IandQ and Sideband 7 10

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S H A R L E N E K A T Z

D A V I D S C H W A R T Z

J A M E S F L Y N N

I and Q Components inCommunications Signals

and Single Sideband

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OVERVIEW

Description of I and Q signal representation

Advantages of using I and Q components

Using I and Q to demodulate signals

I and Q signal processing in the USRP Single Sideband (SSB)

Processing I and Q components of a SSB signal in the

USRP

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Standard Representation of CommunicationsSignals

Modulation Time Domain Frequency Domain

AM

DSB

FM

XAM(f)

f

-fc fc

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Overview of I and Q Representation

I and Q are the In-phase and Quadraturecomponents of a signal.

Complete description of a signal is:

x(t) can therefore be represented as a vector withmagnitude and phase angle.

Phase angle is not absolute, but relates to somearbitrary reference.

( ) ( ) ( )x t I t jQ t

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In Digital Signal Processing (DSP), ultimatereference is local sampling clock.

DSP relies heavily on I and Q signals for processing.

Use of I and Q allows for processing of signals nearDC or zero frequency. If we use real signals (cosine) to shift a modulated signal to

baseband we get sum and difference frequencies

If we use a complex sinusoid to shift a modulated signal tobaseband we ONLY get the sum

This avoids problems with images

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Nyquist frequency is twice highest frequency, nottwice bandwidth of signal.

For example: common frequency used in analog

signal processing is 455 kHz. To sample in digitalprocessing, requires 910 kS/s. But if the signalbandwidth is only 10 kHz. With I & Q, samplingrequires only 20 kS/s.

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I and Q allows discerning of positive and negativefrequencies.

If :

Then:

( )H f a jb

( )H f a jb

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Representing familiar characteristics of a signal with Iand Q:

Amplitude:

Phase:

Frequency:

2 2( ) ( ) ( )A t I t Q t

1 ( )( ) tan( )

Q tt

I t

2 2

( ) ( )( ) ( )( )

( )( ) ( )

Q t I t I t Q tt t tf t

t I t Q t

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DEMODULATION

AM:

SSB:

FM:

PM:

2 2( ) ( ) ( )x t i t q t

( ) ( )x t i t

11 ( ) ( 1) ( ) ( 1)( ) tan( ) ( 1) ( ) ( 1)

i t q t q t i t x t

t i t i t q t q t

1 ( )( ) tan ( )

q tx t i t

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The traditional FM equation:

The analytic equation:

Modulation and Demodulation methods are differentwhen I and Q representation is used

( ) cos( ( ) )FM c mx t t k x t dt

( ) ( ) cos( ) ( )sin( )FM c cx t I t t jQ t t

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USRP DAUGHTER BOARD

I

Q

cos c t

sin c t

LPF

LPF

ADC

ADC

AMP

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FPGA

I

Q

complexmultiply

sin ftn

cos ftn

decimate

decimate

n = samplenumber

I

Q

To USBand PC

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Complex Multiply

I

Qcos (ftn )

cos (ftn )I

Q

(A + j B) * (C + j D) = AC BD + j (BC + AD)

I + j Q

cosft +

sinft 7/22/2010

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Sideband Modulation

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Wheres the intelligence?

A signal carries useful information only when it changes.

Change ofANYcarrier parameter produces sidebands.

The intelligence or information is in the sidebands.

Why not just send the sidebands or just a sideband?

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AM Review

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AM review:

Carrier is modulated by varying amplitude linearlyproportional to intelligence (baseband) signal amplitude.

Block Diagram

m x +

Accosct

x(t) xAM(t)=Ac [1+mx(t)]cosct

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AM: Time Domain

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AM in the Time Domain

Unmodulated

carrier

100% modulatedcarrier

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AM: Frequency Domain

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AM in the Frequency Domain

carrier

uppersideband

lowersideband

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Double Sideband Modulation (DSB)

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Lets just transmit the sidebands

m x

Accosct

x(t) +

X

xDSB(t) = Ac*m*x(t)*cosct

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DSB: Time Domain

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Double Sideband in the Time Domain

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DSB: Frequency Domain

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Double Sideband in the Frequency Domain

carrier was here

uppersideband

lowersideban

d

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Example of a DSB Signal

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DSB Spectrum

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Note: the upper and lower sidebands are the same

Do we need both of them?carrier was here

uppersideband

lowersideband

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SSB Signals

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A sideband signal is obtained by adding a sidebandfilter to capture the upper or lower sideband.

x

Accosct

x(t)Lower

SidebandFilter

Low Pass Filter

f

f f

f

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Example of a USB Signal

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Comparison of DSB and SSB

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Power: SSB requires half of the power of DSB

Bandwidth: SSB requires half of the bandwidth ofDSB

Complexity: SSB modulators/demodulators aremore complex

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SSB Example

Start with arbitrary waveform in baseband:

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SSB Example

Modulate as Upper Sideband Signal:

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SSB Example

I

Q

cos c t

sin c t

LPF

LPF

ADC

ADC

AMP

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SSB Example

I

Q

cos c t

sin c t

LPF

LPF

ADC

ADC

AMP

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SSB Example

I

Q

cos c t

sin c t

LPF

LPF

ADC

ADC

AMP

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SSB Example

I

Q

cos c t

sin c t

LPF

LPF

ADC

ADC

AMP

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SSB Example

I

Q

cos c t

sin c t

LPF

LPF

ADC

ADC

AMP

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SSB Example

I

Q

complexmultiply

sin ftn

cos ftn

decimate

decimate

n = samplenumber

I

Q

To USBand PC

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SSB Example

I

Q

complexmultiply

sin ftn

cos ftn

decimate

decimate

n = samplenumber

I

Q

To USBand PC

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SSB Example

I

Q

complexmultiply

sin ftn

cos ftn

decimate

decimate

n = samplenumber

I

Q

To USBand PC

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SSB Example

I

Q

complexmultiply

sin ftn

cos ftn

decimate

decimate

n = samplenumber

I

Q

To USBand PC

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Practical SSB Reception

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Example above assumed no other signals on theband and perfectly synchronized oscillators

Need to isolate (filter) the signal of interest and deal

with oscillators slightly out of sync GRC tutorial demonstrates Weavers Method of

demodulating SSB that solves these problems

IandQ and Sideband 7 10

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