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.
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? Communication Systems Simulation - I Harri Saarnisaari Part of Simulations and Tools for Telecommunication Course Simulation methods Monte Carlo method • 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 • 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 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) Monte Carlo method Monte Carlo methods • 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 as result = value ± desired conf interval • 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 Monte Carlo methods, BER case Number of simulated symbols 10 expected errors • 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 100 expected errors Monte Carlo methods Monte Carlo methods, estimation • 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 – 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 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 • 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 10 Monte Carlo methods, estimation 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 • 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 11 12 Monte Carlo methods, estimation 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 • 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 • 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 ±σ of the mean and • 95% of samples are within ±2σ of the mean • Accuracy usually increases at rate (1/N)1/2 • As a rule of thumb, the result curves should be smooth, not fluctuating – 95 % accuracy or 2σ (2sigma) accuracy are often used terms in system design no 13 yes 14 Monte Carlo methods, estimation 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 – Depending on application this may be a valid way to it 15 • 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) 16 Communication simulations 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 • 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 17 Communication simulations 18 Some possible requirements • Thus, we have – System level requirements – Bit rates the system has to support • May be different for different services • The overall system has to satisfy the requirements – voice, data, video,… – BER targets – Subsystem level requirements • The subsystems have to satisfy their requirements • 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 – … 19 20 Some possible requirements/limitations 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 – 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 • Transmitter • Propagation medium (optic, wired, wireless) • Receiver –… • At different levels the simulations concern different things 21 22 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 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 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 23 24 Communication simulations Network level 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 • 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 25 Network level simulations 26 Network level simulations • Possible variables – Number of nodes – Density of nodes in certain area – Propagation loss and range between nodes – Mobility of nodes – Interference, • 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 • e.g., co-channel interference effects – Usability and effects of – 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) • 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? 27 28 Network level simulations Network level simulations • 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 • 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) • Robustness of the network – How packets are distributed inside network – How network recovers from problematic situations • In AWGN f() is well known Q-function • E.g., lost connections (auto-recover, self-fixing) • Rush hours • i.e., transceivers are not actually simulated – This saves efforts, time and costs – This is a QA method – What is the utilization rate of the network 29 Network level simulations 30 Link level simulations • 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 • 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) 31 32 Typical elements of a link To RF frequency, power amplification Link simulations Digital signal formation Coding part • 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 – … 33 RF Simulations Effects of RF/DA Other signals R a d i o c h a n n e l Effects of Thermal RF/AD noise Decoding part Digital signal processing for demodulation/synchronization/ channel estimation From RF to IF/baseband 34 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 35 • 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 36 Platform Simulations 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? 37 • How signal flows between different blocks • Simulation of different finite word length algorithms – Filters – Matrix inversions – (I)FFT – • Etc 38 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 39 10 ... (not just inside a network) Networks and links are just means to attain the goal 23 24 Communication simulations Network level simulations • Communication simulations can be divided into several... 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... 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