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 arrival times
– Packet arrival rate
– Number of active users
– Number of connections
– Length of connections
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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 design
• Effects of uncertainties in synchronization/channel
estimation to BER
• Performance of different synchronization and channel
estimators (algorithms) in different environments
• …
• 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)
– Direction-of-arrival (in multiantenna channels)
–…
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Typical elements of a link
Coding part
Digital signal
formation
To RF frequency,
power amplification
Effects of
RF/DA
Other
signals
R
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h
a
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n
e
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Effects of Thermal
RF/AD
noise
Decoding part
Digital signal processing for
demodulation/synchronization/
channel estimation
From RF to
IF/baseband
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