2OutlinesCommunication SystemDigital Communication SystemModulation
3Communication System 1/6 Input Transducer Transmitter Channel Receiver Output Transducer
4Communication System 2/6 Input transducer Messages can be categorized as analog (continuous form)or digital (discrete form).The message produced by a source must be converted by a transducer to a form suitable for the particular type of communication system employed.
5Communication System 3/6 Transmitter The purpose of the transmitter is to couple the message to the channel.ModulationFor ease of radiationto reduce noise and interferenceFor channel assignmentFor multiplexing or transmission of several message over a single channelTo overcome equipment limitation
6Communication System 4/6 Channel Different forms The signal undergoes degradation from transmitter to receiverNoise, fading, interference……
7Communication System 5/6 Receiver The receiver is to extract the desired message from the received signal at the channel output and to convert it to a form suitable for the output transducerDemodulation
8Communication System 6/6 Output Transducer The output transducer completes the communication systemThe device converts the electric signal at its input into the form desired for the system user
10Digital Communication System 2/6Source Encoder/ DecoderThe purpose of source coding is to reduce the number of bits required to convey the information provided by the information source.The task of source coding is to represent the source information with the minimum of symbols.High compression rates (Good compression rates) make be achieved with source encoding with lossless or little loss of information.Source CodingFixed-length codingPulse-code modulation (PCM)Differential Pulse-code modulation (DPCM)Variable-length codingHuffman Coding/ entropy coding
11Digital Communication System 3/6Channel Encoder/ DecoderA way of encoding data in a communications channel that adds patterns of redundancy into the transmission path in order to lower the error rate.The task of channel coding is to represent the source information in a manner that minimizes the error probability in decoding.Error Control CodingError detection codingError correct coding
12Digital Communication System 4/6Error Control CodingLinear block codeConvolutional codeRS codeModulation CodingTrellis codeTurbo code
13Digital Communication System 5/6SynchronizationSymbol/ Timing synchronizationFrequency synchronizationCarrier frequency synchronizationSampling frequency synchronizationTwo basic types of synchronizationData-aid algorithmTraining sequencesPreamblesNon-data-aid algorithmBlind
14Digital Communication System 6/6Channel EstimationA channel estimate is only a mathematical estimation of what is truly happening in nature.Allows the receiver to approximate the effect of the channel on the signal.The channel estimate is essential for removing inter symbol interference, noise rejection techniques etc.Two basic types of channel estimation methodsData-aid algorithmTraining sequencespilotsNon-data-aid algorithmBlind
15Modulation 1/10 Analog Modulation Pulse Modulation Digital Modulation AMFMPMPulse ModulationPAM / PPM / PCM / PWMDigital ModulationASKFSKPSKQAMCarrier:AmplitudeFrequencyPhase
16Modulation 2/10 Mapping Modulation type The process of mapping the information bits onto the signal constellation plays a fundamental role in determining the properties of the modulationModulation typePhase shift keying (PSK)Quadrature Amplitude Modulation (QAM)
17Modulation 3/10 M-ary Phase Shift Keying Consider M-ary phase-shift keying (M-PSK) for which the signal set iswhere is the signal energy per symbol, is the symbol duration, and is the carrier frequency.This phase of the carrier takes on one of the M possible values, namely, , where
18Modulation4/10An example of signal-space diagram for 8-PSK
19Modulation 5/10 Phase shift keying where BPSK QPSK with Gray code M-ary PSKwhere
20Modulation6/10BER versus SNR curves in AWGN channel using BPSK, QPSK, 8-PSK,16-PSK .
21Modulation 7/10 Quadrature Amplitude Modulation The transmitted M-ary QAM signal for symbol n can be expressed aswhere E is the energy of the signal with the lowest amplitude, and , and are amplitudes taking on the valuesNote that M is assumed to be a power of 4.The parameter a can be related to the average signal energy ( ) by
22Modulation8/10An example of signal-space diagram for 16-square QAM.
27Outlines 1/10 Basic Concepts Stationary Process Transmission over Linear Time-Invariant (LTI) Systems
28Basic Concepts 2/10 Why study random processes? Due to the uncertainty of 1. noise and 2. the unpredictable nature of information itself.Information signal usually is randomlikeWe can not predict the exact value of the signalSignal must be distributed by its statistical properties.Ex: mean, variance…..
29Basic Concepts 3/10 Random Variable (r.v.) Consider an experiment with sample space . The element of are the random outcomes, , of the experiment. If to every , we assign a real value , such a rule is called a random variable (r.v.)Real line
30Basic Concepts 4/10 Random Process (r.p.) r.v. A random process is the mapping of the outcomes in into a set of real valued functions of time, called sample functionr.v.: ensemble: sample function(or a realization): r.v.: numerical value
31Basic Concepts 5/10 Classification of random process From the perspective of timeRandom process:for , t has a continuous of valuesRandom sequence:for , t can take on a finite or countably infinite number of values From the perspective of the value ofContinuous:can take on a continuous of valuesDiscrete :Values of are countable
32Basic Concepts 6/10 Classification of random process Continuous random processDiscrete random processContinuous random sequenceDiscrete random sequence
33Basic Concepts 7/10 1st-order distributions function It describes the instantaneous amplitude distribution of a random processMean:2nd-order distributions functionIt distributes the structure of the signal in the time domainAutocorrelation Function (A.F.)
34Basic Concepts 8/10 Autocovariance Cross-correlation If and are orthogonal If and are statistically uncorrelated
35Basic Concepts 9/10 Crosscovariance The autocorrelation function of a real WSS process is
36Basic Concepts10/10The cross-correlation function of two real WSS processand isIf and are orthogonal If and are statistically uncorrelated Power Spectral Density (PSD)PSD represents the distribution of signal strength (ie, energy or power) with frequencyThe PSD of WSS process is the Fourier transform (FT) of the A.F.
37Stationary Process 1/9 Stationary Stationary Process A random process whose statistical properties do not change over timeStationary ProcessStrictly-Sense Stationary (SSS)Wide-Sense Stationary (WSS)Strictly-Sense CyclostationaryWide-Sense Cyclostationary
38Stationary Process 2/9 Strictly-Sense Stationary (SSS) A nth-order strictly-sense stationary process is a process in which for all , all , and allNote: Mth-order stationary of the above equation holds for allExample: 2nd-order SSS process 1st-order SSS process
39Stationary Process3/9A example of 2nd-order stationary
40Stationary Process 4/9 Wide-Sense Stationary (WSS) A random process is wide-sense stationary process (WSS) ifIts mean is constantIts A.F. depends only on the time difference.
41Stationary Process 5/9 The relationship between SSS and WSS SSS WSS (True)SSS WSS (Fault)1st-order SSS 2nd-order SSS For Gaussian process : SSS WSSSince the joint-Gaussian pdf is completely specified by its mean and A.F.
42Stationary Process 6/9 Strictly-Sense Cyclostationary A nth-order strictly-sense cyclostationary process is a process in which for all , all , and integer m( mT is integer multiples of period T )
43Stationary Process 7/9 Wide-Sense Cyclostationary A random process with and is wide-sense cyclostationary ifIts mean satisfiesIts a.F. satisfies
44Stationary Process 8/9 Ergodic Process A random process is strictly ergodic process if all time and ensemble (statistical) average are interchangeable including mean, A.F. PSD, etc.A random process is wise-sense ergodic if it it ergodic in the mean and the A.F.mean ergodicA.F. ergodic
45Stationary Process 9/9 The relationship between ergodic and stationary Ergodic stationary (True)Ergodic stationary (Fault)
46Transmission over LTI Systems 1/3Linear Time-Invariant (LTI) Systems
47Transmission over LTI Systems 2/3Assumptions:and are real-valued and is WSS.The mean of the outputThe cross-correlation function
48Transmission over LTI Systems 3/3The A.F. of the outputThe PSD of the output
49Random Process/ Stochastic Process ReadingsCommunication Systems, 4th edition, Simon Haykin, WileyChapter 1 – 1.1 ~1.7, 1.8