1. Lecture 3-1: Coding and Error Control
ECE591-01

2. Universität Karlsruhe Institut für Telematik
Mobilkommunikation
SS 1998
Signals
Physical representation of data
Function of time and location
Signal parameters: parameters representing the value of data
classification
continuous time/discrete time
continuous values/discrete values
analog signal = continuous time and continuous values
digital signal = discrete time and discrete values
Signal parameters of periodic signals: period T, frequency f=1/T, amplitude A, phase shift 
sine wave as special periodic signal for a carrier: s(t) = At sin(2  ft t + t)
Prof. Dr. Dr. h.c. G. Krüger
E. Dorner / Dr. J. Schiller

3. Universität Karlsruhe Institut für Telematik
Mobilkommunikation
SS 1998
Signals
Different representations of signals
amplitude (amplitude domain)
frequency spectrum (frequency domain)
phase state diagram (amplitude M and phase  in polar coordinates)
Composed signals transferred into frequency domain using Fourier transformation
Digital signals need
infinite frequencies for perfect transmission
modulation with a carrier frequency for transmission (analog signal!)
A [V]
Q = M sin 
A [V]
t[s] 
I= M cos 
f [Hz] 
Prof. Dr. Dr. h.c. G. Krüger
E. Dorner / Dr. J. Schiller

4. Universität Karlsruhe Institut für Telematik
Mobilkommunikation
SS 1998
Multiplexing
Multiplexing in 4 dimensions
space (si)
time (t)
frequency (f)
code (c)
Goal: multiple use of a shared medium
Important: guard spaces needed!
channels ki k1 k2 k3 k4 k5 k6 c t c s1 t s2 f f c t s3 f
Prof. Dr. Dr. h.c. G. Krüger
E. Dorner / Dr. J. Schiller

5. Universität Karlsruhe Institut für Telematik
Mobilkommunikation
SS 1998
Frequency multiplex
Separation of the whole spectrum into smaller frequency bands
A channel gets a certain band of the spectrum for the whole time
Advantages
no dynamic coordination necessary
works also for analog signals
Disadvantages
waste of bandwidth if the traffic is distributed unevenly
inflexible k1 k2 k3 k4 k5 k6 c f t
Prof. Dr. Dr. h.c. G. Krüger
E. Dorner / Dr. J. Schiller

6. Universität Karlsruhe Institut für Telematik
Mobilkommunikation
SS 1998
Time multiplex
A channel gets the whole spectrum for a certain amount of time
Advantages
only one carrier in the medium at any time
throughput high even for many users
Disadvantages
precise synchronization necessary k1 k2 k3 k4 k5 k6 c f t
Prof. Dr. Dr. h.c. G. Krüger
E. Dorner / Dr. J. Schiller

7. Time and frequency multiplex
Universität Karlsruhe
Institut für Telematik
Mobilkommunikation
SS 1998
Time and frequency multiplex
Combination of both methods
A channel gets a certain frequency band for a certain amount of time
Example: GSM
Advantages
protection against frequency selective interference
but: precise coordination required k1 k2 k3 k4 k5 k6 c f
ince different frequency components of the signal are affected independently, it is highly unlikely that all parts of the signal will be simultaneously affected by a deep fade.Frequency-selective fading channels are also dispersive, in that the signal energy associated with each symbol is spread out in time. This causes transmitted symbols that are adjacent in time to interfere with each other. t
Prof. Dr. Dr. h.c. G. Krüger
E. Dorner / Dr. J. Schiller

8. Universität Karlsruhe Institut für Telematik
Mobilkommunikation
SS 1998
Code multiplex
Each channel has a unique code
All channels use the same spectrum at the same time
Advantages
bandwidth efficient
no coordination and synchronization necessary
good protection against interference
Disadvantages
varying user data rates
more complex signal regeneration
Implemented using spread spectrum technology k1 k2 k3 k4 k5 k6 c f t
Prof. Dr. Dr. h.c. G. Krüger
E. Dorner / Dr. J. Schiller

9. Universität Karlsruhe Institut für Telematik
Mobilkommunikation
SS 1998
Modulation
Digital modulation
digital data is translated into an analog signal (baseband)
ASK, FSK, PSK
differences in spectral efficiency, power efficiency, robustness
Analog modulation
shifts center frequency of baseband signal up to the radio carrier
Basic schemes
Amplitude Modulation (AM)
Frequency Modulation (FM)
Phase Modulation (PM)
Prof. Dr. Dr. h.c. G. Krüger
E. Dorner / Dr. J. Schiller

10. Modulation and Demodulation
Universität Karlsruhe
Institut für Telematik
Mobilkommunikation
SS 1998
Modulation and Demodulation
analog
baseband
signal
digital
data
digital
modulation
analog
modulation
radio transmitter
radio
carrier
analog
baseband
signal
digital
data
analog
demodulation
synchronization
decision
radio receiver
radio
carrier
Prof. Dr. Dr. h.c. G. Krüger
E. Dorner / Dr. J. Schiller

11. Universität Karlsruhe Institut für Telematik
Mobilkommunikation
SS 1998
Digital modulation
Modulation of digital signals known
as Shift Keying
Amplitude Shift Keying (ASK):
very simple
low bandwidth requirements
very susceptible to interference
Frequency Shift Keying (FSK):
needs larger bandwidth
Phase Shift Keying (PSK):
more complex
robust against interference 1 1 t 1 1 t
he simplest and most common form of ASK operates as a switch, using the presence of a carrier wave to indicate a binary one and its absence to indicate a binary zero. This type of modulation is called on-off keying, and is used at radio frequencies to transmit Morse code (referred to as continuous wave operation).
More sophisticated encoding schemes have been developed which represent data in groups using additional amplitude levels. For instance, a four-level encoding scheme can represent two bits with each shift in amplitude; an eight-level scheme can represent three bits; and so oninimum frequency-shift keying or minimum-shift keying (MSK) is a particular spectrally efficient form of coherent FSK. In MSK the difference between the higher and lower frequency is identical to half the bit rate. Consequently, the waveforms used to represent a 0 and a 1 bit differ by exactly half a carrier period. This is the smallest FSK modulation index that can be chosen such that the waveforms for 0 and 1 are orthogonal. A variant of MSK called GMSK is used in the GSM mobile phone standard 1 1 t
Prof. Dr. Dr. h.c. G. Krüger
E. Dorner / Dr. J. Schiller

12. Frequency Shift Keying (FSK):

13. Advanced Phase Shift Keying
Universität Karlsruhe
Institut für Telematik
Advanced Phase Shift Keying
Mobilkommunikation
SS 1998 Q I 1
BPSK (Binary Phase Shift Keying):
bit value 0: sine wave
bit value 1: inverted sine wave
0 = Same phase, 1=Opposite phase
A cos(2πft), A cos(2πft+π)
low spectral efficiency
robust, used e.g. in satellite systems
QPSK (Quadrature Phase Shift Keying):
2 bits coded as one symbol
symbol determines shift of sine wave
needs less bandwidth compared to BPSK
11=A cos(2πft+45°),
10=A cos(2πft+135°),
00=A cos(2πft+225°),
01=A cos(2πft+315°) Q I 11 01 10 00 A t 11 10 00 01
Prof. Dr. Dr. h.c. G. Krüger
E. Dorner / Dr. J. Schiller

14. Quadrature Amplitude Modulation
Universität Karlsruhe
Institut für Telematik
Mobilkommunikation
SS 1998
Quadrature Amplitude Modulation
Quadrature Amplitude Modulation (QAM)
combines amplitude and phase modulation
it is possible to code n bits using one symbol
2n discrete levels, n=2 identical to QPSK
Bit error rate increases with n, but less errors compared to comparable PSK schemes
Example: 16-QAM (4 bits = 1 symbol)
Symbols 0011 and 0001 have the same phase φ, but different amplitude
0000 and 1000 have different phase, but same amplitude.
0000
0001
0011
1000 Q I
0010 φ a
Prof. Dr. Dr. h.c. G. Krüger
E. Dorner / Dr. J. Schiller

15. Channel Capacity Capacity = Maximum data rate for a channel
Nyquist Theorem: Bandwidth = B
Data rate < 2 B
Bi-level Encoding: Data rate = 2 × Bandwidth
Multilevel: Data rate = 2 × Bandwidth × log 2 M
Example: M=4, Capacity = 4 × Bandwidth

16. Shannon’s Theorem Bandwidth = B Hz Signal-to-noise ratio = S/N
Maximum number of bits/sec = B log2 (1+S/N)
Example: Phone wire bandwidth = 3100 Hz
S/N = 30 dB
10 Log 10 S/N = 30
Log 10 S/N = 3
S/N = 1000
Capacity = 3100 log 2 (1+1000)
= 30,894 bps