some charts from stallings, modified and added to1 communications systems, signals, and modulation...
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Some charts from Stallings, modified and added to
1
Communications Systems, Signals, and Modulation
Session 3
Nilesh Jha
About Channel Capacity Impairments, such as noise, limit data rate
that can be achieved Channel Capacity – the maximum rate at
which data can be transmitted over a given communication path, or channel, under given conditions
Transmission Impairments Signal received may differ from signal
transmitted Analog - degradation of signal quality Digital - bit errors Caused by
Attenuation and attenuation distortion Delay distortion Noise
Attenuation Signal strength falls off with distance Depends on medium Received signal strength:
must be enough to be detected must be sufficiently higher than noise to
be received without error Attenuation is an increasing function
of frequency
Noise (1) Additional EM energy and signals on the
receiver Thermal -- usually inserted by receiver circuits
Due to thermal agitation of electrons Uniformly distributed White noise
Intermodulation Signals that are the sum and difference of
original frequencies sharing a medium, and falling within the desired signal’s passband
Noise (2) Crosstalk
A signal from one line or channel is picked up by another
Impulse Irregular pulses or spikes e.g. External electromagnetic interference Short duration High amplitude
Multipath See in later Sessions, causes distortions
Signal-to-Noise Ratio Ratio of the power in a signal to the power
contained in the noise that’s present at a particular point in the transmission
Typically measured at a receiver Signal-to-noise ratio (SNR, or S/N)
A high SNR means a high-quality signal, low number of required intermediate repeaters
SNR sets upper bound on achievable data rate
power noise
power signallog10)( 10dB SNR
Signals and Noise
High SNR
Lower SNR
Concepts Related to Channel Capacity
Data rate - rate at which data can be communicated (bps)
Bandwidth - the bandwidth of the transmitted signal as constrained by the transmitter and the nature of the transmission medium (Hertz)
Noise - average level of noise over the communications path
Error rate - rate at which errors occur Error = transmit 1 and receive 0; transmit 0 and receive
1
Nyquist Bandwidth For binary signals (two voltage levels)
C = 2B With multilevel signaling
C = 2B log2 M M = number of discrete signal or voltage levels
Shannon Capacity Formula Equation:
Represents theoretical maximum that can be achieved
In practice, somewhat lower rates achieved Formula assumes white noise (thermal noise)
Worse when other forms of noise are included Impulse noise Attenuation distortion or delay distortion Interference
SNR1log2 BC
Example of Nyquist and Shannon Formulations Spectrum of a channel between 3 MHz and
4 MHz ; SNRdB = 24 dB
Using Shannon’s formula
251SNR
SNRlog10dB 24SNR
MHz 1MHz 3MHz 4
10dB
B
Mbps88102511log10 62
6 C
Example of Nyquist and Shannon Formulations How many signaling levels are required?
16
log4
log102108
log2
2
266
2
M
M
M
MBC
Multiplexing Capacity of transmission medium usually
exceeds capacity required for transmission of a single signal
Multiplexing - carrying multiple signals on a single medium More efficient use of transmission medium
Multiplexing
Reasons for Widespread Use of Multiplexing Cost per kbps of transmission facility
declines with an increase in the data rate Cost of transmission and receiving
equipment declines with increased data rate Most individual data communicating
devices require relatively modest data rate support
Multiplexing Techniques Frequency-division multiplexing (FDM)
Takes advantage of the fact that the useful bandwidth of the medium exceeds the required bandwidth of a given signal --- different users at different frequency bands or subbands
Time-division multiplexing (TDM) Takes advantage of the fact that the achievable bit rate
of the medium exceeds the required data rate of a digital signal --- different users at different time slots
Frequency-division Multiplexing
Time-division Multiplexing
Multiplexing and Multiple Access Both refer to the sharing of a communications resource,
usually a channel Multiplexing usually refers to sharing some resource by
doing something at one site --- eg, at the multiplexer Often a static or pseudo-static allocation of fractions of the
multiplexed channel, eg, a T1 line. Often refers to sharing one resource. The division of the resource can be made on frequency, or time, or other physical feature
Multiple Access shares an asset in a distributed domain ie, multiple users at different places sharing an overall
media, and using a scheme where it is divided into channels based on frequency, or time or another physical feature
Usually dynamic
Factors Used to CompareModulation and Encoding Schemes
Signal spectrum With fewer higher frequency components, less bandwidth required ---
Spectrum Efficiency For wired comms: with no DC component, AC coupling via
transformer possible --- DC components cause problems Transfer function of a channel is worse near band edges -- always
better to constrain signal spectrum well inside the spectrum available Synchronization and Clocking
Determining when 0 phase occurs -- carrier synch Determining beginning and end of each bit position -- bit sync Determining frame sync --- usually layer above physical
Signal Modulation/Encoding Criteria: Demodulating/Decoding Accurately
What determines how successful a receiver will be in interpreting an incoming signal? Signal-to-noise ratio = SNR
signal power/noise power Note: power = energy per unit time
Data rate (R) Bandwidth (BW)
An increase in data rate increases bit error rate An increase in SNR decreases bit error rate An increase in bandwidth allows an increase in data
rate
Factors Used to CompareModulation/Encoding Schemes Signal interference and noise immunity ---
Performance in the presence of interference and noise For a given signal power level, the effect of noise and
interference is then labeled the Power Efficiency For digital modulation, Prob. Of Bit Error = function (SNR) where N
includes the interference terms More exactly, Prob. Bit Error = function (Energy per bit/Noise power
density, with noise including interference and other noise like terms) --- see next chart
Cost and complexity Usually the higher the signal and data rates require a higher
complexity and greater the cost
A Figure of Merit in Communications:Noise Immunity
For digital modulation one bottom line Figure of Merit (FOM) is Probability of Bit Error (Psub e) -- Lowest for Most Accurate Decoding of Bit Stream
Prob. Bit Error= function of (Eb/Nsub 0) Many functions for many different modulation and coding types have been
computed - usually decreases with increasing Eb/Nsub 0 Eb=energy per bit Nsub 0=noise spectral density; Noise Power N= (Nsub 0)* BW
Note: Includes Interference and Intermodulation and Crosstalk (Eb/Nsub 0) is a critically important number for digital comms Eb/Nsub0=(SNR)*(BW/R) ---- important formula -- derive it
SNR is signal to noise ratio, a ratio of power levels BW is signal bandwidth, R is data rate in bits/sec
For analog modulation the FOM is SNR Signal quality given by subjective statistical scores -- voice: 1-5 (high) FM requires a lower SNR than AM for the same signal quality
Basic Modulation/Encoding Techniques
Digital data to analog signal --- Digital Modulation Amplitude-shift keying (ASK)
Amplitude difference of carrier frequency Frequency-shift keying (FSK)
Frequency difference near carrier frequency Phase-shift keying (PSK)
Phase of carrier signal shifted
Basic Encoding Techniques
Amplitude-Shift Keying One binary digit represented by presence of
carrier, at constant amplitude Other binary digit represented by absence of
carrier
where the carrier signal is Acos(2πfct)
ts tfA c2cos0
1binary 0binary
Amplitude-Shift Keying Susceptible to sudden gain changes Inefficient modulation technique On voice-grade lines, used up to 1200 bps Used to transmit digital data over optical
fiber
Binary Frequency-Shift Keying (BFSK) Two binary digits represented by two different
frequencies near the carrier frequency
where f1 and f2 are offset from carrier frequency fc by equal but opposite amounts
ts tfA 12cos tfA 22cos
1binary 0binary
Binary Frequency-Shift Keying (BFSK) Less susceptible to error than ASK On voice-grade lines, used up to 1200bps Used for high-frequency (3 to 30 MHz)
radio transmission Can be used at higher frequencies on LANs
that use coaxial cable
Multiple Frequency-Shift Keying (MFSK) More than two frequencies are used More bandwidth efficient but more susceptible to
error
f i = f c + (2i – 1 – M)f d
f c = the carrier frequency f d = the difference frequency M = number of different signal elements = 2 L
L = number of bits per signal element
tfAts ii 2cos Mi 1
Multiple Frequency-Shift Keying (MFSK) To match data rate of input bit stream,
each output signal element is held for:Ts=LT seconds
where T is the bit period (data rate = 1/T)
So, one signal element encodes L bits
Multiple Frequency-Shift Keying (MFSK) Total bandwidth required
2Mfd
Minimum frequency separation required 2fd=1/Ts
Therefore, modulator requires a bandwidth of
Wd=2L/LT=M/Ts
Multiple Frequency-Shift Keying (MFSK)
Phase Shift Keying (PSK)
The signal carrier is shifted in phase according to the input data stream
2 level PSK, also called binary PSK or BPSK or 2-PSK, uses 2 phase possibilities over which the phase can vary, typically 0 and 180 degrees -- each phase represents 1 bit
can also have n-PSK -- 4-PSK often is 0, 90, 180 and 270 degrees --- each phase then represents 2 bits
Each phase called a ‘symbol’
Each bit or groups of bits can be represented by a phase value (eg, 0 degrees, or 180 degrees), or bits can be based on whether or not phase changes (differential keying, eg, no phase change is a 0, a phase change is a 1) --- DPSK
Phase-Shift Keying (PSK) Two-level PSK (BPSK)
Uses two phases to represent binary digits
ts tfA c2cos tfA c2cos
1binary 0binary
tfA c2cos
tfA c2cos1binary 0binary
Phase-Shift Keying (PSK) Differential PSK (DPSK)
Phase shift with reference to previous bit Binary 0 – signal burst of same phase as previous
signal burst Binary 1 – signal burst of opposite phase to previous
signal burst
Phase-Shift Keying (PSK) Four-level PSK (QPSK)
Each element represents more than one bit
ts
42cos
tfA c 11
4
32cos
tfA c
4
32cos
tfA c
42cos
tfA c
01
00
10
Quadrature PSK More efficient use by each signal element (or
symbol) representing more than one bit e.g. shifts of /2 (90o) In QPSK each element or symbol represents two bits Can use 8 phase angles and have more than one amplitude
-- then becomes QAM then (combining PSK and ASK) QPSK used in different forms in a many cellular digital
systems Offset-QPSK: O-QPSK: The I (0 and 180 degrees) and Q (90 and
270 degrees) quadrature bits are offset from each other by half a bit --- becomes a more efficient modulation, with phase changes not so abrupt so better spectrally, and more linear
Pi/4-QPSK is a similar approach to O-QPSK, also used
Multilevel Phase-Shift Keying (MPSK)
Multilevel PSK Using multiple phase angles multiple signals
elements can be achieved
D = modulation rate, baud R = data rate, bps M = number of different signal elements or symbols = 2L
L = number of bits per signal element or symbol eg, 4-PSK is QPSK, 8-PSK, etc
M
R
L
RD
2log
Quadrature Amplitude Modulation
QAM is a combination of ASK and PSK Two different signals sent simultaneously on
the same carrier frequency
tftdtftdts cc 2sin2cos 21
Quadrature Amplitude Modulation
Quadrature Amplitude Modulation (QAM)
The most common method for quad (4) bit transfer
Combination of 8 different angles in phase modulation and two amplitudes of signal
Provides 16 different signals (or ‘symbols’), each of which can represent 4 bits (there are 16 possible 4 bit combinations)
90
45
0
135
180
225
270
315
amplitude 1
amplitude 2
Quadrature Amplitude Modulation Illustration -- example of Constellation Diagram
Notice that there are16 circles or nodes, eachrepresents a possible amplitude and phase, and each represents 4 bits
Obviously there are manysuch constellation diagramspossible --- the technicalissue winds up being thatas the nodes get closer toeach other any noise can lead to the receiver confusingthem, and making a bit error
Performance of Digital Modulation Schemes
Bandwidth or Spectral Efficiency ASK and PSK bandwidth directly related to bit rate FSK bandwidth related to data rate for lower
frequencies, but to offset of modulated frequency from carrier at high frequencies
Determined by C/BW ie bps/Hz Noise Immunity or Power Efficiency: In the
presence of noise, bit error rate of PSK and QPSK are about 3dB superior to ASK and FSK ---- ie, x2 less power for same performance Determined by BER as function of Eb/Nsub0
Spectral Performance
Bandwidth of modulated signal (BT) ASK, PSK BT=(1+r)R
FSK BT=2DF+(1+r)R
R = bit rate 0 < r < 1; related to how signal is filtered DF = f2-fc=fc-f1
SPECTRAL Performance Bandwidth of modulated signal (BT)
MPSK
MFSK
L = number of bits encoded per signal element M = number of different signal elements
RM
rR
L
rBT
2log
11
R
M
MrBT
2log
1
In Stallings
In Stallings
By Sklar, from Gibson
Power-Bandwidth Efficiency Plane
Analog Modulation Techniques Analog data to analog signal Also called analog modulation
Amplitude modulation (AM) Angle modulation
Frequency modulation (FM) Phase modulation (PM)
AM MODULATION
Top left: source (baseband) signal to be modulated; bottom left: modulated signal, carrier lines inside white; right: demodulated after it is transmitted and received (note after 1.e-3 similarity except for attenuation)
Input Voice and Received Voice after Transmission and Reception, Using FM --- Only a Little Noise -- Notice Similarity
Input Voice and Received Voice after Transmission and Reception, Using FM --- Lots More Noise in Channel -- Notice that Received Signal is NOT What Was Transmitted
Amplitude Modulation
tftxnts ca 2cos1
Amplitude Modulation
cos2fct = carrier x(t) = input signal na = modulation index
Ratio of amplitude of input signal to carrier
a.k.a double sideband transmitted carrier (DSBTC)
Spectrum of AM signal
Amplitude Modulation Transmitted power
Pt = total transmitted power in s(t)
Pc = transmitted power in carrier
21
2a
ct
nPP
Single Sideband (SSB) Variant of AM is single sideband (SSB)
Sends only one sideband Eliminates other sideband and carrier
Advantages Only half the bandwidth is required Less power is required
Disadvantages Suppressed carrier can’t be used for synchronization
purposes
Angle Modulation Angle modulation
Phase modulation Phase is proportional to modulating signal
np = phase modulation index
ttfAts cc 2cos
tmnt p
Angle Modulation Frequency modulation
Derivative of the phase is proportional to modulating signal
nf = frequency modulation index
tmnt f'
Angle Modulation Compared to AM, FM and PM result in a
signal whose bandwidth: is also centered at fc
but has a magnitude that is much different Angle modulation includes cos( (t)) which
produces a wide range of frequencies
Thus, FM and PM require greater bandwidth than AM
Angle Modulation Carson’s rule
where
The formula for FM becomes
BBT 12
BFBT 22
FMfor
PMfor
2
B
An
B
F
An
mf
mp
Coding Encoding sometimes is used to refer to the way in which analog
data is converted to digital signals eg, A/D’s, PCM or DM
Source Coding refers to the way in which basic digitized analog data can be compressed to lower data rates without loosing any or to much information -- eg, voice, video, fax, graphics, etc.
Channel coding refers to signal transformations used to improve the signal’s ability to withstand the channel propagation impairments --- two types
waveform coding --- transforms signals (waveforms) into better ones --- able to withstand propagation errors better --- this refers to different modulation schemes, M’ary signaling, spread spectrum
Sequence coding, also generally labelled error coding or FEC, transforms data bits sequences into ones less error prone, by inserting redundant bits in a smart way -- eg, block and convolutional codes
Basic Encoding Techniques Analog data to digital signal Used for digitization of analog sources
Pulse code modulation (PCM) Delta modulation (DM)
After the above, usually additional processing done to compress signal to achieve similar signal quality with fewer bits --- called source coding
Analog to Digital Conversion Once analog data have been converted to
digital signals, the digital data: can be transmitted using NRZ-L can be encoded as a digital signal using a code
other than NRZ-L can be modulated to an analog signal for
wireless transmission, using previously discussed techniques
Pulse Code Modulation Based on the sampling theorem Each analog sample is assigned a binary
code Analog samples are referred to as pulse
amplitude modulation (PAM) samples The digital signal consists of block of n bits,
where each n-bit number is the amplitude of a PCM pulse
Pulse Code Modulation
Pulse Code Modulation By quantizing the PAM pulse, original
signal is only approximated Leads to quantizing noise Signal-to-noise ratio for quantizing noise
Thus, each additional bit increases SNR by 6 dB, or a factor of 4
dB 76.102.6dB 76.12log20SNR dB nn
Delta Modulation Analog input is approximated by staircase
function Moves up or down by one quantization level
() at each sampling interval The bit stream approximates derivative of
analog signal (rather than amplitude) 1 is generated if function goes up 0 otherwise
Delta Modulation
Delta Modulation Two important parameters
Size of step assigned to each binary digit () Sampling rate
Accuracy improved by increasing sampling rate However, this increases the data rate
Advantage of DM over PCM is the simplicity of its implementation
Source Coding Voice or Speech or Audio
Basic PCM yields 4 KHz*2 samples/Hz*8 bits/sample=64 Kbps -- music/etc up to 768 Kbps
Coding can exploit redundancies in the speech waveform -- one way is LPC, linear predictive coding --- predicts what’s next, sends only the changes expected
RPE and CELP (Code Excited LPC) used in cell phones, using LPC, at rates of 4 to 9.6 to 13 kbps
Graphics and Video: eg, JPEG or GIF, MPEG
Reasons for Growth of Digital Modulation and Transmission Growth in popularity of digital techniques for sending analog or
digital source data Cheaper components used in creating the modulations and doing the
encoding, and similarly on the receivers Best performance in terms of immunity to noise and in terms of spectral
efficiency --- improved digital modulation and channel coding techniques Great improvements in digital voice and video compression
Voice to about 8 Kbps at good quality, video varies to below 1 Mbps provide increased capacity in terms of numbers of users in given BW
Dynamic and efficient multiple access and multiplexing techniques using TDM, TDMA and CDMA, even when some larger scale Frequency Allocations (FDMA) -- labeled as combinations
Easier and simpler implementation interfaces to the digital landline networks and IP
Duplex Modes Duplex modes refer to the ways in which two way traffic is arranged One way vs two way:
simplex (one way only), half duplex (both ways, but only one way at a time), duplex (two ways at the same time)
If duplex, question is then how one separates the two ways In wired systems, it could be in different wires (or cables, fibers, etc) Both wired and wireless one way is to separate the two paths in frequency ---
FDD, frequency division duplex If two frequencies, or frequency bands, are separate enough, no cross interference Cellular systems are all FDD It’s clean and easy to do, good performance, but it limits channel assignments and is
not best for asymmetric traffic TDD is time division duplex, same frequencies are used both ways, but time slots
are assigned one way or the other Good for asymmetrical traffic, allows more control through time slot reassignments But strong transmissions one way could interfere with other users Mostly not used in cellular, but 3G has one such protocol, and low tier portables also
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