Introduction to Digital Communications by Erol Seke For the course - PowerPoint PPT Presentation

Introduction to Digital Communications by Erol Seke For the course “ Digital Communications ” OSMANGAZI UNIVERSITY

The Goal Transfer information from source point to destination correctly (and in shortest possible time, in most cases) Information Channel Information Information Generator User Source point Destination point Noise Sources

Information The probability of an event occurring Low High High self-information Low self-information Example : Consider the statement “ We will have an exam tomorrow ” The statement has highly valuable, since it is the beginning of a new semester and an exam at this time is very unusual (low probability) Self-info of the event   1      I ( E ) log log( P ( E ))   P ( E )   Probability of the event

Noise Sources • Electronic / Thermal noise • Electrical discharges in the atmosphere / nearby devices • Interference / Crosstalk between channels and multipath effects • Solar / Cosmic effects • Distortion from nonlinearities of the electronics / media (quantization noise and granular noise are evaluated in different contexts) Channel input Channel output Noise is usually assumed to be (this assumption is not baseless)   S kS N A dditive : o i W hite : | F ( N )|=c (has the same power at all frequencies) So it is AWGN G aussian : Probability distribution function is Gaussian

Little More Detailed Information System Source coder / decoder : Codes for efficient transmission, removes redundancy (compression) Channel coder / decoder : Codes for reliable transmission, adds redundancy Some examples of (electronic) source, channel and destination Microphone – Twisted pair of wire - Amplifier Modem - Twisted pair of telephone line - Modem Fax scanner – Telephone system – Fax printer Computer – Ethernet cable - Computer Computer’s data storage medium – Fiber optic network – Another computer’s storage Digital data generator – Magnetic disk – Digital data user Radio transmitter – Air – Radio receiver Digital TV data from satellite – Atmosphere – Digital TV receiver TV Remote controller – Air – IR sensor/receiver on TV

Little More Detailed Communication System

The Problem distortion/bandlimiting additive noise The noise is the most important obstacle in front of the fast and reliable data transmission Q : What are other problems/factors that limit the data transmission rate and reliability?

SX 10 PHz EUV 10 nm 1 PHz NUV 1 µm fiber NIR 100 THz 10 µm MIR 10 THz 100 µm FIR 1 THz 1 mm radar EHF 100 GHz microwave terrestrial 10 mm SHF satellite 10 GHz 100 mm UHF 1 GHz 1 m TV VHF FM 100 MHz AM radio 10 m HF coax 10 MHz 100 m MF 1 MHz Twisted pair 1 km LF 100 kHz 10 km VLF 10 kHz 100 km VF 1 kHz ELF

Simplest Design channel binary stream. transmitter receiver binary stream. noise Transmitter D in clk Receiver might be a twinax cable with common ground output buffers of Tr. propagation delay 1 2 3 0 bits 1 2 3 0

Let us assume that data and clock line lengths differ by 10 cm one of the signals arrive 0.5 picoseconds late. (speed of e.m. wave on copper is about 2x10 8 m/s) Problem is : for a 1GHz clock, 0.5 ps is about half a clock cycle. what you need/want what you get

Solution to clock lead/lag problem Solution is to generate clock from data at the receiver. Transmitter D in clk sync. Receiver The data signal should necessarily be designed to allow such an operation received data signal bit synchronizer generated clock A Phase Locked Loop (PLL) can be used if there are enough transitions in the signal Same approach is used in wireless comm. systems

Simplest System (what to send) baseband channel receiver binary stream. binary stream. detector modulation noise mapping waveform generation T b A … B …010011010010… … is mapped to what? … There are several waveform choices to represent 0/1 or 00/01/10/11 or … There are also voltage/power range and bit-period issues

Spectrum and Media Sharing Issues receiver binary stream. transmitter problem ! binary stream. media (air) does not belong to anyone tr-5 tr-n transmitter-1 tr-2 tr-4 tr-3 f available bandwidth is shared among transmitters (must be managed by a central authority) How? : bandpass modulation bandpass f modulation f f c baseband signal spectrum transmitted signal spectrum

Modulation means : controlling a quantity/feature/property by another quantity in communications : controlling amplitude/phase/frequency/shape of a signal by another signal baseband modulation : doing modulation and still keeping the resulting signal in baseband baseband : a frequency band that centers at the zero frequency (lower frequencies implied) bandpass modulation : doing modulation in order to move the center frequency of the original signal to a different (possibly higher) frequency Why? 1) adapt the characteristics of the signal to the channel's and improve efficiency 2) share the transmission media by other transmitters 3) in case of RF, improve antenna efficiency 4) other reasons; spread spectrum, security, reliability, necessity etc. fiber optics

Basic System bandpass baseband binary stream. transmitter modulator modulator channel carrier bit/symbol sync noise synchronization receiver bandpass binary stream. receiver demodulator detector Since the spectrum of the signal is very important property and changed several times on the communication path, we urgently need to recall some junior- sophomore knowledge on frequency/spectrum issues.

Fourier Series Any periodic waveform (with some limits, of course) can be constructed by an infinite sum of sin and cos signals   1             f o n 0 , 1 ,..., 2 f y ( t ) b cos( n t ) c sin( n t ) and o o n o n o T   n 0 n 1 n   is called the n th harmonic of the fundamental frequency where o o y ( t ) Example periodic waveform 1 t -1 T The coefficients b n and c n can be calculated using 1 2 2 T / 2 T / 2 T / 2         b y ( t ) dt b y ( t ) cos( n t ) dt c y ( t ) sin( n t ) dt o n o n o T T T    T / 2 T / 2 T / 2  n 1 , 2 , 3 , 

1   T / 2 T         b dt ( 1 ) dt 0 (mean value is zero, just as seen in the figure)   o T 0 T / 2   2 2       T / 2 T         T / 2   T b  cos( n t ) dt cos( n t ) dt  sin( n t ) sin( n t )   n o o o o  0 T / 2 T Tn 0 T / 2 o   1 1         T / 2   T        sin( n 2 t / T ) sin( n 2 t / T ) sin( n ) sin( 0 ) sin( 2 n ) sin( n )  0 T / 2  n n  b 0 (we see this from the figure, thus no need for integration. It is an odd function) n   2 1       0 T / 2   0 T / 2            c sin( n t ) dt sin( n t ) dt cos( n 2 t / T ) cos( n 2 t / T )  n  o o  T / 2 0  T n  T / 2 0  0 , n is even    1 2 2                  n c n 1 cos( n ) cos( n ) 1 1 cos( n ) 1 ( 1 ) 4  , n is odd    n n n    n c n   sin( n t )   y ( t ) 4 o Therefore  n  n 1 , 3 ... interpretation: infinite sum of odd harmonics of fundamental frequency. The magnitude of the sin- waves decreases inversely with the harmonic n number

   jn t  jn t e e o o   cos( n t ) o 2 exponential Fourier series Euler eq.’s    jn t  jn t e e o o    sin( n t )    jn t o y ( t ) a e j 2 o n   n         y ( t ) b cos( n t ) c sin( n t ) n o n o coefficients of exponential   n 0 n 0 Fourier series 2 T / 2    b y ( t ) cos( n t ) dt n o 1 T  T / 2 T / 2     jn t a y ( t ) e dt o 2 n T T / 2  T / 2    c y ( t ) sin( n t ) dt n o T  T / 2    2 : Fundamental Angular Frequency o T o n  : Harmonics o a : Zero frequency component or DC value (or mean) o Any periodic signal which satisfies Dirichlet conditions can be represented by a weighted sum of (possibly infinite number of) sinusoids with different magnitude and delay (phase)

Example : Periodic Pulse Signal  2    (zero crossing (doesn’t have to coincide with a component)) (envelope)    sinc      T T   o o Larger T o means tighter components     T (continuous) (not periodic) the number of components per cycle if o We call it the Fourier Transform