S. Mandayam/ ECOMMS/ECE Dept./Rowan University

Electrical Electrical Communications SystemsCommunications Systems

ECE.09.331ECE.09.331 Spring 2010Spring 2010

Shreekanth MandayamECE DepartmentRowan University

http://engineering.rowan.edu/~shreek/spring10/ecomms/

Lecture 7bLecture 7bMarch 3, 2010March 3, 2010

S. Mandayam/ ECOMMS/ECE Dept./Rowan University

PlanPlan• Recall: Costas Loop• QAM• Complex Envelope• SSB Modulation

• Angle Modulation Systems• Definitions - Phase and Frequency Modulation

• Complex Envelope• Time Domain

• Analyzing FM Signals - Battle Plan!!!!

Signals SystemsTime DomainComplex EnvelopeSpectrumPower

PerformanceTransmittersReceiversStandards

Modulation IndexEfficiencyBandwidthNoise

S. Mandayam/ ECOMMS/ECE Dept./Rowan University

ECOMMS: TopicsECOMMS: Topics

Probability

Inform ation

Entropy

Channel Capacity

Discrete

Pow er & Energy Signals

Continuous Fourier Transform

Discrete Fourier Transform

Baseband and Bandpass Signals

Com plex E nvelope

G aussian Noise & SNR

Random VariablesNoise Calculations

Continuous

Signals

AMSw itching M odulator

Envelop Detector

DSB-S CProduct M odulatorCoherent Detector

Costas Loop

SSBW eaver's MethodPhasing M ethod

Frequency M ethod

Frequency & P hase M odulationNarrow band/W idebandVCO & Slope Detector

P LL

Analog

Source EncodingHuffm an codes

E rror-control EncodingHamm ing Codes

Sam plingPAM

Q uantizationPCM

Line Encoding

Tim e Divis ion M uxT1 (DS 1) S tandards

Packet Sw itchingEthernet

ISO 7-Layer Protocol

BasebandCO DE C

ASKPSKFSK

BPSK

Q PSK

M -ary PSK

Q AM

BandpassM O DEM

DigitalDigita l Com m Transceiver

Systems

Electrical Comm unication Systems

S. Mandayam/ ECOMMS/ECE Dept./Rowan University

Recall: Costas PLLRecall: Costas PLL

s(t)

v1(t) (t)m~ProductModulator

BasebandLPF

VCO LPF

-90o

Phase Shift

X

v2(t)Product

ModulatorBaseband

LPF

v3(t)v4(t)

PhaseDiscriminator

I-Channel

Q-Channel

S. Mandayam/ ECOMMS/ECE Dept./Rowan University

Quadrature Amplitude Quadrature Amplitude Modulation (QAM)Modulation (QAM)

ProductModulator

LocalOscillator

-90o

Phase Shift

ProductModulator

m1(t)

m2(t)

s(t) ProductModulator

LocalOscillator

-90o

Phase Shift

ProductModulator

LPF

LPF

(t)1m~

(t)2m~

Tx RxI-Channel

Q-Channel

S. Mandayam/ ECOMMS/ECE Dept./Rowan University

Complex Envelope RepresentationComplex Envelope Representation

• We want a common mathematical representation for• information transfer from baseband to bandpass• any bandpass signal• any time of modulation• signal/noise and signal+noise

Modulatormessage: m(t)

carrier: c(t)s(t): radio signal

S. Mandayam/ ECOMMS/ECE Dept./Rowan University

Spectrum of a Bandpass Spectrum of a Bandpass SignalSignal

S. Mandayam/ ECOMMS/ECE Dept./Rowan University

Single Sideband (SSB) Single Sideband (SSB) ModulationModulation

• Recall: DSB-SC Spectrum

• USSB - Signal with zero-valued spectrum for |f| < fc

• LSSB - Signal with zero-valued spectrum for |f| > fc

-fc-B -fc -fc+B 0 fc-B fc fc+B

|S(f)|

f

S. Mandayam/ ECOMMS/ECE Dept./Rowan University

The Hilbert TransformThe Hilbert Transform

-1

-0.5

0

0.5

1

1.5

0 1 2 3 4 5 6 7

time, t in sec

(t)w(t)w » t=0:0.1:2*pi;» w=sin(t);» plot(t,w)» holdCurrent plot held» H=hilbert(w);» plot(t,imag(H),'r');» xlabel('time, t in sec')

S. Mandayam/ ECOMMS/ECE Dept./Rowan University

SSB GenerationSSB Generation

ProductModulator

Carrier -90o

Phase Shift

ProductModulator

-90o

Phase Shift

m(t) s(t)

SidebandFilter

Carrier

ProductModulatorm(t) s(t)

Phasing Method

Filter Method

S. Mandayam/ ECOMMS/ECE Dept./Rowan University

SSB Generation: SSB Generation: Weaver’s MethodWeaver’s Method

S. Mandayam/ ECOMMS/ECE Dept./Rowan University

ECOMMS: Topics

Probability

Inform ation

Entropy

Channel Capacity

Discrete

Pow er & Energy Signa ls

Continuous Fourier Transform

Discrete Fourier Transform

Baseband and Bandpass Signals

Com plex Envelope

G aussian Noise & SNR

Random VariablesNoise Calcula tions

Continuous

Signals

AMSw itching M odulator

Envelop Detector

DSB-S CProduct M odulatorCoherent Detector

Costas Loop

SSBW eaver's M ethodPhasing M ethod

Frequency M ethod

Frequency & Phase M odulationNarrow band/WidebandVCO & S lope Detector

PLL

Analog

Source EncodingHuffman codes

Error-control EncodingHam m ing Codes

Sam plingPAM

QuantizationPCM

Line E ncoding

Tim e Division M uxT1 (DS1) S tandards

Packet Sw itchingEthernet

IS O 7-Layer Protocol

BasebandCO DEC

AS KPS KFSK

BPSK

Q PSK

M -ary P SK

QAM

BandpassM O DEM

DigitalDigital Comm Transceiver

Systems

Electrical Comm unication Systems

S. Mandayam/ ECOMMS/ECE Dept./Rowan University

Angle Modulation Systems

• Signal Representation• Complex Envelope• Time Domain Representation

• Terminology• Phase Sensitivity• Frequency Deviation• Instantaneous Frequency• Phase & Frequency Modulation Indices

Phase Modulation (PM) Frequency Modulation(FM)

Matlab Demo:anglemod.m

Instrument Demo

S. Mandayam/ ECOMMS/ECE Dept./Rowan University

Angle Modulation Systems

• Signal Representation• Complex Envelope• Time Domain Representation

• Terminology• Phase Sensitivity• Frequency Deviation• Instantaneous Frequency• Phase & Frequency Modulation Indices

Phase Modulation (PM) Frequency Modulation(FM)

Matlab Demo:anglemod.m

Instrument Demo

S. Mandayam/ ECOMMS/ECE Dept./Rowan University

Analyzing FM Signals - Battle Plan!!!Instrument Demo

Signals SystemsTime Domain

Complex Envelope

Spectrum• Single-tone FM

• Narrowband FM• Wideband FM

• Bessel FunctionsPower

Performance

Transmitters

Receivers

Standards

Modulation Index

Efficiency

Bandwidth

Noise

S. Mandayam/ ECOMMS/ECE Dept./Rowan University

SummarySummary