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