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

Electrical Electrical Communications SystemsCommunications Systems

ECE.09.331ECE.09.331 Spring 2010Spring 2010

Shreekanth MandayamECE Department

Rowan University

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

Lecture 7aLecture 7aMarch 2, 2010March 2, 2010

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

PlanPlan• Complex Envelope Representation

• Spectrum of a bandpass signal

• DSB-SC Modulation

• Costas Loop• QAM• SSB

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 Envelope

Gaussian 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 & Phase M odulationNarrowband/WidebandVCO & Slope Detector

PLL

Analog

Source EncodingHuffm an codes

Error-control EncodingHam m ing Codes

Sam plingPAM

QuantizationPCM

Line Encoding

Tim e Division M uxT1 (DS1) Standards

Packet Sw itchingEthernet

ISO 7-Layer Protocol

BasebandCODEC

ASKPSKFSK

BPSK

QPSK

M -ary PSK

QAM

BandpassM ODEM

DigitalDigital Com m Transceiver

Systems

Electrical Comm unication Systems

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

DSB-SC ModulationDSB-SC Modulation

Signals SystemsTime DomainComplex EnvelopeSpectrumPower

PerformanceTransmittersReceiversStandards

Modulation IndexEfficiencyBandwidthNoise

-B 0 +B

|M(f)|

f

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

|S(f)|

f

Message Spectrum

DSB-SC Spectrum

Matlab Demo

http://engineering.rowan.edu/~shreek/spring10/ecomms/demos/dsbsc.m

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

DSB-SC: Coherent DetectorDSB-SC: Coherent Detector

ProductModulator

Aocos2fct

s(t)

LocalOscillator

BasebandLPF

v(t)(t)m~

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

Synchronous Coherent Synchronous Coherent Detection: Costas PLLDetection: Costas PLL

s(t)

v1(t) (t)m~ProductModulator

BasebandLPF

VCO LPF

-90o

Phase Shift

X

v2(t)

ProductModulator

BasebandLPF

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

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

ProductModulator

m(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

SummarySummary