modems - wireless innovation forum · the radio channel frequency band vlf lf mf hf vhf uhf shf ehf...
TRANSCRIPT
-
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
MORE
MORE
MORE
MORE
MORE
MORE
MORE
MORE
MORE
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
MORE MORE
MOREMORE
MORE MORE
MOREMORE
MORE
MORE
MORE
MORE
MORE
MORE
MORE
MORE
MORE
MORE
M MO
O
R
RE
E
MORE
MORE
MORE
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