Communication Theory PDF

1. Introduction ◼ Model of A Communication System ◼ Communication Channels ◼ Classification of Communications ◼ Mathematical Models for Communication Channels ◼ What Shall We Learn in This Course? University of Waterloo, O. Damen ECE 318 1  Basi...

1. Introduction ◼ Model of A Communication System ◼ Communication Channels ◼ Classification of Communications ◼ Mathematical Models for Communication Channels ◼ What Shall We Learn in This Course? University of Waterloo, O. Damen ECE 318 1  Basic Terms System: An integrated structure of hardware devices (e.g., electronic circuits, antennas, fiber optics, computer processors) and software algorithms (e.g., digital signal processing algorithms, network protocols) designed to achieve a specified function. Communication: The transfer of information from one “point” to another point (in space and/or time). This process involves electronic transmitting / receiving / processing of information. Analog communication: Information is encoded as an analog signal (i.e., a continuous-amplitude continuous-time waveform over time). Digital communication: Information is encoded as a digital signal (i.e., a discrete-time sequence of finite-alphabet symbols). University of Waterloo, O. Damen ECE 318 2 Sources of Channel Destination Information Transmitter (noise, fading, Receiver of interference) Information Model of a communication system ◼ Transmitter: Converts the above electronic signal into a form suitable for analog transmission through the propagation channel. ◼ Receiver: Performs the inverse of the transmitter operations in order to recover the original message signal. ◼ Channel: Transmission medium. University of Waterloo, O. Damen ECE 318 3  Communication Channels Channel: The propagation medium (analog in nature) linking the transmitter and the receiver. Channel types: wire-line channels: - copper wire telephone line and coaxial cable - fiber-optics cable wireless channels: - cellular wireless radiowave communication (landmobile or satellite) - indoor infrared optical communication - underwater acoustical communication - visible light communication storage channels: storage and retrieval systems (tape, CD, DVD, …) Channel impairments: As the transmitted signal travels through this analog medium, the signal degrades in various ways: additive (thermal) noise multiplicative noise (Rayleigh fading or signal attenuation) time-delayed multipath (intersymbol interference) Thermal noise is produced at the receiver front end (as a result of the thermally excited random motion of free electrons in a conducting medium, such as a resistor.) University of Waterloo, O. Damen ECE 318 4  Classification of Communications To classify the communications based on the format of the information to be sent: To classify the communication based on the characteristics of the channel. Analog communication system: The information to be transmitted is in Wireline communication: form of an analog signal. wireline channels Wireless communication: Digital communication system : wireless channels (mobile The message signal to be transmitted is and fixed). in digital form consisting of discrete symbols (both amplitude and time take on discrete values) University of Waterloo, O. Damen ECE 318 5  Analog Communication Systems Information Signal Propagation Signal Information Source Modulator Channel Demodulator Destination will be studied in ECE 318 Analog signals may be transmitted directly via carrier modulation over the propagation channel and to be carrier-demodulated at the receiver. Despite a general trend towards digital communications, analog communication systems remain widely used, especially in audio broadcasting. University of Waterloo, O. Damen ECE 318 6  Digital Communication Systems An analog (i.e., continuous-amplitude continuous-time) information-signal may be converted into a discrete-time discrete- amplitude digital signals by time-sampling and amplitude- quantization. The resulting digitized information signal will be modulated back into an analog waveform for propagation through the channel (ECE 414, ECE 611). The following figure is a typical block diagram of a digital communication system. University of Waterloo, O. Damen ECE 318 7  Optional From other sources Spread Information code source Essential gen. Band- Spread T Format Source Encrypt Channel Multi- Pulse spectrum R encode pass A/D encode Auth. plex modu. modu. modu. X mi ui gi(t) si(t) Digital input Wave- h(t) form noise Bit Timing and Digital baseband/ channel chan- stream synch- impulse ronization bandpass nel waveform response (band- width Digital limited) output m̂i ûi z(T) r(t) Source Decrypt Channel Demul- Demod- Spread R Format tiplex spectrum D/A decode Verify decode Detect ulate & X sample despread Information To other destinations Block Diagram of a DCS sink 8 University of Waterloo, O. Damen ECE 318 Format: transforms the Channel encode/decode: add redundancy, source information into in a controlled manner, to message bits (A/D converter if it is symbols and the decoder can use this analog). redundancy to detect and correct errors. Source encode/decode: Modulation, demodulation/detection: remove redundancy generate signal waveform which is suitable existing in the source for transmission over the channel. information so that it can be represented efficiently. Spread spectrum modulation/Despread: an Encrypt/Decrypt: protect additional level of modulation beyond pulse privacy of the information modulation and bandpass modulation. The Authentication/Verify: transmitted signal is much wider than and provide integrity checking independent of the bandwidth of the for origin of the information information to be transmitted. source (this block can be placed after any block before Timing and synchronization: a clock signal, is modulation). involved in the control of almost every blocks. 9 University of Waterloo, O. Damen ECE 318  Digital Versus Analog Performance Criteria Analog: Fidelity criterion such as signal-to-noise ratio, % distortion, or expected mean square error (MSE) between the transmitted and received waveforms. Digital: The probability of incorrectly detecting a digit or a packet of symbols, i.e., the probability of error Pe University of Waterloo, O. Damen ECE 318 10  Mathematical Models for Communication Channels 1. The Additive White Gaussian Noise (AWGN) Channel The transmitted signal s(t) is corrupted by an additive white Gaussian noise process n(t) (one of the simplified mathematical models for various physical communications channels including wired channels and some radio channels) s(t) r(t) = s(t) + n(t) + For an AWGN process n(t): - The power spectral density (psd) is constant, N0/2, as a function of frequency (i.e., white noise). n(t) - For any time instant t, the probability density function (pdf) of n(t) follows a Channel Gaussian distribution. A white Gaussian noise is uncorrelated and hence independent: E[n(0)n(t)]=N0/2 (t) 11 University of Waterloo, O. Damen ECE 318  2. The Linear Time Invariant Filter Channel In general, a wired (and some fixed wireless) channel can be modeled as a linear time invariant (LTI) system, which can be mathematically described by the impulse response of the system. s(t) LTI r (t ) = ( s  h )(t ) + n(t ) h(t) +  =  s(t −  )h( )d + n(t ) − n(t) Channel The LTI filter channel with an AWGN University of Waterloo, O. Damen ECE 318 12  The Relationship Between Information Rate, Bandwidth and Noise The most important question associated with a communication channel is the maximum rate at which it can reliably transfer information. A signal that doesn’t change doesn’t carry information! Information can be carried by the values and the rate of the changes. Nyquist’s Discovery: Analogue signals passing through physical channels may not change arbitrarily fast. The rate at which a signal may change is determined by its bandwidth. A signal of bandwidth W may change at a maximum rate of 2W. If each change takes one of M different values, then, the maximum information rate is 2W log2 (M) bits/s (without consideration of noise, i.e., we can increase M indefinitely). Claude Shannon’s Discovery: Established the following fundamental limits for communication systems. Given a transmitted power constraint P, a bandwidth W, and an additive white Gaussian noise (AWGN) channel with bilateral power spectral density (psd) of N0/2, then the channel capacity is given by C=W log2(1+P/WN0) bits/s, where P/WN0 is the signal-to-noise ratio or SNR. bit=binary information unit. If we take the natural logarithm instead of log2, then the information is measured by nats=natural units. 13 University of Waterloo, O. Damen ECE 318  Claude Elwood Shannon Born: 30 April 1916 in Gaylord, Michigan, USA Died: 24 Feb 2001 in Medford, Massachusetts, USA His seminal work “A Mathematical Theory of Communication” in the Bell System Technical Journal (1948) founded the subject of information theory (based on probability theory): measure of information, mathematical model of communication channels, capacity limit, existence of codes that approach the capacity). Within fifty years, (discovery of Turbo codes and the re-discovery of LDPC codes) the goal of achieving the Shannon capacity was reached, from an engineering viewpoint (i.e., error rates of 10-6 achievable within a fraction of a dB of the Shannon limit). University of Waterloo, O. Damen ECE 318 14  What Shall We Learn in This Course? To learn to design a communication system that is: (1) Reliable: information message received ≅ information message sent,  high fidelity, low probability of system outage. (2) Efficient in frequency spectrum & transmission power. (3) Simple (thus economical) in transmitter/receiver hardware/software. Accuracy & To achieve the above objectives Reliability in Transmission through studying: Principles of AM / FM / PM analog communication (Chapters 3 & 4 & 6) Basic digital coding & modulation: Simplicity in (Chapter 7 & 8) Efficiency in Underline signal processing Hardware & Power & BW Software (Chapters 2 & 5) Selected topics (ISI channels, OFDM, Chapters 10, 11) University of Waterloo, O. Damen ECE 318 15  Digital Communications Related Courses in ECE Original information Source Channel Modulator A/D signal (analog) Encoder Encoder ECE 604 ECE 313 ECE 611 ECE 414 ECE 313 ECE 612 Channel ECE 603 ECE 710-5 ECE 604 ECE 614 Recovered ECE 710-5 information Source Channel De- D/A signal (analog) Decoder Decoder modulator In an ideal system, the recovered signal will be exactly the same as the original one. University of Waterloo, O. Damen ECE 318 16 Some Related Courses ◼ ECE313: Digital Signal Processing ◼ ECE414: Wireless Communication ◼ ECE603: Statistical Signal Processing ◼ ECE604: Stochastic Processes ◼ ECE611: Advanced Digital Communications ◼ ECE612: Information Theory ◼ ECE614: Communications over Fading Channels ◼ ECE710: Coding Theory University of Waterloo, O. Damen ECE 318 17