fred harris

30 November - 3 December 2010

MODEMS

http://www.sdsu.edu/

What The Customer Wants

What The Customer Expects to Pay

MO R EMO R E

MO R EMO R E

MO R E MO R E MO R E MORE MO R E

MO RE

MO R E

MOREMORE

MORE MORE

MORE

MORE MORE MORE

MORE MORE

MOREMORE

MORE MORE

MOREMORE

MORE MORE

MOREMORE

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MORE

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MORE

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MORE

M MO

O

R

RE

E

MORE

MORE

MORE

S LESSS LESSS EVEN

LESS

When The Customer Wants it

MO R EMO R E

MO R EMO R E

MO R E MO RE MO R E MORE MO R E

MO RE

MO R E

MOREMORE

MORE MORE

MORE

MORE MORE MORE

MORE MORE

MOREMORE

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MOREMORE

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MOREMORE

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M MO

O

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NEXTWEEKTOMORROW THISAFTERNOON

What Size Customer Wants

Why Digital Communications?

But Let Your Communications Be

Yea, Yea: Nay, Nay:

Sermon on the Mount,

Matthew, Ch. 5, verse. 37

For What So Ever is More Than

These Cometh of Evil.

To Paraphrase

the Great Bard

The World is an Analog Stage

In Which Digital

Plays A Bit Part

The Basic Communication System

MODULATORINFORMATION SOURCE

INFORMATION DESTINATION

DEMODULATORCHANNEL

BANDLIMITED

AWGN

fx

AmplitudeDistribution

SpectralDistribution

The Radio Channel Frequency Band

VLF LF MF HF VHF UHF SHF EHF Infrared Visible Light

10kHz

1MHz

100MHz

100kHz

10MHz

1GHz

10GHz

100GHz

30km

3km

300 m

30 m

3m

30cm

3cm

3mm

The Electromagnetic Spectrum

Visible Light

Radio Microwave Infrared UV X-Ray Gamma Ray

1010 10 10 10 10 10 10 10 10 10 10 101026242220181614121086420f(Hz)

f(Hz)FiberSatellite

TerrestrialMicrowave FM

Radio AMRadio

Twisted Pair

Coax

Maritime

TV

Optics

Band LF MF HF VHF UHF SHF EHF THF

10 10 10 10 10 10 10 10 10 10 10 10 1016151413121110987654

Spectral Utilization

Band Frequency Wavelength Some Uses

VLF 3 - 30 kHz 100 km - 10 kmLong range navigation and marine

radio

LF 30 - 300 kHz 10 km - 1 km Aeronautical and marine navigation

MF 300 kHz - 3 MHz 1 km - 100 mAM radio and radio

telecommunication

HF 3 - 30 MHz 100 m - 10 m Amateur radio bands, NRC time signal

VHF 30 - 300 MHz 10 m - 1 mTV, FM, cordless phones, air traffic

control

UHF 300 MHz - 3 GHz 1 m - 10 cm UHF TV, satellite, air traffic radar, etc

SHF 3 - 30 GHz 10 cm - 1 cm Mostly satellite TV and other satellites

EHF 30 - 300 GHz 1 cm - 1 mm Remote sensing and other satellites

Radio Spectrum

Radio Spectrum Wavelength

Parts of the Electromagnetic Spectrum

The ISM bands in the United States.

...

...

...

...

Bandwidth

26MHz

83.5MHz

125MHz

Freq 902MHz

928MHz

2.42 GHz

2.4835 GHz

5.735 GHz

5.860 GHz

Cross-Over Probabilities0

0

0

0

0

0

0

0

0

1

1

1

11

1

1

1

1

2

23 3

4

4

e

p(0|0)

p(0|0)

p(1|1)

p(1|1)

p(1|0)

p(1|0)

p(0|1)

p(0|1)

p(e|1)

p(e|0)e

ES/N0 Required for Specified BER

QPSK, 16-QAM, & 64-QAM Constellations

for 10-5 BER

Spectral Levels of Signal and Noise for QPSK,

16-QAM, & 64-QAM for 10-5 BER

Channel Coding:

Add Structured Redundancy

Source

Source

Source

Source

Source

Source

ChannelEncoder

ChannelEncoder

ChannelDecoder

ChannelDecoder

Modulator

Modulator

Modulator

Demodulator

Demodulator

Demodulator

Channel

Channel

Channel

1

1 1

1

1

1

0

0

0

e1

1 1

1

1

1 11 1

1

1

e0

0 0

0

0

0 0

0

0

e1

1 1

1

1

1 1

1

1

e1

0 00 0

1

x x

Super Channel

Bit Error Performance Waterfall

Other Channel Impairments

ChannelIn

In

Out

Out

f f fff

G( ) C( )

Gain PhaseDistortion

fixedfrequency offset

FadingFreq Dep Flat

Non Uniform Gain Amplitude- to-Phase

doppler

interefernce

noise

t

Modern Physical Layer Modem Recipe:

Add these Ingredients, Stir, Bake for 20 Minutes at 300o.

Let Cool! Enjoy your Modem!

First Tier Processing: Modulation and Demodulation Shaping Filters

Spectral Translation

Signal Conversion

Second Tier Processing: Parameter Estimation Carrier Frequency and Phase Synchronization

Timing Frequency and Phase Synchronization

Automatic Gain Control

SNR Estimate

Third Tier Processing: Channel and Hardware (Dirty RF) Equalization

I-Q Balance

DC-Cancel

Peak-to-Average Ratio Control

Predistortion

Interference Suppression

Intrusion Suppression

Diversity

http://schools-demo.clipart.com/search/close-up?oid=3786885&q=witches&s=1&a=a&cid=&fic=0

Modulator and Demodulator

DATATRANSFORMS

WAVEFORMTRANSFORMS

SPECTRALTRANSFORMS

BITS

M-ARYALPHABET

BASEBANDWAVEFORM

RADIOFREQUENCYWAVEFORM

DIGITAL ANALOG

MODULATOR

MODULATOR CHANNEL DEMODULATORBITS RF RF BITS

DATATRANSFORMS

WAVEFORMTRANSFORMS

SPECTRALTRANSFORMS

BITS M-ARYALPHABET

BASEBANDWAVEFORM

RADIOFREQUENCYWAVEFORM

DIGITALANALOG

DEMODULATOR

Claude Shannon

Information is measurable.

Noise Does not Limit Fidelity.

'The world has only 10

kinds of people.

Those who get binary,

and those who don't.'

DISCRETE CHANNEL DIGITALMODULATOR

DIGITALDEMODULATOR

BITS

M-ARYALPHABET

M-ARYALPHABET

DATATRANSFORMS

WAVEFORMTRANSFORMS

SPECTRALTRANSFORMS

SPECTRALTRANSFORMS

WAVEFORMTRANSFORMS

DATATRANSFORMS

BASEBANDWAVEFORM

RF

CH

AN

NEL

RF

BASEBANDWAVEFORM

BITS

Shannon’s Communication System

Shannon’s Model

BITS

BITS

BANDWIDTH REDUCING

BANDWIDTHPRESERVING

BANDWIDTHEXPANDING

CH

AN

NEL

SOURCEENCODING

CHANNELENCODING

CHANNELDECODING

SOURCEDECODING

ENCRYPTION

DECRYPTION

Shannon’s Legacy

Communication System Resources

Bandwidth

Signal to Noise Ratio

Memory and Computations

A Communication System needs a

Computer in Modulator and Demodulator!

We have a Computer on Board!

We can use it to do some other Heavy Lifting!

Four Pillars of Modern Communications

BAN

DW

IDTH

SIG

NAL t

o N

OIS

E R

ATIO

DATA T

RAN

SFO

RM

S

SIG

NAL T

RAN

SFO

RM

S

MODERN

COMMUNICATIONS

The Modulator Digital to Analog

Interface Moves Towards the RF

BASEBAND

BASEBAND

BASEBAND

RF

RF

RF

M-ARY

M-ARY

M-ARY

TUNER

TUNER

TUNER

ANALOG

ANALOG

ANALOG

DIGITAL

DIGITAL

DIGITAL

SIGNALCONDITIONER

SIGNALCONDITIONER

SIGNALCONDITIONER

The Demodulator Analog to Digital

Interface Moves Towards the RFBASEBAND

BASEBAND

BASEBAND

RF

RF

RF

M-ARY

M-ARY

M-ARY

ANALOG

ANALOG

ANALOG

DIGITAL

DIGITAL

DIGITAL

TUNER

TUNER

TUNER

SIGNALCONDITIONER

SIGNALCONDITIONER

SIGNALCONDITIONER

SECOND GENERATION

DSP CENTRIC MODEL

SAMPLED DATA CHANNEL DIGITAL MODULATOR

DSP MODULATOR

DSP DEMODULATOR

DIGITALDEMODULATOR

BITS

M-ARYALPHABET

M-ARYALPHABET

DATATRANSFORMS

WAVEFORMTRANSFORMS

SPECTRALTRANSFORMS

SPECTRALTRANSFORMS

WAVEFORMTRANSFORMS

DATATRANSFORMS

BASEBANDWAVEFORM

RF

CH

AN

NEL

RF

BASEBANDWAVEFORM

BITS

ANALOGSIGNALS

DIGITALSIGNALS

DATASIGNALS

THIRD GENERATION

DSP CENTRIC MODEL

ANALOG CHANNEL DIGITAL MODULATOR

DSP MODULATOR

DSP DEMODULATOR

DIGITALDEMODULATOR

BITS

M-ARYALPHABET

M-ARYALPHABET

DATATRANSFORMS

WAVEFORMTRANSFORMS

SPECTRALTRANSFORMS

SPECTRALTRANSFORMS

WAVEFORMTRANSFORMS

DATATRANSFORMS

BASEBANDWAVEFORM

RF

CH

AN

NEL

RF

BASEBANDWAVEFORM

BITS

ANALOGSIGNALS

DIGITALSIGNALS

DATASIGNALS

Modem: Bits In - RF Out, RF In - Bits Out

ANALOG CHANNEL DIGITALMODULATOR

DSPMODULATOR

DIGITALDEMODULATOR

DSPDEMODULATOR

BITS BITS M-ARYALPHABET

M-ARYALPHABET

SourceEncoding

SourceDecoding

ChannelEncoding

ChannelDecoding

WaveformTransforms

WaveformTransforms

SpectralTransforms

SpectralTransforms

Encryption

Decryption

BASEBANDWAVEFORM

RF

CH

AN

NEL

RF BASEBANDWAVEFORM BITS BITS

DATASIGNALS

DIGITALSIGNALS

ANALOGSIGNALSMODEM

Early Radios Were Mechanical:

(Many Moving Parts)

Spark Transmitter and Early Receiver

Spark Transmitter: Damped Oscillations

Arc Transmitter: Continuous Oscillation

Replace Sparks with an ArcNegative Resistance Injects EnergyAs Opposed to Dissipates Energy

Valdemar Poulsen, 1869-1942

Poulsen 100 KW Arc Transmitter

The path to the Triode Thermonic Valve,

Thomas Edison, John Fleming, Lee de Forest

Lee De Forest, 1877-1961 Patent No. 879532

Regenerative Receiver:

A Little Feedback Goes a Long Way

Tuned RF (TRF) Radio

Edwin Armstrong’s

Super Heterodyne Receiver

Vacuum Tube Replacement

Solid State Amplifier

John Walter William

Bardeen Brattain Shockley

1908-1991 1902-1987 1910-1989

1947

Noble Prize 1956

Integrated Circuits

Robert Noyce,

Intel

Jack Kilby

TI

1958

1923-2005 1928-1990

Noble Prize 2000 Noyce Founded Intel

Ted Hoff worked for Noyce

20102000199019801970196019501947

1,000

10,000

100,000

1,000,000

10,000,000

100,000,000

1,000,000,000

10,000,000,000

Trans

istor

s

per c

hip

8080 4,500

8088 29,000

286 134,000

386 275,000

486 1.2 Million

Pentium 3.1 Million

Pentium II

Celeron 7.5 Million

Pentium 4

Itanium

Xeon 42 Million

Itanium 2

Itanium2

8008 3,500

4004 First

processor 2,000

7.5 Million

5.5 MillionPentium Pro

42 Million

25 Million

220 Million

592 Million

1977Apple II

1947TransistorInvented

1965Gordon MooreStates his famousaxiom, later calledMoore’s law

1958Jack Kilby (TI) &Robert Noyce (intel) InventIntegrated Circuit

1983 Motorola FirstMobile Phone

1991 Kodak FirstDigital Camera

1996 DVDPlayers

1999 Blackberry

Moo

re’s

Law:

The

dens

ity o

f tra

nsist

ors o

n a

chip

dou

bles

eve

ry 24

mon

ths

More, More, MooreCritics have predicted the imminentdemise of Moore’s law ever sinceGordon Moore stated it in 1965.Electrical Engineers continue todefy physical challenges, squeezing ever morecircuitry into less spaceand making informationfly ever moreswiftly.

We all own

a billion Transistors

We have an amazing wealth of

resources at our disposal!

Just how big is a Billion?

A stack of a billion bank notes would be

76.2 kilometers High.

A billion seconds is 32.5 years!

For Comparison, the Eiffel Tower

Contains 18,084 Parts. It is

Fastened Together by 2.5 Million Rivets

The world manufactures more

transistors than it grows grains of rice.

0.13-micron, Intel Pentium 4

300-mm silicon wafer.

Long Grain Jasmine Rice

Wow!

How big is a billion grains of rice?

8mm x 2mm x 2mm (Long Grain)

1-billion grains of rice

8 Meters x 2 Meters x 2 Meters

Or 32 Cubic Meters

Or a cube 3.2 Meters on a side

It weighs 24,000 kg (26.6 tons)

It costs $26,000 (3-rd week April 2008)

CLS-350 Mercedes Benz weighs 2,200 kg

A Billion Transistors costs $20.0

0.00000001

Gordon_Moore_ISSCC-02-10-03

Adam @ HomeBrian Basset

It’s all done with Computer Chips

Harry Nyquist, (1889-1960)

The Sampling Theorem

fS>BW

Analog-to-Digital

Converter

A-to-D

ADC

Digital-to-Analog

Converter

DAC

D-to-A

Communication over Band

Limited, AWGN Channel

Shaping Filter

Band Limited Channel

Matched Filter

AWGN

d(n) s(t) r(t) d(n)^H1(w)

H2(w)

H2( ) = H1*( ) e j

Hd(w)

Hd( ) = H1( ) H1*( ) e j = |H1( )|

2 e j

|H1( )|2 e j = HNYQ( ) e

j t

H1( ) = SQRT{HNYQ( )}

(Maximize SNR)

(Zero ISI)

Band Limited Channel

Zero ISI and Causal Response

f f

t t

Tsym1

Tsym1

Tsym

Tsym

Tsym

Tsym

Tsym

........

2

Nyquist Spectrum Nyquist Spectrum

With Cosine Taper

Infinite Duration

Nyquist Pulse

Finite Duration

Nyquist Pulse

It’s not what you don’t know that gets you in trouble!

It’s what you know for sure to be true that just ain’t so!

Samuel Clemens

Spectral Resolution

Gaussian Window

-0.5 -0.4 -0.3 -0.2 -0.1 0 0.1 0.2 0.3 0.4 0.50

0.2

0.4

0.6

0.8

1

Gaussian Window and Spectrum, Maximum Level Sidelobe -60 dB

Am

plit

ud

e

Normalized Time Interval

-0.5 -0.4 -0.3 -0.2 -0.1 0 0.1 0.2 0.3 0.4 0.5-80

-60

-40

-20

0

Normalized Frequency

Atte

nu

atio

n (

dB

)

-0.1 -0.05 0 0.05 0.1-80

-60

-40

-20

0

Frequency

(dB

)

Zoom to Main Lobe

-0.5 -0.4 -0.3 -0.2 -0.1 0 0.1 0.2 0.3 0.4 0.50

0.2

0.4

0.6

0.8

1

Kaiser Window and Spectrum, Maximum Level Sidelobe -60 dB

Normalized Time Interval

Am

plitu

de

-0.5 -0.4 -0.3 -0.2 -0.1 0 0.1 0.2 0.3 0.4 0.5-80

-60

-40

-20

0

Normalized Frequency

Atte

nu

atio

n (

dB

)

Spectrum

-0.1 -0.05 0 0.05 0.1-80

-60

-40

-20

0

Frequency

(dB

)

Zoom to Main Lobe

Spectral Resolution

Kaiser-Bessel Window

Spectral Resolution, Remez Minimum

BW Window with -6-dB/Oct. Side Lobes

-0.5 -0.4 -0.3 -0.2 -0.1 0 0.1 0.2 0.3 0.4 0.5

0

0.2

0.4

0.6

0.8

1

Remez Window and Spectrum, -6 dB/Octave, Maximum Level Sidelobe -60 dB

Normalized Time

Am

plit

ud

e

-0.5 -0.4 -0.3 -0.2 -0.1 0 0.1 0.2 0.3 0.4 0.5-80

-60

-40

-20

0

Spectrum

Normalized Frequency

Atte

nu

atio

n (

dB

)

-0.1 -0.05 0 0.05 0.1-80

-60

-40

-20

0

Zoom to Main Lobe

Frequency

dB

Cosine Tapered Nyquist Spectrum

2

sin( ) cos( )1

( ) ( )2

( ) [1 ( ) ]RC

tt

T Th ttT

tT T

0 2(1- ) (1+ )1

2 22fsym

f

1

2

Square-Root

Cosine Tapered Nyquist Filter

0 2(1- ) (1+ )1

2 22fsym

f

1

22

Discontinuous

First Derivative

2

2

(4 )cos( (1 ) )1

( ) ( )

( )[1 (4 ) ]

sin( (1 ) )1

( )

( )[1 (4 ) ]

SR RC

t t

T Th tt tT

T T

t

Tt tT

T T

SQRT-RC Impulse Response

Finite Duration, Rectangle Window

0.08 dB

(0.009)

-35 dB

(0.0178)

Spectra of SR-hM and

SR-RC Nyquist Filter

SR-RC

SR-RC

SR-hM

SR-hM

ISI Levels: RC-RC and hM-hM

Transmitter and Receiver

Modulator and Demodulator

Modulator Band Limited Channel

Demodulator

AWGN

b(n) s(t) r(t) d(n)^

( )

( ) Re{[ ( )] }

Re{ ( ) }

c

c

j t

k

k

j tj t

s t I g t kT e

R t e e

( )( )( )

( )

( ) Re{[ ( )* ( ) ] }

( )

c

c

j tj t

j t

r t A t R t e e

n t e

First Tier, Primary Signal Processing Tasks

in a Typical Transmitter and Receiver

IFSTAGE

RFSTAGE

IFSTAGE

DDS

DDS

S-P

P-S

Clock

Clock

CARRIER PLL

TIMING PLL

DAC

ADC

DIGITALLOW-PASS

DIGITALLOW-PASS

DIGITALLOW-PASS

DIGITALLOW-PASS

DIGITALLOW-PASS

DIGITALLOW-PASS

DIGITALLOW-PASS

DIGITALLOW-PASS

Shape &Upsample

Matched Filter

Interpolate

Decimate

I-Q Table

Detect

cos( n)

cos( n)

sin( n)

sin( n)

Modulator

Demodulator

f

Analog Analog

Analog

Oscillator

PA

RF Carrier

GainControl

Oscillator

CarrierWaveform

VGALNA

RF Carrier

IF

Channel Channel

BPSK Phase Error

x

y

A exp(j )

A cos( )

A sin( )

2

2

( )* ( ) cos( )*sin( )

sin(2 )2

x n y n A

AConsider x(n) y(n)

-0.5 -0.4 -0.3 -0.2 -0.1 0 0.1 0.2 0.3 0.4 0.5

-1

-0.8

-0.6

-0.4

-0.2

0

0.2

0.4

0.6

0.8

1

-

Inputs to Product Detector

cosine

sgn(cosine)

-0.5 -0.4 -0.3 -0.2 -0.1 0 0.1 0.2 0.3 0.4 0.5

-1

-0.8

-0.6

-0.4

-0.2

0

0.2

0.4

0.6

0.8

1

-

S-Curve Product Detector sign(x)*y

-0.5 -0.4 -0.3 -0.2 -0.1 0 0.1 0.2 0.3 0.4 0.5

-1

-0.8

-0.6

-0.4

-0.2

0

0.2

0.4

0.6

0.8

1

-

S-Curve Product detector x*y

-0.5 -0.4 -0.3 -0.2 -0.1 0 0.1 0.2 0.3 0.4 0.5

-1

-0.8

-0.6

-0.4

-0.2

0

0.2

0.4

0.6

0.8

1

-

Inputs to Product Detector

Phase Detectors for Modulated BPSK

Second Tier Signal Processing Task,

Carrier Recovery Phase Locked Loop

Matched Filter

Polyphase

Polyphase

Matched Filter

Tanh( )

Phase Accumulator

PI Loop FilterCLK

r(t, ) r(nT, )

x(nT, )

y(nT, )

KI

KP

ZZ-1-1exp(-j )^

^

^

2-to-1

2-to-1

DDS

SNR

SNR

Phase Detectors for Modulated QPSK

-0.5 -0.4 -0.3 -0.2 -0.1 0 0.1 0.2 0.3 0.4 0.5

-1

-0.8

-0.6

-0.4

-0.2

0

0.2

0.4

0.6

0.8

1

-

S-Curve Product Phase Detector: sign(x)*y-sign(y)*x

-0.5 -0.4 -0.3 -0.2 -0.1 0 0.1 0.2 0.3 0.4 0.5

-1

-0.8

-0.6

-0.4

-0.2

0

0.2

0.4

0.6

0.8

1

-

Inputs to Phase Detector

QPSK PLL

FIRLPF

r(n)

LoopFilter

FIRLPF

cos( + )0

-Sin( + )0

^

^

Direct Digital Synthesizer

x(n) I(n)

y(n)Q(n)

DDS

+

-

^

^

^ ^I(n)y(n)-Q(n)x(n)

~sin( (n))

^ ^

x(n)+jy(n)

I(n)+jQ(n)(n)

Maximum Likelihood Timing Recovery

Matched Filter

Tanh( )

VCO LOOPFILTER

2E N

B

0

2E N

B

0

SAMPLE

SAMPLE

r(t, ) y(t, )

y(t, )

ddt

.

Derivative with Help of Nearby Neighbors

(Early and Late)

Advance Pointer

RetardPointer

HoldPointer

Derivative

DerivativeD

erivat

ive

Early-Late Gate Derivative

Matched Filter

Early Filter

Late Filter

Tanh( )

VCO LOOPFILTER

2E N

B

0

2E N

B

0

SAMPLE

SAMPLE

r(t, ) y(t, )

y(t, ).

-

Combining Early and Late Gates in a

One Derivative Filter

Matched Filter

Early-Late Filter

Derivative Filter

Tanh( )

VCO LOOPFILTER

2E N

B

0

2E N

B

0

SAMPLE

SAMPLE

r(t, ) y(t, )

y(t, ).

Slide Sampler to Input and Perform Timing

Offset with Polyphase Digital Filter

Matched Filter

Polyphase

Polyphase

DerivativeMatched Filter

Tanh( )

VCO LOOPFILTER

2E N

B

0

2E N

B

0

SAMPLE

r(t, ) r(nT, )

y(nT+ T, )

y(nT+ T, ).

T

T

Approximating Tanh(x)

-4 -3 -2 -1 0 1 2 3 4

-1

-0.8

-0.6

-0.4

-0.2

0

0.2

0.4

0.6

0.8

1

Tanh(x) and Piecewise Linear Approximation

x

tan

h(x

)

Sub Optimal Approximations

Replace 2Eb/N0, SNR Gain with a Constant.

Replace tanh(x) with Large SNR Approximation:

tanh(x) ~ sign(x)

Replace tanh(x) with Piecewise Approximation:

tanh(x) ~ x for |x| < 1

tanh(x) ~ sign(x) for |x| > 1

Sub Optimal Approximation

Matched Filter

Polyphase

Polyphase

DerivativeMatched Filter

f(x)

VCO LOOPFILTER

SAMPLE

r(t, ) r(nT, )

y(nT+ T, )

y(nT+ T, ).

T

T

x

Second Tier Signal Processing Task,

Timing Recovery Phase Locked Loop

Matched Filter

Polyphase

Polyphase

DerivativeMatched Filter

Tanh( )

Phase AccumulatorLoop Filter

CLK

r(t, )

r(nT, )

y(nT+ T, )

y(nT+ T, ).

T k

T k

Integer Part

KI

KP

ZZ-1-1

k

k

SNR

SNR

Band Edge Filter: BE( )=dH( )/d

Spectrum: Matched Filter

Spectrum:Frequency Derivative of Matched Filter

Spectrum: Output of Frequency Matched Filter

G ( )

G ( )

MF

FMF

Band Edge Filter Based

Frequency Locked Loop

Matched Filter

FrequencyMatched Filter

DDSLoopFilter

Re(--)

^

{R(n)e }j (n) j n

e *

*

Energy Difference in Band Edges

Sufficient Statistic to Frequency Lock Spectrum: Frequency Matched Filter

Spectrum: Frequency Matched Filter

Spectrum: Centered Input Signal

Spectrum: Shifted Input Signal

Spectrum: Response to Centered Input Signal

Spectrum: Response to Non Centered Input Signal

Mean and Variance of DC Term of

Function of Frequency Offset

Spectra of

Shaping and Band Edge Filters

Spectra of Signals From Band Edges

Combined to form Two New Signals

f

f

f

-f

symbol

symbol

symbol

symbol

2

2

2

2

A(f- )

B(f+ )

v (f)1 v (f)2

f

f

f

f

Eye Diagrams of Matched Filter and

Sum and Difference Band-Edge Filters

Spectra of SQRT Nyquist Shaped Modulation

Signals over Range of Excess BW

Eye Diagrams Matched Filter Output

Cyclostationary Mean and Variance

Eye Diagrams Magnitude Matched Filter

Spectral Lines from Excess BW: MF( )xMF( )*

Eye Diagrams Band Edge Filter Output

Cyclostationary Mean and Variance

Eye Diagrams Magnitude Band Edge Filter

Spectra of BE( )xBE( )*

Amplitude of Spectral Timing Line

from Excess Bandwidth

What Happens if there is no excess BW?

As we reduce excess BW to obtain more efficient use of spectrum, we reduce the ability of the receiver to synchronize.

When there is no excess BW we need to allocate a fraction of transmitted energy to pilot signals.

Example: OFDM Has No excess Energy in Modulation Waveform: Excess Energy Resides in added secondary signals: Preamble, Cyclic Prefix, Unmodulated Stationary and Moving Pilots.

Interesting Question: Is this energy accounted for when people discuss error correcting codesoperating near Shannon Limit? (I’m sure it is not!)

The Synchronizers’ Needle Point

Band Edge Filters and Approximations

Linear and Minimum Phase BE Filters

Frequency Offset Spectra and BE Filters in

Frequency Lock Loop

Phase Profiles of Freq Lock Loop

Time Series from BE Filters During Frequency Acquisition

Frequency Offset Spectra and Minimum Phase

BE Filters in Frequency Lock Loop

Phase Profiles of Freq Lock Loop

Time Series from BE Filters During Frequency Acquisition

Frequency Offset Spectra and Linear Phase FIR

Substitute for BE Filters in Frequency Lock Loop

Phase Profiles of Freq Lock Loop

Time Series from BE Filters During Frequency Acquisition

Asymmetric Processing

BITS

INPUTCLOCK

CARRIERREFERENCE

OUTPUTCLOCK

BITS

TIMING

TIMINGCONTROL

EQUALIZECONTROL

CARRIERCONTROL

GAINCONTROL

TIMING

CARRIER

CARRIER

MAP

DETECT

NOISE

CHANNEL

UNKNOWN TIME DELAY andATTENUATION

MAP

SHAPING FILTER

SHAPING FILTEREQUALIZER

AMPLITUDE and PHASE

TRANSMITTER

RECEIVER

AMPLITUDEQUANTIZEDAMPLITUDE

BASEBANDWAVEFORM

BASEBANDWAVEFORM

CARRIERWAVEFORM

CARRIERWAVEFORM

VGA

First Generation Receiver

Analog Signal Conditioning

LOW-PASS FILTER

LOOPFILTER

LOOPFILTER

I-F FILTER

IMAGEREJECT FILTER

MATCHED FILTER

FIRST LO

SAMPLER

DATADETECTOR

PHASEDETECTOR

CARRIER VCO

TIMING VCO

LNA

TUNING

GAIN

Second Generation Receiver

DSP Based Signal Processing

LOW-PASS FILTER

LOOPFILTER

LOOPFILTER

I-F FILTER

IMAGEREJECT FILTER

MATCHED FILTER

FIRST LO

SAMPLER

DATADETECTOR

PHASEDETECTOR

CARRIER VCO

TIMING VCO

LNA

TUNING

GAIN

Third Generation Receiver DSP Based

Signal Conditioning

LOW-PASS FILTER

LOOPFILTER

LOOPFILTER

I-F FILTER

IMAGEREJECT FILTER

MATCHED FILTER

FIRST LO

SAMPLER

DATADETECTOR

PHASEDETECTOR

SECOND LO

SAMPLING CLOCK

CARRIER DDS

TIMING DDS

LNA

TUNING

GAIN

INTERPOLATOR

Build Your Own Carrier

for Final Down Conversion

AMPAMP

AMPAMP

ANT

/2

BASEBANDPROC

TUNE

RF IF

CARRIER

First Generation Digital Receiver

AMPAMP

AMP

ADC

ADC

AMPAMP

ANT

/2

BASEBANDPROC

TUNE

RF IF

TIMINGCARRIER

Second Generation Digital Receiver

AMPAMPADC

AMPAMP

ANT

BASEBANDPROC

TUNE

IFRF

ACCUM

TRIGTABLE

DIRECT DIGITAL

SYNTHESIZER

DIGITAL

TIMINGCARRIER

DIGITAL

M:1

M:1

Third Generation Digital Receiver

AMPAMPADC

AMPAMP

ANT

BASEBANDPROC

TUNE

IFRF

ACCUM

ACCUM

TRIGTABLE

DDS

DIGITAL

CLOCK CARRIER

Timing

M:1

M:1

Signals and Underlying Structure of Analog

Radio, DSP Radio, and Software Defined Radio

AnalogModulation

Software Control and Upgrades

DigitalModulation

New WaveformsEvolving Standards

Modulation

Analog Radio

DSP Radio

Software Defined Radio

Modulation Type BandwidthFrequency Band

Modulation Type Bandwidth

Frequency Band Source CodingChannel Coding

Modulation Type Bandwidth

Frequency Band Source Coding Channel Coding Configuration Control

Fixed Parameters

Fixed Parameters

Programmable Parameters

Software Defined Radio: A Tutorial

IEEE Instrumentation and Measurement

Magazine, February 2010

fred harris and Wade Lowdermilk

High Level Block Diagram of Software Defined Radio. Radio is

segmented into RF Processing Front End Block, Baseband

Waveform Digital Signal Processing Back End Block, and

Interface to Data Processing Higher Level User Application and

Interface Blocks.

Tunable Filters and LNA

Tunable Filters and LNA

User Interface Periphials

Power Manager

Tunable Filters &Power Amplifier

Mixer

Mixer

IF/AGC

IF/AGC

ADC

DAC

DSPs GPPs

SpecializedCo-Processors

FPGAs

D

up

lexe

r, A

nte

nna

Ma

na

ge

me

nt

& T

une

r

RF-Front End Digital Back End

First Tier, Primary Signal Processing Tasks

in a Typical Transmitter and Receiver

IFSTAGE

RFSTAGE

IFSTAGE

DDS

DDS

S-P

P-S

Clock

Clock

CARRIER PLL

TIMING PLL

DAC

ADC

DIGITALLOW-PASS

DIGITALLOW-PASS

DIGITALLOW-PASS

DIGITALLOW-PASS

DIGITALLOW-PASS

DIGITALLOW-PASS

DIGITALLOW-PASS

DIGITALLOW-PASS

Shape &Upsample

Matched Filter

Interpolate

Decimate

I-Q Table

Detect

cos( n)

cos( n)

sin( n)

sin( n)

Modulator

Demodulator

f

Analog Analog

Analog

Oscillator

PA

RF Carrier

GainControl

Oscillator

CarrierWaveform

VGALNA

RF Carrier

IF

Channel Channel

Second Tier Signal Processing Task,

Carrier Recovery Phase Locked Loop

Matched Filter

Polyphase

Polyphase

Matched Filter

Tanh( )

Phase Accumulator

PI Loop FilterCLK

r(t, ) r(nT, )

x(nT, )

y(nT, )

KI

KP

ZZ-1-1exp(-j )^

^

^

2-to-1

2-to-1

DDS

SNR

SNR

Second Tier Signal Processing Task,

Timing Recovery Phase Locked Loop

Matched Filter

Polyphase

Polyphase

DerivativeMatched Filter

Tanh( )

Phase AccumulatorLoop Filter

CLK

r(t, )

r(nT, )

y(nT+ T, )

y(nT+ T, ).

T k

T k

Integer Part

KI

KP

ZZ-1-1

k

k

SNR

SNR

Estimate Signal Mean and Variance

at High SNR and Low SNR

ConditionalDensities

ConditionalDensities

Density ofObservableMAG

Density ofObservableMAG

AA

AA M1

-A-A

Estimate of Mean is too High

Estimate of variance is too Low

Estimates of Moments and SNR as Function of SNR

Skewness: A Measure of Estimated SNR Error

Skewness : the third central moment of X,

divided by the cube of its standard deviation

BPSK Large SNR Approximation to ML

0 100 200 300 400 500 600 700 800 900 1000-2

-1

0

1

2Input and Output Phase Slopes, and Detected Phase Error

det(n) = sign(I(n))*Q(n): Large SNR Approximation to ML Carrier Recoverysnr = 10.21dB

-2 0 2-2

-1

0

1

2

Constellation Diagram

0 500 10000

0.2

0.4

0.6

0.8

1

Variance Estimate

-1 -0.5 0 0.5 1-4

-2

0

2

4

Eye Diagram

0 20 40 60 80 100 120-2

-1

0

1

2

De-Spun Matched Filter Outputerror rate = 0.00 %

MF Resp.

Det. Data

Input Data

BPSK Large SNR Approximation to ML

0 100 200 300 400 500 600 700 800 900 1000

0

0.2

0.4

0.6

0.8

1

Error Locations

0 100 200 300 400 500 600 700 800 900 1000-40

-30

-20

-10

0

10

20

30

40

Phase Error for det(n) = sign(I(n))*Q(n)

(de

g)

BPSK ML Carrier Recovery Loop

0 100 200 300 400 500 600 700 800 900 1000-2

-1

0

1

2Input and Output Phase Slopes, and Detected Phase Error

det(n) = tanh[snr*sign(I(n)]*Q(n): ML Carrier Recoverysnr = 10.02dB

-2 0 2-2

-1

0

1

2

Constellation Diagram

0 500 10000

0.5

1

1.5

Variance Estimate

-1 -0.5 0 0.5 1-4

-2

0

2

4

Eye Diagram

0 20 40 60 80 100 120-2

-1

0

1

2

De-Spun Matched Filter Outputerror rate = 0.00 %

MF Resp.

Det. Data

Input Data

BPSK ML Carrier Recovery Loop

0 100 200 300 400 500 600 700 800 900 1000

0

0.2

0.4

0.6

0.8

1

Error Locations

0 100 200 300 400 500 600 700 800 900 1000-30

-20

-10

0

10

20

30

Phase Error for det(n) = tanh[snr*I(n)]*Q(n)

(de

g)

BPSK Large SNR Approximation to ML

0 100 200 300 400 500 600 700 800 900 1000-2

-1

0

1

2Input and Output Phase Slopes, and Detected Phase Error

det(n) = sign(I(n))*Q(n): Large SNR Approximation to ML Carrier Recoverysnr = 3.42dB

-2 0 2-2

-1

0

1

2

Constellation Diagram

0 500 10000

0.5

1

1.5

2

2.5

Variance Estimate

-1 -0.5 0 0.5 1-4

-2

0

2

4

Eye Diagram

0 20 40 60 80 100 120-2

-1

0

1

2

De-Spun Matched Filter Outputerror rate = 48.53 %

MF Resp.

Det. Data

Input Data

BPSK Large SNR Approximation to ML

0 100 200 300 400 500 600 700 800 900 1000

0

0.2

0.4

0.6

0.8

1

Error Locations

0 100 200 300 400 500 600 700 800 900 1000-300

-200

-100

0

100

200

300

Phase Error for det(n) = sign(I(n))*Q(n)

(de

g)

BPSK ML Carrier Recovery Loop

0 100 200 300 400 500 600 700 800 900 1000-2

-1

0

1

2

Input and Output Phase Slopes, and Detected Phase Errordet(n) = tanh[snr*sign(I(n)]*Q(n): ML Carrier Recovery

snr = 3.46dB

-2 0 2-2

-1

0

1

2

Constellation Diagram

0 500 10000

0.5

1

1.5

2

2.5

Variance Estimate

-1 -0.5 0 0.5 1-4

-2

0

2

4

6

Eye Diagram

0 20 40 60 80 100 120-2

-1

0

1

2

De-Spun Matched Filter Outputerror rate = 12.44 %

MF Resp.

Det. Data

Input Data

BPSK ML Carrier Recovery Loop

0 100 200 300 400 500 600 700 800 900 1000

0

0.2

0.4

0.6

0.8

1

Error Locations

0 100 200 300 400 500 600 700 800 900 1000-40

-30

-20

-10

0

10

20

30

40

50

Phase Error for det(n) = tanh[snr*I(n)]*Q(n)

(de

g)

Automatic Gain Control (1)

z-1

x(n)

A(n)

y(n)=A(n)x(n))

R

-

2.0.cthatnote

]1[)()1(

then

constantcu(n),cx(n)Suppose

)](1[)()1(

)]()([)()1(

)]([)()1(

)()()(

RcnAnA

RnxnAnA

nxnARnAnA

nyRnAnA

nxnAny

sientshort tran,largeiscIf.transientlongsmall,iscIf

samples.c1/isconstanttimeThe

R.levelreferencedesiredtheequalsleveloutput

statesteadyTheR.orR/ccis)y(outputstate

steadytheandR/cis)A(gainstatesteady

that theso1/cissystemthisofstateSteady

Automatic Gain Control (2)

z-1

x(n)

Log[A(n)]

y(n)=A(n)x(n))

Log[R]

-

EXP Log[Mag]

2.0.thatnote

]/[]1[)]([)]1([

then

constantcu(n),cx(n)Suppose

]/)([]1[)]([)]1([

)]}()([][{

)]([)]1([

)]}([][{[

)]([)]1([

)()()(

RcLognALognALog

RnxLognALognALog

nxnALogRLog

nALognALog

nyLogRLog

nALognALog

nxnAny

amplitude.inputoftindependenisand

samples,1/isconstanttimeTheR.levelreference

desiredtheequalsleveloutputstatesteadyThe

R.orR/ccis)y(outputstate

steadytheandR/cis)A(gainstatesteady

that theso1/cissystemthisofstateSteady

Linear Loop AGC Responses

Linear Loop AGC Responses: with Filter Delays

Log Loop AGC Responses

Log Loop AGC Responses: with Filter Delays

Linear Loop AGC Output and Control Levels

Log Loop AGC Output and Control Levels

DC Canceller,

DC Notch Filter

z-1-

x(z)

f(z)

y(z)

)1(

1)(

Z

ZZH

+

1-

Spectral Response

DC Canceller with Embedded

Sigma-Delta Converter

Z

Z

-1

-1

-

-

R1

R2

x(n)y (n)2

Qq_loop

q_out

Suppress Bit Growth with

Sigma-Delta Converter in

Feedback Path

DC Canceller Time Series

Spectra

Input and Output of Canceller

Tunable Notch,

Spin the Delay Line

z-1-

x(z)

f(z)

y(z)

je

j

j

eZ

eZZH

)1()(

+1-

Spectral Response

Tuning With LP-to-BP

Transformation

z-1-

x(z)

f(z)

y(z)

c

cZ

cZ1

)cos(:)21()1(2

12)(

2

2

cZcZ

cZZZH

++

1-

1-

Implementing LP-to-BP

Transformation

-

-z z

-1 -1

c=cos( ) mu

x y

b1 b1

Z Z

Z ZZ

-1 -1

-1

-1

-1 -1-1

- -

x(z) x(z)

y(z) y(z)Y(z) z

Y(z) z

1-cZ

Z-c

Spectral Response

Self Tuning:

Reference Cancelingy(n)x(n)

r(n)

Z-1

w(n) w(n+1)**

y(n)x(n)

ej n

ej n

Z-1

w(n) w(n+1)**

Filters have Same Transfer Function

y(n)x(n)

ej n

ej n

Z-1

w(n) w(n+1)**

z-1-

x(z)

f(z)

y(z)

je

Block Diagram of Receiver with

Ideal Signal Processing Blocks

Analog I/QDown Convert

Digital I/QDown Convert

AnalogLow Pass

Filters

AnalogBand Pass

Filter

A-to-DConverters

Rest ofReceiver

ChannelEqualize

Synthesizer DDSClock

Block Diagram of Receiver with Non-

Ideal Signal Processing Blocks and

Associated Compensating Blocks

Analog I/QDown Convert

Digital I/QDown Convert

AnalogLow Pass Filters

AnalogBand Pass Filter

A-to-DConverters

DCCancel

PhaseBalance

GainBalance

Rest ofReceiver

FilterCompensate

ChannelEqualize

Synthesizer Clock DDSAnalog Signals Digital Signals

Gain and Phase Imbalance in Analog

I-Q Mixers Used for Up or Down Conversion

Complex Baseband & Real Band-Centered

Complex Down Conversion

I-Q Gain and Phase Imbalance

MatchMatch

MatchMatch

cos( t)cos( t)

sin( t+ )sin( t) ( )

I(t)I(t)

Q(t)Q(t)

^

^

^

^

^^

Balanced Imbalanced

I-Q Imbalance: Image Spectral Terms

f f

f f

f f

RealReal

RealReal

RealReal

ImagImag

ImagImag

ImagImag

A

AA

A

A

A

A

A

A

A

A

A

A

A

A

2

22

2

2

2

2

2

2

2

2

2

2

_

__

_

_

_

_

_

_

_

_

_

_

(1+ )

(1+ )

-

f0

f0

f0

f0

f0

-f0

-f0

-f0 -f0

-f0

-f0

f0

A cos(2 f t)0

A cos(2 f t)0

(1+ ) A sin(2 f t+0

A sin(2 f t)0

A exp(j 2 f t)0

X={ }

X=F{ }

i Y={ i }

i Y=F{i }

X+i Y={ }

X+i Y=F{sum}

Effect of I-Q Imbalance

Balanced Mixers

Gain Imbalance

Phase Imbalance

Gain and Phase Imbalance

Filter Imbalance

IFSTAGE

ADC

ADC ANALOGLOW-PASS

ANALOGLOW-PASS

DIGITALLOW-PASS

DIGITALLOW-PASS

AGC DC CANCEL

I-Q MIXER GAIN & PHASE BALANCE ANALOG FILTER GAIN & PHASE BALANCECARRIER & TIMINGCHANNEL & FILTER EQUALIZER

PWRDVDR

cos( t)

-sin( t)fs

fs

4:1

4:1

Gain and Phase Of Mismatched

Analog Low-Pass Filter

Gain and Phase Contributions of I-Q

Matched Low Pass Filters

Gain and Phase Contributions of I-Q

Mismatched Low Pass Filters

I-Q Imbalance and Self Mixing

LNA

FrequencySynthesizer

Low Pass Filter

Low Pass Filter

ParasiticCoupling

f f f

DC Offset: Self MixingDesired Component: MixingSpectral Image: I-Q Imbalance

Truncating Quantizers: DC Bias

X X

-X -X

X X

X(n) X(n)

Xq Xq

Xq Xq

X (n)q X (n)qADC ADC

Rounding Quantizer Truncating Quantizer

CLK CLK

Round Floor

2’s Complement Arithmetic; DC Bias

0 +Nmax-Nmin

b-bitsb-bits

(b-2)-bits(b-2)-bits ErrorError

Positive numbers:Measure displacement from reference. Reference = 0

Negative numbers:Measure displacement from reference. Reference = -Nmin

QuantizedNumber Line

Errors Due to finite Arithmetic

x1 x

x2 hQ

hQh

qA qMqC

s = x + x +q1 2 A p = x h +qQ M.

Quantize Addition Quantize Coefficient Quantize Multiplication

Finite Arithmetic in Radix-2 FFT Algorithm

+

+

+

-

SCL

(2 , 20 -1)

e-j

N k

N

N N

N

N

N

NN N

2 22

2

22 2

-Pnt

-Pnt

DFT

DFT

k1

n1

n2

k

k+k2

Time Time Freq Freq

n

Radix-2 FFT Signal Flow Diagram

000

011

110

001

100

111

010

101

-

-

- -

-

- -

-

- - -

-

w0

w0

w0

w2

w2

w2

w3

w1

Algorithm Noise Due to

Finite Arithmetic and Coefficient Noise

Algorithm Noise due to

Finite Arithmetic Scaling Noise

Signal Through Filter

with Gain Distortion

x(t) y(t)h(t)

H( )=1+ cos( )p

p

X( )

H( )

Model of Gain Distortion

H( )=1+ cos( )p

Y( )=X( ) H( )=X( )[1+ cos( )]

=X( )+p

p

p p

p p

X cos( )

=X( )+0.5 X exp(j )+0.5 X exp(-j )

y(t)=x(t)+0.5 x(t+T )+0.5 x(t-T )

Paired Echos

Pre-and-Post Echoes

x(t) y(t)

x(t-T )D

0.5 x(t-T -T )D p0.5 x(t-T +TD p)

Paired Echos: The Effect of Passband Ripple

TD TD P+TTD P-Tt t

Nyquist Pulse Time and Frequency

Pulse: Time and Frequency

Pulse Response and ISI Component

Recursive Filter Time & Frequency

Pulse Response and ISI Component

Pulse Response and ISI Component

QPSK Modulator Eye-Diagram,

Constellation, and Spectrum

QPSK Demodulator, Eye-Diagram

Constellation, and Spectrum

QPSK Demodulator with RCVR Filter

16-QAM Modulator Eye-Diagram,

Constellation, and Spectrum

16-QAM Demodulator with RCVR Filter

Signal Flow Path in XMTR & RCVR

Shaping Filter

XMTR & RCVR Filters

Matched Filter

Equalizer

AdaptiveAlgorithm

Detector

d(n) r(n)

e(n)

d(n)x(n) y(n) ^

-

Decision Directed, Gradient Descent (LMS)

Tapped Delay Line Equalizer

............

......

x(n)

y(n)

c (n)-k c (n)-k+1 c (n)-k+2 c (n)-k+3 c (n)k-1 c (n)k

x(n-1) x(n-2) x(n-3) x(n-N+2) x(n-N+1)

* ** *

*

**

z -1z -1z -1

z -1 z -1z -1

z -1

z -1 z -1 z -1

Ik

Ik

^

~

Detectore(n)+

-

Input

Output

Received Signal and SpectrumNo Channel Distortion

Constellation:

Equalizer Input and Output

Received Signal and SpectrumWith Channel Distortion

Constellation:

Equalizer Input and Output

I-Q Imbalance Requires DC Cancellers

I II ’

Q QQ’

(1+

I-Q Imbalance

DCCancel

PhaseBalance

GainBalance

DCCancel

g^ ^

~

~

Sequence of 16-Phase Constellations

During Phase Balancing

Sequence of 16-Phase Constellations

During Gain and Phase Balancing

Sequence of 16-QAM Constellations

During Phase Balancing

Sequence of 16-QAM Constellations

During Phase and Gain Balancing

Spectral Images

Due to I-Q Mismatch

Constellations of

Channel +k and -k

Crosstalk Between Channels k and –k

Due to gain and Phase Imbalance

Constellation after Gradient Descent

Correction of Gain and Phase Imbalance

Crosstalk Between Channel k and Empty Channel –k

Constellation after Gradient Descent Correction of

Gain and Phase Imbalance

DAC Sin(x)/(x) Baseband Distortion

0

0

0

fs 2fs

fs fs

fs

-fs-2fs

-fs-2fs

-fs

f

f

f

sin(x) sin(x)

sin(x)

(x) (x)

(x)

Spectral Response of DAC

Spectrum of Sampled Data Shaping Filter

Spectrum of Analog Output from DAC

Distortion Correction

Analog Fi lter

Analog Fi lter

sin(x)

sin(x)

(x)

(x)

-1

-1

DAC

DAC

Modem

I(n)

Q(n)

cos( t)c

sin( t)c

-Analog IF

Baseband Filter DAC Predistortion

CIC [Sin(x)/(x)] P Compensator

DAC Sin(x)/(x) Digital IF Distortion

0

0

0

fs 2fs

fs fs

fs

-fs-2fs

-fs-2fs

-fs

f

f

f

sin(x) sin(x)

sin(x)

(x) (x)

(x)

Spectral Response of DAC

Spectrum of Sampled Data Shaping Filter

Spectrum of Analog Output from DAC

Distortion Correction

Analog Fi lter

sin(x)(x)

-1DACModem

Analog IFDigital IF

Sin(x)/(x) Predistortion

....

....

..

....

....

..

....

....

....

....

..

..

....

....

....

....

....

......

......

......

......

..

..

..

32PntIFFT

32Pnt

IFFT

32PntIFFT

32PntIFFT

16PntIFFT

32Path

Filter

32PathFilter

32Path

Filter

32Path

Filter

16PathFilter

Shape &InterpFilters

Shape &

InterpFilters

Shape &InterpFilters

Shape &

InterpFilters

Interp Filter

DDS

sin(x)

Circ

ula

r Bu

ffer

Circ

ula

r Bu

ffer

Circ

ula

r Bu

ffer

Circ

ula

r Bu

ffer

Circ

ula

r Bu

ffer

16Ports

10Ports

16Ports

16Ports

16Ports

(x)

-1DAC

1-to-8 Up-Samplerin 16-Path Channelizer

1-to-16 Up-Samplersin 32-Path Channelizers

1-to-2192 MHz

1.536 MHz

3.072 MHz

192 MHz

192 MHz

192 MHz

12 MHz

12 MHz

12 MHz

12 MHz

5.36.. MHz

5.36.. MHz

5.36.. MHz

5.36.. MHz 1

2

3

10

DAC SIN(X)/X CORRECTION

DAC Sin(x)/(x) IF Predistortion

Power Amplifier Linearization

AnalogSynthesizer

DDS

2

2

DAC

ADC

1-to-8 Filter

LPFilter

IFFilter

IFFilter

Pre-Distort

NLModel

GainCorrect Table

sin(x)

(x)

PA

Comp

PA Linearization

Peak-to-Average Ratio Control

Non Linear Amplifier and Pre-Compensating Gain

Transition Diagram Input and Output of Amplifier

and Input and Output of Precompensator

16-QAM Input and Output Envelopes. Saturation and 1-

dB Compression Circles

-2 -1 0 1 2

-2

-1.5

-1

-0.5

0

0.5

1

1.5

2

Envelope at Output of Amplifier

-2 -1 0 1 2

-2

-1.5

-1

-0.5

0

0.5

1

1.5

2

Envelope at Input to Amplifier

Saturation at 2-Times RMS Signal Level

Saturation Saturation

1-dB

Compression

1-dB

Compression

Limiting Amplifier Effect on Received QAM Constellation

-1 -0.5 0 0.5 1

-1

-0.8

-0.6

-0.4

-0.2

0

0.2

0.4

0.6

0.8

1

Matched Filter Applied to Input of Amplifier

-1 -0.5 0 0.5 1

-1

-0.8

-0.6

-0.4

-0.2

0

0.2

0.4

0.6

0.8

1

Matched Filter Applied to Output of Amplifier

16-QAM ( =0.2) Envelope Statistics

0 0.5 1 1.5 2 2.50

0.002

0.004

0.006

0.008

0.01

0.012

0.014

0.016

16-QAM Histogram at Amplifier Input

Normalized Amplitude (x/x)

0 0.5 1 1.5 2 2.50

0.002

0.004

0.006

0.008

0.01

0.012

0.014

0.016 std dev =1.03 clip level

16-QAM Histogram at Amplifier Output

Normalized Amplitude (x/x)

0 0.5 1 1.5 2 2.5 310

-6

10-5

10-4

10-3

10-2

10-1

100

Probabilty of Level Crossing

Normalized Amplitude (x/x)

Limiting Amplifier Effect on Signal Spectra

-4 -3 -2 -1 0 1 2 3 4

-60

-50

-40

-30

-20

-10

0

10Spectrum at Input to Amplifier

Normalized Frequency (f/fsym

)

Log M

agnitude (

dB

)

-4 -3 -2 -1 0 1 2 3 4

-60

-50

-40

-30

-20

-10

0

10Spectrum at Output of Amplifier

Normalized Frequency (f/fsym

)

Log M

agnitude (

dB

)

SPECTRAL REGROWTH

Spectra: Input and Output of Amplifier and Output

of Pre-Compensator and Pre-Compensated Amplifier

OFDM Input and Output Envelopes:

Saturation and 1-dB Compression Circles

-3 -2 -1 0 1 2 3

-3

-2

-1

0

1

2

3

Envelope at Input to Amplifier

-3 -2 -1 0 1 2 3

-3

-2

-1

0

1

2

3

Envelope at Output of Amplifier

Saturation at 2-Times RMS Signal Level

Saturation Saturation

1-dB

Compression

1-dB

Compression

Limiting Amplifier Effect on OFDM Constellation

-1 -0.5 0 0.5 1

-1

-0.8

-0.6

-0.4

-0.2

0

0.2

0.4

0.6

0.8

1

OFDM Constellation at Input to Amplifier

-1 -0.5 0 0.5 1

-1

-0.8

-0.6

-0.4

-0.2

0

0.2

0.4

0.6

0.8

1

OFDM Constellation at Output of Amplifier

OFDM Envelope Statistics

0 1 2 3 40

0.005

0.01

0.015OFDM Histogram at Amplifier Input

Normalized Amplitude (x/x)

0 1 2 3 40

0.005

0.01

0.015

std dev =1.06 clip level

OFDM Histogram at Amplifier Output

Normalized Amplitude (x/x)

0 1 2 3 410

-6

10-5

10-4

10-3

10-2

10-1

100

Probabilty of Level Crossing

Normalized Amplitude (x/x)

To Clip or Not to Clip:

That is the Question!

s (t)1

s (t)=3 s (t)-s (t)2 1

+LCLIP

-LCLIP

s (t)2

-LCLIP

-LCLIP -LCLIP

LCLIPLCLIP

LCLIP

s2 s3

s1 s1

Band Limited

Subtractive Clipping

L L

-L -L

S (n)1

S (n)3

a1

a1

a2

a2

C(k )1

k1 k1

k1

k2

k2 k2

C(k )2

-

Band-Limited Clipping

LCLIP

s (t)2

s (t)3

s (t)1CLIP-1

-

LCLIP

s (t)2

s (t)3

s (t)1

CLIP-2

LCLIP

s (t)2

s (t)3s (t)4

s (t)1

CLIP-2 Filter

Delay

Input Signal, Clipping Component and

Clipped Signal

0 200 400 600 800 1000 1200 1400 1600 1800 20000

0.5

1

1.5

2

2.5Magnitude of Input Signal

0 200 400 600 800 1000 1200 1400 1600 1800 20000

0.1

0.2

0.3

0.4Magnitude of Input Signal Exceeding Top

0 200 400 600 800 1000 1200 1400 1600 1800 20000

0.5

1

1.5

2

2.5Magnitude of Input Signal - Level Exceeding Top

Spectra: Input Signal, Band Limited Clipping

Component and Clipped Signal

0 200 400 600 800 1000 1200 1400 1600 1800 20000

0.5

1

1.5

2

2.5Magnitude of Input Signal

0 200 400 600 800 1000 1200 1400 1600 1800 20000

0.1

0.2

0.3

0.4Magnitude of Input Signal - Level Exceeding Top and Filtered Version

0 200 400 600 800 1000 1200 1400 1600 1800 20000

0.5

1

1.5

2

2.5Magnitude of Input Signal - Filtered Level Exceeding Top

Spectra: Input, Clip Component, Band Limited Clip,

and Band Limited Clip

Spectra: Input and Output of Amplifier and Output of PAPR Controlled and

Pre-Compensator and Pre-Compensated Amplifier

DSP Radio (DSP Everywhere!)

Polyphase Matched Filter 32-to-1

Polyphase Derivative Matched Filter

PolyphaseBand-Edge Filter

Timing Loop

Equalizer 2-to-1 Downsample

LMSAlgorithm

CarrierLoop Filter & DDS

CarrierLoop Filter & DDS

Detector

20 Msmpl/S

10 Msmpl/S

20 Msmpl/S

-

*

Channel Filtering, Channel Estimate, Equalization,

AGC, DC-Cancelling, I-Q Balance, Line Canceller,

Interference Canceller, Matched Filter, SNR

Estimate, Band Edge Filter, Frequency Lock Loop,

Carrier Lock Loop, Interpolator, Timing Lock Loop

Actually, A design Project

For my Modem Design Class

Professor harris, may I be excused?

My brain is full.

Yes: That is True!

SOFTWAREDEFINEDRADIOMAN

Is Open For Questions