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 in Communications Signals

and Single Sideband

7/22/2010

1

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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2

Standard Representation of Communications Signals

Modulation Time Domain Frequency Domain

AM

DSB

FM

XAM(f)

f-fc fc

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3

Overview of I and Q Representation

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

Complete description of a signal is:

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

Phase angle is not absolute, but relates to some arbitrary reference.

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

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Overview of I and Q Representation

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

DSP relies heavily on I and Q signals for processing. Use of I and Q allows for processing of signals near DC 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 to baseband we ONLY get the sum

This avoids problems with images

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Overview of I and Q Representation

Nyquist frequency is twice highest frequency, not twice bandwidth of signal.

For example: common frequency used in analog signal processing is 455 kHz. To sample in digital processing, requires 910 kS/s. But if the signal bandwidth is only 10 kHz. With I & Q, sampling requires only 20 kS/s.

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Overview of I and Q Representation

I and Q allows discerning of positive and negative frequencies.

If :

Then:

( )H f a jb

( )H f a jb

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Overview of I and Q Representation

Representing familiar characteristics of a signal with I and Q:

• Amplitude:

• Phase:

• Frequency:

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

1 ( )( ) tan

( )

Q tt

I t

2 2

( ) ( )( ) ( )

( )( )

( ) ( )

Q t I tI t Q t

t t tf tt 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 tx t

t i t i t q t q t

1 ( )( ) tan

( )

q tx t

i t

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Overview of I and Q Representation

The traditional FM equation:

The analytic equation:

Modulation and Demodulation methods are different when 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 ωc t

sin ωc t

LPF

LPF

ADC

ADC

AMP

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11

FPGA

I

Q

complexmultiply

sin ωf tn

cos ωf tn

decimate

decimate

n = sample number

I

Q

To USB and PC

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Complex Multiply

I

Qcos (ωf tn )

cos (ωf tn )I

Q

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

I + j Qcosft +

sinft 7/22/2010

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Sideband Modulation

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Where’s the intelligence?

A signal carries useful information only when it changes.

Change of ANY carrier parameter produces sidebands.

The intelligence or information is in the sidebands.

Why not just send the sidebands or just a sideband?

14

AM Review

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AM review:

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

Block Diagram

m x +

Accosct

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

15

AM: Time Domain

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AM in the Time Domain

Unmodulatedcarrier

100% modulated carrier

16

AM: Frequency Domain

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AM in the Frequency Domain

carrier

upper sideband

lower sideband

17

Double Sideband Modulation (DSB)

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Let’s just transmit the sidebands

m x

Accosct

x(t) +

X

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

18

DSB: Time Domain

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Double Sideband in the Time Domain

19

DSB: Frequency Domain

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Double Sideband in the Frequency Domain

carrier was here

upper sideband

lower sideban

d

20

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

upper sideband

lower sideband

22

SSB Signals

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

x

Accosct

x(t)Lower

Sideband Filter

Low Pass Filter

f

f f

f

23

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 of DSB

Complexity: SSB modulators/demodulators are more complex

25

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 ωc t

sin ωc t

LPF

LPF

ADC

ADC

AMP

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SSB Example

I

Q

cos ωc t

sin ωc t

LPF

LPF

ADC

ADC

AMP

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SSB Example

I

Q

cos ωc t

sin ωc t

LPF

LPF

ADC

ADC

AMP

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SSB Example

I

Q

cos ωc t

sin ωc t

LPF

LPF

ADC

ADC

AMP

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SSB Example

I

Q

cos ωc t

sin ωc t

LPF

LPF

ADC

ADC

AMP

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SSB Example

I

Q

complexmultiply

sin ωf tn

cos ωf tn

decimate

decimate

n = sample number

I

Q

To USB and PC

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SSB Example

I

Q

complexmultiply

sin ωf tn

cos ωf tn

decimate

decimate

n = sample number

I

Q

To USB and PC

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SSB Example

I

Q

complexmultiply

sin ωf tn

cos ωf tn

decimate

decimate

n = sample number

I

Q

To USB and PC

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SSB Example

I

Q

complexmultiply

sin ωf tn

cos ωf tn

decimate

decimate

n = sample number

I

Q

To USB and PC

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Practical SSB Reception

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37

Example above assumed no other signals on the band and perfectly synchronized oscillators

Need to isolate (filter) the signal of interest and deal with oscillators slightly out of sync

GRC tutorial demonstrates Weaver’s Method of demodulating SSB that solves these problems