Communication System Overview Gwo-Ruey Lee

Outlines Communication System Digital Communication System Modulation

Communication System 1/6 Input Transducer Transmitter Channel Receiver Output Transducer

Communication 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.

Communication System 3/6 Transmitter The purpose of the transmitter is to couple the message to the channel. Modulation For ease of radiation to reduce noise and interference For channel assignment For multiplexing or transmission of several message over a single channel To overcome equipment limitation

Communication System 4/6 Channel Different forms The signal undergoes degradation from transmitter to receiver Noise, fading, interference……

Communication 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 transducer Demodulation

Communication System 6/6 Output Transducer The output transducer completes the communication system The device converts the electric signal at its input into the form desired for the system user

Digital Communication System 1/6

Digital Communication System 2/6 Source Encoder/ Decoder The 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 Coding Fixed-length coding Pulse-code modulation (PCM) Differential Pulse-code modulation (DPCM) Variable-length coding Huffman Coding/ entropy coding

Digital Communication System 3/6 Channel Encoder/ Decoder A 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 Coding Error detection coding Error correct coding

Digital Communication System 4/6 Error Control Coding Linear block code Convolutional code RS code Modulation Coding Trellis code Turbo code

Digital Communication System 5/6 Synchronization Symbol/ Timing synchronization Frequency synchronization Carrier frequency synchronization Sampling frequency synchronization Two basic types of synchronization Data-aid algorithm Training sequences Preambles Non-data-aid algorithm Blind

Digital Communication System 6/6 Channel Estimation A 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 methods Data-aid algorithm Training sequences pilots Non-data-aid algorithm Blind

Modulation 1/10 Analog Modulation Pulse Modulation Digital Modulation AM FM PM Pulse Modulation PAM / PPM / PCM / PWM Digital Modulation ASK FSK PSK QAM Carrier: Amplitude Frequency Phase

Modulation 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 modulation Modulation type Phase shift keying (PSK) Quadrature Amplitude Modulation (QAM)

Modulation 3/10 M-ary Phase Shift Keying Consider M-ary phase-shift keying (M-PSK) for which the signal set is where 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 .

Modulation 4/10 An example of signal-space diagram for 8-PSK

Modulation 5/10 Phase shift keying where BPSK QPSK with Gray code M-ary PSK where

Modulation 6/10 BER versus SNR curves in AWGN channel using BPSK, QPSK, 8-PSK,16-PSK .

Modulation 7/10 Quadrature Amplitude Modulation The transmitted M-ary QAM signal for symbol n can be expressed as where E is the energy of the signal with the lowest amplitude, and , and are amplitudes taking on the values Note that M is assumed to be a power of 4. The parameter a can be related to the average signal energy ( ) by

Modulation 8/10 An example of signal-space diagram for 16-square QAM.

Modulation 9/10 QAM

Modulation 10/10 BER versus SNR curves in AWGN channel using BPSK/QPSK, 16QAM, 64QAM, 256QAM.

Communication System Overview Readings Any book about communications

Random Process/ Stochastic Process

Outlines 1/10 Basic Concepts Stationary Process Transmission over Linear Time-Invariant (LTI) Systems

Basic 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 randomlike We can not predict the exact value of the signal Signal must be distributed by its statistical properties. Ex: mean, variance…..

Basic 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

Basic 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 function . r.v. 1. : ensemble 2. : sample function (or a realization) 3. : r.v. 4. : numerical value

Basic Concepts 5/10 Classification of random process From the perspective of time Random process: for , t has a continuous of values Random sequence: for , t can take on a finite or countably infinite number of values  From the perspective of the value of Continuous: can take on a continuous of values Discrete : Values of are countable

Basic Concepts 6/10 Classification of random process Continuous random process Discrete random process Continuous random sequence Discrete random sequence

Basic Concepts 7/10 1st-order distributions function It describes the instantaneous amplitude distribution of a random process Mean: 2nd-order distributions function It distributes the structure of the signal in the time domain Autocorrelation Function (A.F.)

Basic Concepts 8/10 Autocovariance Cross-correlation If and are orthogonal  If and are statistically uncorrelated 

Basic Concepts 9/10 Crosscovariance The autocorrelation function of a real WSS process is

Basic Concepts 10/10 The cross-correlation function of two real WSS process and is If and are orthogonal  If and are statistically uncorrelated  Power Spectral Density (PSD) PSD represents the distribution of signal strength (ie, energy or power) with frequency The PSD of WSS process is the Fourier transform (FT) of the A.F.

Stationary Process 1/9 Stationary Stationary Process A random process whose statistical properties do not change over time Stationary Process Strictly-Sense Stationary (SSS) Wide-Sense Stationary (WSS) Strictly-Sense Cyclostationary Wide-Sense Cyclostationary

Stationary Process 2/9 Strictly-Sense Stationary (SSS) A nth-order strictly-sense stationary process is a process in which for all , all , and all Note: Mth-order stationary of the above equation holds for all . Example: 2nd-order SSS process  1st-order SSS process

Stationary Process 3/9 A example of 2nd-order stationary

Stationary Process 4/9 Wide-Sense Stationary (WSS) A random process is wide-sense stationary process (WSS) if Its mean is constant Its A.F. depends only on the time difference.

Stationary 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  WSS Since the joint-Gaussian pdf is completely specified by its mean and A.F.

Stationary 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 )

Stationary Process 7/9 Wide-Sense Cyclostationary A random process with and is wide-sense cyclostationary if Its mean satisfies Its a.F. satisfies

Stationary 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 ergodic A.F. ergodic

Stationary Process 9/9 The relationship between ergodic and stationary Ergodic  stationary (True) Ergodic  stationary (Fault)

Transmission over LTI Systems 1/3 Linear Time-Invariant (LTI) Systems

Transmission over LTI Systems 2/3 Assumptions: and are real-valued and is WSS. The mean of the output The cross-correlation function

Transmission over LTI Systems 3/3 The A.F. of the output The PSD of the output

Random Process/ Stochastic Process Readings Communication Systems, 4th edition, Simon Haykin, Wiley Chapter 1 – 1.1 ~1.7, 1.8