advanced modulation techniques for telemetry

Advanced Modulation Techniques for Telemetry

A Short Course at theInternational Telemetering Conference

Las Vegas, NV • October 24, 2011Terry Hill, Quasonix

2011 International Telemetering ConferenceTerry Hill - [email protected]

Course OutlineHistorical PerspectivePerformance MetricsModulation UniverseLife on the Unit Circle

ARTM Tier 0ARTM Tier IARTM Tier II

DemodulationDiversity CombiningChannel Impairments & Mitigation

Adjacent Channel InterferenceMultipath Propagation

Adaptive EqualizationSpace-Time Coding

Forward Error Correction (FEC)Performance Comparison & Summary


Evolution of Telemetry

The Good Ol’ Days1960’s to mid-1990’sNo spectrum shortageRange Commander’s Council (RCC) codifies PCM/FM in IRIG 106

Wireless Everything EraLate 1990’sCongress auctions telemetry spectrum to commercial interestsTest article complexity and telemetry data payloads balloon exponentially More data, less bandwidth…Now what?


ARTM ProgramAdvanced Range Telemetry (ARTM) program, initiated in mid-1990’sFunded through OSD, CTEIP (Central Test and Evaluation Investment Program)Fostered R&D in spectrally efficient modulation techniques

Tier I (2 x the spectral efficiency of PCM/FM)Tier II (2.5 x)

Both Tier I & II adopted by the RCCFully defined and characterized in IRIG 106-04Latest version (IRIG 106-09): http://www.irig106.org/docs/106-09/


ARTM DeploymentReceiving infrastructure in place today

Edwards AFBEglin AFBPatuxent River NASChina LakeWhite SandsPt. MuguVandenbergKwajalein

Numerous commercial usersBoeingHoneywellSandiaLawrence LivermoreLockheed AircraftLockheed Missiles


World View of Communications

Figure from "Digital Communications: Fundamentals and Applications," by Bernard Sklar, 2nd Edition, Prentice-Hall, 2001. Reprinted by permission of the author.

We’re in here


Performance Metrics

Information FidelityAdditive White Gaussian Noise (AWGN) channels

Bit Error Probability (BEP) or Bit Error Rate (BER)

Bursty (dropout) channelsCumulative error count

Bandwidth EfficiencyPower spectral densityFractional Out-of-band PowerChannel spacing with adjacent channel interference (ACI)

Bandwidth-Power plane


Eb = signal energy per bit (in Joules/bit or Watt-seconds/bit)= carrier power × bit time= C Tb

= carrier power / bit rate= C/Rb

N0 = noise level (in Watts/Hz)= Boltzmann’s constant × Equivalent System Temperature= k × Teq

= k × (F-1)T0 (where F = system noise figure)

Bit Error Rate - in AWGNKey Ratio =

0NEb

In terms of Carrier-to-Noise Ratio C/N:

b

b

RBW

NC

NE

=0

Figure from " Quadrature Modulation for Aeronautical Telemetry”, by Michael Rice, BYU and Robert Jefferis, Tybrin Corp, ITC 2001. Reprinted by permission of the authors.


Aeronautical Channels

From http://www.ee.byu.edu/telemetry/projects/widebandchannel/


Cumulative Error Countsin Bursty Channels

Bit Error Accumulation HistoryARTM flight 78, frequency diversity, 5 m antenna, high altitude corridor, easterly, 20k ft. altitude

0.0E+00

5.0E+06

1.0E+07

1.5E+07

2.0E+07

2.5E+07

0 500 1000 1500 2000 2500

Elapsed Time - Seconds

Bit

Erro

rs

ERR NDERR DBS

Figure from Robert Jefferis, Tybrin, Edwards AFB. Reprinted by permission of the author.


Which Bandwidth?

Fixed level-60 dBc is common-25 dBm is “standard” in IRIG-106

Fractional out-of-band power99%, 99.9%, 99.99% are all used

Minimum frequency separationAccounts for receive-side effects

Receiver IF filteringDemodulator interference toleranceRelative levels of interfering signalsDepends on application


Power Spectral Density (PSD)


Fractional Out-of-band Power

5 Mbps


Channel Spacing


Bandwidth-Power PlaneSimultaneous representation of

Bandwidth Efficiency (Bandwidth normalized to Bit Rate)Power Efficiency (Eb/No required to achieve 10-5 BEP)

Eb/No (dB) Required for 10-5 BEP

% B

andw

idth

in B

it R

ates

Spec

tral

Effi

cien

cy

Detection Efficiency

same BW,worse BEP

Same BW,better BEP

Sam

e B

EP,

bette

r BW

sam

e B

EP,

wor

se B

W

worse BW,worse BEP

worse BW,better BEP

better BW,worse BEP

better BW,better BEP


Bandwidth-Power Tradeoffs

Figure from "Digital Communications: Fundamentals and Applications," by Bernard Sklar, 2nd Edition, Prentice-Hall, 2001. Reprinted by permission of the author.


The Modulation Universe

Analog, DigitalAmplitude modulation Quadrature amplitude modulationAngle modulations

Frequency modulationPhase modulation


Angle ModulationsIncludes both frequency modulation and phase modulationSome have an amplitude modulation component

BPSKQPSKOffset QPSK

Some are constant envelopeBinary FM

FSK, MSK, premod filtered MSK, GMSK

M-ary FSKSOQPSKMulti-h continuous phase modulationNo amplitude variation

Saturated power amplifiers are ideal for constant envelope waveforms


Saturated Power Amplifiers

DC-to-RF conversion efficiency is importantMinimizes cooling requirementsMaximizes battery life

Maximizing efficiency demands nonlinear operationNon-linear operation creates AM-AM and AM-PM conversion:


Constant Envelope ModulationsBefore ARTM (Tier 0)

PCM/FM“Legacy” waveform for telemetry

Advanced Range Telemetry (ARTM) ProgramARTM Tier 1

Proprietary Feher-patented FQPSKFQPSK-B, Revision A1FQPSK-JR

SOQPSK-TGEquivalent in performance to FQPSKNon-proprietary

ARTM Tier 2 Multi-h CPM (M=4, L=3RC, h1 = 4/16, h2 = 5/16)

PCM/FM, SOQPSK and Multi-h CPM are all continuous phase modulations


CPM Notation and Parameters

Where αi represents an M-ary symbol sequenceαi derived from input bits di

h is the modulation indexg(t) is the frequency pulse shape in the interval 0 < t < LT

L = 1 is “full response” signalingL > 1 yields “partial response”

CPM is a modulation with memory due to the constraint of continuous phase. Further memory is introduced with L > 1.

-∞< t <+∞

]),(2cos[/2)( oo ttfTEts φαφπ ++=

∫ ∑∞−

+∞

−∞=

−=t

ii diTght τταπαφ )(2),(


Key Parameters

M – Order of Modulation (2-ary, 4-ary, etc.)g(t) - Frequency Pulse (Rectangular, Raised Cosine, etc.)L – Length of Frequency Pulseh – Modulation IndexIncrease Spectral Efficiency by

Increasing MReducing hIncreasing LChoosing Smoother Frequency Pulse Shape

In general, increasing spectral efficiency decreases detection efficiency


CPM Tradeoffs

To reduce bandwidth of a CPM signal, the phase transitions must be smoothed by:

Requiring phase to have more continuous derivativesSpreading the phase change over more intervals (i.e., L > 1)Reducing h

The shape of g(t) determines the smoothness of the information-carrying phaseAn endless variety of CPM schemes can be obtained by choosing different g(t) pulse shapes and varying the parameters h and M.


Frequency Pulse Shapes

LREC - Rectangular pulse, length LL=1, h = 0.5 gives MSK

LRC - Raised cosine, pulse length LTime domain RC pulse

LSRC - Spectral raised cosine, length LSpectral domain RC filter response

TFM - Tamed FMGMSK - Gaussian shaped MSK


CPM CharacteristicsContinuous PhaseConstant envelopeSignals are described by their phase trajectories

Phase tree representation is completePSD and BER can be “traded” by

Varying h, modulation indexChanging g(t), the frequency pulse shape

Phase trellis decoder is optimum for any variant of CPM Footnote

FQPSK-B (Revision A1) is not a CPM waveform because of its AM component; i. e., requires I/Q implementationFQPSK-JR is constant envelope, so it could be described in CPM terminology, but this raises patent issues


CPM Examples

Minimum Shift Keying (MSK)Gaussian MSK (GMSK)

GSM Cell phones (Europe)

SOQPSKUHF SATCOM (MIL-STD-188-181A, -181B(draft), -182A, -183A)-TG (IRIG 106-04)

FQPSK (or very similar)“CPM”

Nearly unlimited variation


QPSK and CPM

QPSK CPM


SOQPSK-TG as a CPM Example


Phase Tree Representation

-2

-1.5

-1

-0.5

0

0.5

1

1.5

2

0 1 2 3 4 5 6 7Time in bits

Phas

e in

Cyc

les

-2

-1.5

-1

-0.5

0

0.5

1

1.5

2

0 1 2 3 4 5 6 7Time in bits

Phas

e in

Cyc

les

-2

-1.5

-1

-0.5

0

0.5

1

1.5

2

0 1 2 3 4 5 6 7Time in bits

Phas

e in

Cyc

les

-2

-1.5

-1

-0.5

0

0.5

1

1.5

2

0 1 2 3 4 5 6 7Time in bits

Phas

e in

Cyc

les

-2

-1.5

-1

-0.5

0

0.5

1

1.5

2

0 1 2 3 4 5 6 7Time in bits

Phas

e in

Cyc

les

-2

-1.5

-1

-0.5

0

0.5

1

1.5

2

0 1 2 3 4 5 6 7Time in bits

Phas

e in

Cyc

les


Modulator Designs

Angle modulatorsCombine frequency pulses and apply to frequency modulator.Combine phase pulses and apply to phase modulator.

FrequencyPulse

Generator

PhasePulse

Generator


CPM as Frequency Modulation

LPF FMModulator

bipolarNRZ-L

∫∞−

=t

d dmft λλπφ )(2)(frequency is the time-derivative of the phasesince the phase is proportional to the integral of m(t), the frequency is proportional to m(t).

)(tm)(tx

( ))(2cos)( 0 ttfAtx φπ +=

time-varying phase



CPM as Phase Modulation

)(tφ

)(tφ

( )dtfd ∫π2LPF PhaseModulator

bipolarNRZ-L )(tm

)(tx



CPM as QAM

4342143421)2sin())(sin()2cos())(cos())(sin()2sin())(cos()2cos(

))(2cos()(

00

00

0

tftAtftAttfAttfA

ttfAtxYX

πφπφφπφπ

φπ

−=−=

+=

( ) YXYXYX sinsincoscoscos −=+

Apply the trigonometric identity

to our expression for the CPM modulated carrier:

“quadrature carriers”

( )dtfd ∫π2

cos( )

sin( )

~ LO

phase shift

Σ+

−

The Equations What the Equations Tell Us to Build

)(tm )(tφ

)(cos tφ

)(sin tφ

)2cos( 0tfπ

)2sin( 0tfπ

)(tx



CPM Quadrature Signals

cos( )

sin( )

~ LO

phase shift

Σ+

−)(tm )(tφ

)(cos tφ

)(sin tφ

)2cos( 0tfπ

)2sin( 0tfπ

)(tx

)(tφ

)(tm

)(cos tφ

)(sin tφ

( )dtfd ∫π2



M=2, h=1/2, 1REC (MSK)

- 2

-1.5

- 1

-0.5

0

0 . 5

1

1 . 5

2

0 1 2 3 4

CPM Phase Tree

Mul

tiple

of π

Time in Symbols

RECShaping1/2h2M1L

-120

-100

-80

-60

-40

-20

- 2 -1.5 - 1 -0.5 0 0.5 1 1.5 2

PS

D in

dB

c/H

z

CPM PSD

Frequency (Bit Rates)

PSD vertical axis is dBc per FFT bin1 FFT bin = 1/64 * symbol rate


M=4, h=1/4, 1REC

- 3

- 2

- 1

0

1

2

3

0 1 2 3 4

CPM Phase Tree

Mul

tiple

of π

Time in Symbols

RECShaping1/4h4M1L

-120

-100

-80

-60

-40

-20

- 2 -1.5 - 1 -0.5 0 0.5 1 1.5 2

PS

D in

dB

c/H

z

CPM PSD




M=4, h=1/4, 1RC

-120

-100

-80

-60

-40

-20

- 2 -1.5 - 1 -0.5 0 0.5 1 1.5 2

PS

D in

dB

c/H

z

CPM PSD


- 3

- 2

- 1

0

1

2

3

0 1 2 3 4

CPM Phase Tree

Mul

tiple

of π

Time in Symbols

R CShaping1/4h4M1L



M=4, h=1/4, 2RC

-120

-100

-80

-60

-40

-20

- 2 -1.5 - 1 -0.5 0 0.5 1 1.5 2

PS

D in

dB

c/H

z

CPM PSD


- 3

- 2

- 1

0

1

2

3

0 1 2 3 4

CPM Phase Tree

Mul

tiple

of π

Time in Symbols

R CShaping1/4h4M2L



M=4, h=1/4, 3RC

-120

-100

-80

-60

-40

-20

- 2 -1.5 - 1 -0.5 0 0.5 1 1.5 2

PS

D in

dB

c/H

z

CPM PSD


- 2

- 1

0

1

2

3

0 1 2 3 4

CPM Phase Tree

Mul

tiple

of π

Time in Symbols

R CShaping1/4h4M3L



Multi-h CPM

Cyclically rotates through multiple “sets” of FSK tonesIncreases minimum distance in trellis

Improves BER performance

Widely proposed for high-performance nonlinear channels

MIL-STD-188-181B


M=2, h1=1/4, h2=1/2, 1REC

-1.5

- 1

-0.5

0

0 . 5

1

1 . 5

0 1 2 3 4

CPM Phase Tree

Mul

tiple

of π

Time in Symbols

RECShaping1/4, 1/2h

2M1L

-120

-100

-80

-60

-40

-20

- 2 -1.5 - 1 -0.5 0 0.5 1 1.5 2

PS

D in

dB

c/H

z

CPM PSD




M=4, h1=4/16, h2=5/16, 3RC

- 2

- 1

0

1

2

3

4

0 1 2 3 4

CPM Phase Tree

Mul

tiple

of π

Time in Symbols

R CShaping4/16, 5/16h

4M3L

-120

-100

-80

-60

-40

-20

- 2 -1.5 - 1 -0.5 0 0.5 1 1.5 2

PS

D in

dB

c/H

z

CPM PSD



ARTM Tier II Waveform


PCM/FM (Tier 0)

LPF FMModulator

bipolarNRZ-L

∫∞−

=t

d dmft λλπφ )(2)(frequency is the time-derivative of the phasesince the phase is proportional to the integral of m(t), the frequency is proportional to m(t).

)(tm)(tx


time-varying phase



Tier 0 in CPM Notation

M = 2 (binary)αi = 2di - 1

di = 0, 1, αi = -1, +1h = 0.7g(t) is the normalized impulse response of a high order Bessel filter with 3 dB bandwidth = 0.7 * bit rate

Normalized such that the integral over all time = 1/2

-∞< t <+∞


∫ ∑∞−

+∞

−∞=

−=t



PCM/FM as a Phase Modulation


Power Spectral Density (PSD)



5 Mbps


PCM/FM Summary

Legacy waveformEquipment is ubiquitous

Constant envelopeSeveral practical implementations99.9% bandwidth: 2.03 times bit rate

M αi h g(t)2 -1, +1 0.7 Normalized impulse response of a high order

Bessel filter with 3 dB bandwidth = 0.7 * bit rate


Tier I OverviewShaped OQPSK (SOQPSK)

Constant envelope modulation(s) introduced by Hill (ITC 2000)Defined by 4 parameters ( ρ, B, T1, T2 )Compatible with existing efficient non-linear class C power amplifierNon-proprietary waveformComparable in performance and interoperable with FQPSK

FQPSKPatented by K. FeherDefined by I and Q componentsNon-constant envelopeDetails are proprietary, contact Digcom


SOQPSK in CPM Notation

M = 3 (ternary)

αi = -1, 0, +1

ai = 2di - 1

ai = -1, +1, di = 0, 1

h = 0.5g(t) = windowed impulse response of spectral raised cosine


-∞< t <+∞


∫ ∑∞−

+∞

−∞=

−=t


α i = −1( ) i+1 ai−1(ai − ai−2)2

,


Definition of SOQPSK Pulse

g(t) = n(t) * w(t), where

n(t) =Acos(πρ Bt T)1− 4(ρ Bt T )2 *

sin(π Bt T )(π Bt T )

w(t) =

1, for t T < T1

12

+12

cosπ ( t T −T1)

T2

, for T1 < t T < T1 + T2

0, for t T > T1 + T2

⎧

⎨ ⎪ ⎪

⎩ ⎪ ⎪

⎫

⎬ ⎪ ⎪

⎭ ⎪ ⎪


Frequency Pulse Shape, g(t)


SOQPSK Variants

99.9

9% B

andw

idth


Optimal SOQPSK Variants99

.99%

Ban

dwid

th


Unshaped Offset QPSK


Slightly Shaped OQPSK


MIL-STD SOQSPK


SOQPSK-TG


SOQPSK-TG Phase Tree

-2

-1.5

-1

-0.5

0

0.5

1

1.5

2

0 1 2 3 4 5 6 7 8Time in bits

Phase

in C

ycle

s

-2

-1.5

-1

-0.5

0

0.5

1

1.5

2

0 1 2 3 4 5 6 7 8Time in bits

Phase

in C

ycle

s

-2

-1.5

-1

-0.5

0

0.5

1

1.5

2

0 1 2 3 4 5 6 7 8Time in bits

Phase

in C

ycle

s

-2

-1.5

-1

-0.5

0

0.5

1

1.5

2

0 1 2 3 4 5 6 7 8Time in bits

Phase

in C

ycle

s

-2

-1.5

-1

-0.5

0

0.5

1

1.5

2

0 1 2 3 4 5 6 7 8Time in bits

Phase

in C

ycle

s

-2

-1.5

-1

-0.5

0

0.5

1

1.5

2

0 1 2 3 4 5 6 7 8Time in bits

Phase

in C

ycle

s

-2

-1.5

-1

-0.5

0

0.5

1

1.5

2

0 1 2 3 4 5 6 7 8Time in bits

Phase

in C

ycle

s

-2

-1.5

-1

-0.5

0

0.5

1

1.5

2

0 1 2 3 4 5 6 7 8Time in bits

Phase

in C

ycle

s


Power Spectral Density


SOQPSK-A Eye Pattern

-1.5

-1

-0.5

0

0.5

1

1.5

0 0.25 0.5 0.75 1 1.25 1.5 1.75 2Time (Symbols)

I Cha

nnel


SOQPSK & FQPSK, Linear PA


FQPSK, Non-Linear PA


SOQPSK-A, Non-Linear PA


SOQPSK & FQPSK, Non-Linear


Measured PSD (Tier 0 & 1)



5 Mbps


Shaped Offset QPSK SummaryConstant envelope, CPM waveformAdjustable shaping factor for BW and detection efficiency trade-offImproved spectral containment over OQPSKCompatible with standard OQPSK receivers and demodulatorsAdopted as an ARTM Tier I waveform99.9% bandwidth: 0.98 times bit rateInteroperable with FQPSK

M αi h g(t)3 -1, 0, +1 0.50 Normalized windowed impulse response of a

spectral raised cosine


Tier II Overview

Multi-h CPM characteristicsEasy to trade off bandwidth and detection efficiency.Constant envelope is ideal for high efficiency non-linear power amplifiers.Detection efficiency is enhanced by periodically varying the modulation index (h).

Extends the point at which competing paths remerge thereby increasing the minimum distance and decreasing the probability of symbol error.

Nearly 2.5x improvement over PCM/FM in spectral efficiency with similar detection efficiency.


ARTM Tier II in CPM Notation

M = 4 (quaternary)

αi = 2 [2d1i + d0i] - 3αi = -3, -1, +1, +3di = 0, 1

h = 4/16, 5/16, alternatingg(t) = raised cosine, 3 symbols (6 bits) in duration


-∞< t <+∞


∫ ∑∞−

+∞

−∞=

−=t



Frequency Pulse & Phase Tree

0 0.5 1 1.5 2 2.5 30

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

TIME (SYMBOLS)

NO

RM

ALI

ZED

FR

EQ

UE

NC

Y/P

HA

SE

LENGTH 3 RC FREQUENCY PULSE AND CORRESPONDING PHASE PULSE


PSD (Tier 0, I, & II)



5 Mbps


Tier II Multi-h CPM Summary

Similar detection efficiency to PCM/FM.Constant envelope waveform is ideal for efficient non-linear PA’s.Enhanced performance gained by increasing demodulator complexity.99.9% bandwidth: 0.75 times bit rate

M αi h g(t)4 -3, -1, +1, +3 4/16, 5/16 Normalized raised cosine, 3 symbols

(6 bits) long


Side by Side SummaryTier M αi h g(t)

0 2 -1, +1 0.7 Normalized impulse response of a high order Bessel filter with 3 dB bandwidth = 0.7 * bit rate

I 3 -1, 0, +1 0.5 Normalized windowed impulse response of a spectral raised cosine, 8 bits long

II 4 -3, -1, +1, +3 4/16, 5/16 Normalized raised cosine, 3 symbols (6 bits) long


Demodulation

As the shop manual says, “Installation is reverse of removal.”Demodulation is intrinsically more difficult

Unknown carrier frequencyUnknown carrier phaseUnknown clock frequency and phaseSignal corruption

Noise InterferenceMultipathDoppler shift


Demodulation Overview

Tier 0 Tier I Tier II

Single-Symbol Countless vendorsBER = 1e-5 @12.1 to 13.0 dB Eb/N0

Numerous vendorsBER = 1e-5 @11.7 to 12.5 dB Eb/N0

Not practical

Multi-Symbol(Trellis)

Two vendorsBER = 1e-5 @8.6 to 9.4 dB Eb/N0

One vendorBER = 1e-5 @11.2 dB Eb/N0

Two vendorsBER = 1e-5 @11.4 to 12.1 dB Eb/N0

Legacy (nearly exclusive prior to 2001)


Tier 0 Single-Symbol Detection

Differentiate the phase to get frequencyLimiter-discriminatorPhase locked loopDigital processing

If the frequency in this symbol > 0, data = 1If the frequency in this symbol < 0, data = 0


∫ ∑∞−

+∞

−∞=

−=t



Tier 0 Frequency Detection


Tier 0 Phase Tree

-4

-3

-2

-1

0

1

2

3

4

0 1 2 3 4 5 6 7Time in bits

Phase

in C

ycle

s

h = 0.7


Phase Trajectory Never Forgets

-4

-3

-2

-1

0

1

2

3

4

0 1 2 3 4 5 6 7Time in bits

Phas

e in

Cyc

les

-4

-3

-2

-1

0

1

2

3

4

0 1 2 3 4 5 6 7Time in bits

Phas

e in

Cyc

les

If this bit is different, the phase trajectory is forever shifted…

Therefore, later bits can help make decisions about earlier bits.


Multi-Symbol Detector Example

Phase1

1 1

10

0 0

000001010

100101110111

011

Correlators

ChooseLargest

Magnitude

MiddleBit

Multi-SymbolDetector Span


Tier 0 BER Performance

1.E-07

1.E-06

1.E-05

1.E-04

1.E-03

1.E-02

1.E-01

2 3 4 5 6 7 8 9 10 11 12 13 14Eb/N0 (dB)

BER

Conventional Single-Symbol (1990's)

First Generation Multi-Symbol (2001)

Second Generation Multi-Symbol (2004)

MLSE (Theoretical Limit)


Legacy PCM/FM Transmitters

-4

-3

-2

-1

0

1

2

3

4

0 1 2 3 4 5 6 7Time in bits

Phase

in C

ycle

s

h = 0.6

-4

-3

-2

-1

0

1

2

3

4

0 1 2 3 4 5 6 7Time in bits

Phase

in C

ycle

s

h = 0.7h = 0.8

-4

-3

-2

-1

0

1

2

3

4

0 1 2 3 4 5 6 7Time in bits

Phase

in C

ycle

s


Effect of TX Deviation Error

8

9

10

11

12

13

0.60 0.65 0.70 0.75 0.80Modulation Index, h

Eb/N

0 (

dB)

for

BER =

1.0

e-5

Conventional Single-Symbol (1990's)

First Generation Multi-Symbol (2001)

Second Generation Multi-Symbol (2004)

MLSE (Theoretical Limit)


SOQPSK Detection

Can be detected by conventional (non-shaped) offset QPSK demodNon-matched filtering loss of about 2 dBButterworth lowpass filter is reasonable approximation to matched filterTrellis detection is optimum, but more complex


SOQPSK-A Eye Pattern

-1.5

-1

-0.5

0

0.5

1

1.5

0 0.25 0.5 0.75 1 1.25 1.5 1.75 2Time (Symbols)

I Cha

nnel

Single-symbol detection ignores memory inherent in waveformCan be detected by conventional (non-shaped) offset QPSK demodI&D detector endures additional loss due to waveform mismatch


SOQPSK Constellations


SOQPSK-TG Phase Tree

-2

-1.5

-1

-0.5

0

0.5

1

1.5

2

0 1 2 3 4 5 6 7 8Time in bits

Phase

in C

ycle

s

-2

-1.5

-1

-0.5

0

0.5

1

1.5

2

0 1 2 3 4 5 6 7 8Time in bits

Phase

in C

ycle

s

-2

-1.5

-1

-0.5

0

0.5

1

1.5

2

0 1 2 3 4 5 6 7 8Time in bits

Phase

in C

ycle

s

-2

-1.5

-1

-0.5

0

0.5

1

1.5

2

0 1 2 3 4 5 6 7 8Time in bits

Phase

in C

ycle

s

-2

-1.5

-1

-0.5

0

0.5

1

1.5

2

0 1 2 3 4 5 6 7 8Time in bits

Phase

in C

ycle

s

-2

-1.5

-1

-0.5

0

0.5

1

1.5

2

0 1 2 3 4 5 6 7 8Time in bits

Phase

in C

ycle

s

-2

-1.5

-1

-0.5

0

0.5

1

1.5

2

0 1 2 3 4 5 6 7 8Time in bits

Phase

in C

ycle

s

-2

-1.5

-1

-0.5

0

0.5

1

1.5

2

0 1 2 3 4 5 6 7 8Time in bits

Phase

in C

ycle

s


SOQPSK Detection Efficiency


SOQPSK-TG

1.E-08

1.E-07

1.E-06

1.E-05

1.E-04

1.E-03

1.E-02

1.E-01

2 3 4 5 6 7 8 9 10 11 12 13 14Eb/N0 (dB)

BER

Tier I, QSX-DMS

Tier I, MMD-44, Temple


BER Performance of FQPSK

From Gene Law’s Oct 98 paper


Cumulative Error Countsin Bursty Channels

Bit Error Accumulation HistoryARTM flight 78, frequency diversity, 5 m antenna, high altitude corridor, easterly, 20k ft. altitude

0.0E+00

5.0E+06

1.0E+07

1.5E+07

2.0E+07

2.5E+07

0 500 1000 1500 2000 2500


Bit

Erro

rs

ERR NDERR DBS



Synchronization TestTransmit randomized ones patternMeasure time at which demod output becomes “all ones” (or mostly)

IRIG Randomizer Modulator Add Noise

Noise

Switch

Demodwith

DerandomizerTimer

OnesDetector

All ones

Controller

Start

Stop


SOQPSK Synchronization, No Noise


SOQPSK Synchronization, 6 dB10 Mbps, 6 dB Eb/N0

0

200

400

600

800

1000

1200

1400

1600

1800

0

100

200

300

400

500

600

700

800

900

1000

Synchronization Time (Bits)

Freq

uenc

y

0%

20%

40%

60%

80%

100%

120%

FrequencyCumulative %



0

200

400

600

800

1000

1200

1400

1600

1800

0

100

200

300

400

500

600

700

800

900

1000


Freq

uenc

y

0%

20%

40%

60%

80%

100%

120%



SOQPSK Synchronization, -1 dB10 Mbps, -1 dB Eb/N0

0

200

400

600

800

1000

1200

1400

1600

1800

0

100

200

300

400

500

600

700

800

900

1000


Freq

uenc

y

0%

20%

40%

60%

80%

100%

120%



Multi-h CPM Detection

Modulator intentionally creates severe inter-symbol interference

3-symbol RC premod filter

Symbol-by-symbol detection is essentially uselessTrellis detection is requiredEnormously complex machine

12.5 million gates


Demodulator Architecture


Demodulator Complexity

If signal can be represented in a finite state trellis, the Viterbi Algorithm can be used for demodulation.Modulation indices = h = 2k/p

M=4, L=3, h1 = 4/16, h2 = 5/16

Receiver implementation complexityNumber of Correlations ML = 64Number of Phase States p = 32Number of Branch Metrics pML = 2048Number of Trellis States pML-1 = 512


BER Performance Comparison

1.E-07

1.E-06

1.E-05

1.E-04

1.E-03

1.E-02

1.E-01

2 3 4 5 6 7 8 9 10 11 12 13 14Eb/N0 (dB)

BER

Tier 0: Conventional Single-Symbol (1990's)

Tier 0: First Generation Multi-Symbol (2001)

Tier 0: Second Generation Multi-Symbol (2004)

Tier I (SOQPSK-TG)

Tier II (Multi-h CPM)


If One is Good…

Two must be betterMany telemetry systems utilize multiple antenna feeds

Spatial separationFrequency separationOrthogonal polarizations

Combining two (or more) copies of the same signalDiversity combiningCreates a third signal to be demodulatedBER performance of third signal is better than either of the individual signals


Maximal Ratio Combining

Weight each signal in proportion to its SNR and addYields optimum SNR on combined channel in AWGNSNRcombined = SNRa + SNRb


BER Results - Fading Signals


Measured Combiner BER - Tier 0PCMFM

Ch 0 Eb/N0 = Ch 1 Eb/N0

1.E-07

1.E-06

1.E-05

1.E-04

1.E-03

1.E-02

1.E-01

0 5 10 15Eb/N0 (dB)

BER

Ch 0Ch 1Ch 2 (90º)Theory

PCMFMCh 0 Eb/N0 = 6

1.E-07

1.E-06

1.E-05

1.E-04

1.E-03

1.E-02

1.E-01

-2 0 2 4 6 8 10 12 14Ch 1 Eb/N0 (dB)

BER



Measured Combiner BER - Tier ISOQPSK


1.E-07

1.E-06

1.E-05

1.E-04

1.E-03

1.E-02

1.E-01

0 5 10 15Eb/N0 (dB)

BER


SOQPSKCh 0 Eb/N0 = 6

1.E-07

1.E-06

1.E-05

1.E-04

1.E-03

1.E-02

1.E-01

-2 0 2 4 6 8 10 12 14Ch 1 Eb/N0 (dB)

BER



Measured Combiner BER - Tier IIMHCPM


1.E-07

1.E-06

1.E-05

1.E-04

1.E-03

1.E-02

1.E-01

0 5 10 15Eb/N0 (dB)

BER


MHCPMCh 0 Eb/N0 = 9

1.E-07

1.E-06

1.E-05

1.E-04

1.E-03

1.E-02

1.E-01

-2 0 2 4 6 8 10 12 14Ch 1 Eb/N0 (dB)

BER



PSD is Half the Story

Overall spectral efficiency is determined by spacing between channelsReceiver selectivity affects channel spacingA valid comparison must account for both transmitted spectrum and “tolerable” receiver filteringNot all modulations are equally “tolerant” of IF filtering and interferenceMulti-channel testing accounts for these factors


Multi-channel ACI Test Set


9 Mbps Multi-h CPM, Multichannel


BER as a Function of ∆F0


I/C=20 dB

ACI Summary


Frequency Separation Rulewhere:

• ∆F0 = the minimum center frequency separation in MHz• Rs = bit rate of desired signal in Mb/s• Ri = bit rate of interfering signal in Mb/s

∆F0 = as*Rs + ai*Ri

Modulation Type as ai Rs = Ri

NRZ PCM/FM 1for receivers with RLC final Intermediate Frequency (IF) filters

1.2 2.2

0.7for receivers with Surface Acoustic Wave (SAW) or digital IF filters

1.2 1.9

0.5with multi-symbol detectors (or equivalent devices)

1.2 1.7

FQPSK-B, FQPSK-JR, SOQPSK-TG 0.45 0.65 1.1ARTM CPM 0.35 0.5 0.85

The NRZ PCM/FM signals are assumed to be premodulation filtered with a multi-pole filter with 3 dB point of 0.7 times the bit rate and the peak deviation is assumed to be approximately 0.35 times the bit rate.The receiver IF filter is assumed to be no wider than 1.5 times the bit rate and provides at least 6 dB of attenuation of the interfering signal.The interfering signal is assumed to be no more than 20 dB stronger than the desired signal.The receiver is assumed to be operating in linear mode; no significant intermodulation products or spurious responses are present.


Multipath Propagation

This image cannot currently be displayed.

Dry lake bed = smooth reflecting surface

Narrow beam receive antennaAirborne transmitter Line-of-sight communications link

Irregular terrain

Low elevation angle

Figure from Dr.Michael Rice, BYU Telemetry Laboratory, Provo, Utah. Reprinted by permission of the author.


AssumptionsChannel can be modeled as LTI system over “short enough” time interval

( ) ( ) ( )( )

( ) ( ) ( )( )∑

∑−

=

−

−

=

−

−Γ+=

−Γ=

1

1

1

0

)(

);(

L

kk

xjk

L

kk

xjk

xtext

xtexxth

kc

kc

τδδ

τδ

τω

τω

Line-of-sight propagation path

L-1 multipath propagation paths



ARTM Experiments127-PNsource LPF BPSK

modlinearPA

bipolar NRZ @10 Mbits/sec

aircraft fuselage

hemisphericallyomni-directionalantenna

tracking antenna

widebandtelemetryreceiver

70 MHz IF high speeddigital

oscilloscope

BPSKdemod

BERanalyzer

triggercircuit

AGC A/D

PC

GPS

sampling trigger

L-Band 1500 MHzS-Band 2200 MHz



Edwards AFB Flight Paths



Signal Processing

-8 -6 -4 -2 0 2 4 6 8123456789

10

Frequency (MHz), relative to carrier

S x(e

jΩ

) (dB

)

-8 -6 -4 -2 0 2 4 6 80

2

4

6

8

10

12

14

Sy(e

j Ω) (

dB)

Frequency (MHz), relative to carrier

-35

-30

-25

-20

-15-10

-5

0

5

10

-8 -6 -4 -2 0 2 4 6 8Frequency (MHz), relative to carrier

|H(e

jΩ)|2

(dB

)

Power spectral density of transmitted signal

Power spectral density of received signal

Estimate of channel transfer function



Modeling Procedure

This image cannot currently be displayed.

( ) ( )( )ωωω

SRH =

) power spectral density of received signalpower spectral density of transmitted signal



Measurement and Modeling



Channel Transfer Function

1 (0 dB)

M

D

1

2τπ

2

2τπ

ω0

( )2ωH (dB)

(3-Ray Model)( )2ωH (dB)

(2-Ray Model)

2121 and Assumes Γ>Γ< ττ



Frequency-Dependent Parametersmagnitude of first multipath reflection: Γ1“sweep rate” of multipath null

( )2ωH

ω

( )211 Γ+=M

(dB)

( )211 Γ−=D

1 (0 dB)

1111 Γ+=Γ∠+ θτωτω cc

1

2τπ

0

null “sweep rate” ~11 Γ+θτω &&c



Received Signal Strength HistoryARTM flight 78, Cords Road, westerly

1

1.5

2

2.5

3

3.5

4

0 100 200 300 400 500 600 700 800


RSS

- Vo

lts (1

0 dB

/Vol

t)

AGC1AGC4

Measured Data

Frequency Diversity



Received Signal Strength HistoryARTM flight 78, Cords Road, westerly

0

0.5

1

1.5

2

2.5

3

3.5

100 120 140 160 180 200 220 240 260 280 300


RSS

- Vo

lts (1

0 dB

/Vol

t)

AGC1AGC4


Classic Two-Ray Multipath


Bit Error Accumulation HistoryARTM flight 78, frequency diversity, FQPSK-JR, 5 Mb/s, Cords westerly

0.0E+00

5.0E+05

1.0E+06

1.5E+06

2.0E+06

2.5E+06

3.0E+06

3.5E+06

4.0E+06

4.5E+06

5.0E+06

0 100 200 300 400 500 600 700 800 900 1000


Bit

Erro

rs

ERR NDERR DBS

Classic 2-ray Multipath

Frequency Diversity Example 1



Frequency Diversity Example 2Bit Error Accumulation History

ARTM flight 78, frequency diversity, 5 m antenna, high altitude corridor, easterly, 20k ft. altitude

0.0E+00

5.0E+06

1.0E+07

1.5E+07

2.0E+07

2.5E+07

0 500 1000 1500 2000 2500


Bit

Erro

rs

ERR NDERR DBS



Spatial Diversity Example 1Bit Error Accumulation History

ARTM flight 71, spatial diversity, 1.2 m antennas, 5 Mb/s FQPSK-JR, Cords Rd., Easterly, 5k ft. altitude

0.E+00

1.E+06

2.E+06

3.E+06

4.E+06

5.E+06

6.E+06

0 200 400 600 800 1000 1200


Bit E

rror

s

ERR DBSERR ND




ARTM flight 71, spatial diversity, 1.2 m antennas, 5 Mb/s FQPSK-JR, Bk. Mtn., Westerly, 5k ft. altitude

0.E+00

1.E+05

2.E+05

3.E+05

4.E+05

5.E+05

6.E+05

7.E+05

8.E+05

0 100 200 300 400 500 600 700 800 900


Bit

Erro

rs

ERR DBSERR ND




ARTM flight 69, spatial diversity, 1.2 m antennas Bk. Mtn, westerly, 5 Mb/s FQPSK-JR, 5k ft. altitude

0.0E+00

2.0E+06

4.0E+06

6.0E+06

8.0E+06

1.0E+07

1.2E+07

1.4E+07

1.6E+07

1.8E+07

2.0E+07

0 200 400 600 800 1000 1200

Elapsed Time - seconds

Bit E

rror

s

ERR DBSERR ND



Multipath Summary

Your channel may - or may not - exhibit multipath propagation effectsIf so, there will be intervals during which no useful data is recoveredLoss of bit count integrity is likely

Encrypted links will lose crypto syncWhat to do?Rewind to slide 130Use diversity!


Adaptive Equalization

Consider the multipath channel to be a filterVaries over time

Consider building a filter which “undoes” the filtering imposed by the channel

Let it keep track of the the channel and continuously adapt itself to the channel

Presto! You have an adaptive equalizerCan repair damage done by multipathWorks with a single receiverRequires no bandwidth expansion


Adaptive Equalizer


PCM/FM in Multipath


SOQPSK in Multipath


CPM in Multipath


Is Equalization Helpful?Adaptive equalizer can “undo” multipath distortionHowever, it must adaptAdaptation has limitations

Equalizer length (number of taps, and total span)Adaptation rate

Trade off accuracy for speedFast adaptation necessarily degrades BER performance (relative to no equalizer)

Within these limits, equalization helpsWhen the equalizer gets lost, re-synchronization time is increased by the time required to re-adaptIn severe multipath, equalization can do more harm than goodRapid synchronization and low acquisition threshold are always beneficial


Polarizationreceive diversity

Space-Time Coding

Air vehicle maneuveringmasks Tx antenna andcauses polarization mismatch

Ground bouncecreates multipathinterference

Spatial transmit diversity

Ronald C. Crummett, Michael A. Jensen, Michael D. RiceDepartment of Electrical and Computer EngineeringBrigham Young University


Difficulties with TX Diversity

30

210

60

240

90

270

120

300

150

330

180 0

Antenna 2

Antenna 1

Spatially Separated Antennas CreateInterference Pattern


MIMO CommunicationsMIMO: Multiple-Input Multiple-Output

Exploit multiple communication modes

HSpace-TimeEncoder

Data Space-TimeDecoder

Data

Potential Benefits: • Diversity (robust communications)• Increased data throughput


Alamouti Space-Time Coding

A B C D E F G H I J K L ...

space-timeencoder

A -B* C -D* E -F* G -H* I -J* K -L* ...

B A* D C* F E* H G* J I* L K* ...

traditional

1st block 2nd block

• 2 transmit antennas + 1 receive antenna version• 2 transmit antennas + 2 receive antennas version• Calderbank showed that the Alamouti schemes are special cases of more

general “orthogonal designs”


Traditional TransmissionEach symbol is simultaneously sent from both antennas

Received signal energy

With the noise energy as No, the received SNR is

r =12

h1 + h2( )s + ηPower equally

divided between antennas

ET = Ε12

h1 + h2( )s[ ]*h1 + h2( )s

⎧ ⎨ ⎩

⎫ ⎬ ⎭

=12

h1 + h22Ε s2 =

12

h1 + h22 Es

SNRT =12

h1 + h22 Es

No


Alamouti Space-Time CodingSignal energy over one symbol time:

Received noise energy:

Signal-to-Noise Ratio:

EA ,1 = Ε12

h12 + h2

2( )⎡ ⎣ ⎢

⎤ ⎦ ⎥

2

s1*s1

⎧ ⎨ ⎩

⎫ ⎬ ⎭

=12

h12 + h2

2( )⎡ ⎣ ⎢

⎤ ⎦ ⎥

2

Es

NA ,1 = Ε12

h1*η1 + h2η2

*( )*h1

*η1 + h2η2*( )⎧

⎨ ⎩

⎫ ⎬ ⎭

=12

h12Ε η1

2 +12

h22Ε η2

2 =12

h12 + h2

2( )No

SNRA =12

h12 + h2

2( ) Es

No


Symbol Error Rate - QPSK

P E( ) = 2Q Es

No

⎛

⎝ ⎜

⎞

⎠

If the aircraft is rotated 360° in the horizontal plane

SER for QPSK in AWGN

Using two transmit antennas (traditional signaling)

P E |θ,φ( ) = 2Q Es

No

h1 θ,φ( ) + h2 θ,φ( ) 2

2

⎛

⎝

⎜ ⎜

⎞

⎠

P E |θ( ) =1

2π2Q Es

No

h1 θ,φ( ) + h2 θ,φ( ) 2

2

⎛

⎝

⎜ ⎜

⎞

⎠

⎟ ⎟ dφ

0

2π

∫


Symbol Error Rate - QPSK

For Alamouti signaling

P E |θ( ) =1

2π2Q Es

No

h1 θ,φ( ) 2+ h2 θ,φ( ) 2

2

⎛

⎝

⎜ ⎜

⎞

⎠

⎟ ⎟ dφ

0

2π

∫Only magnitudes oftransfer functionsused in sum

Traditional signaling

P E |θ( ) =1

2π2Q Es

No

h1 θ,φ( ) + h2 θ,φ( ) 2

2

⎛

⎝

⎜ ⎜

⎞

⎠

⎟ ⎟ dφ

0

2π

∫Addition of transferfunctions leads toreduction in effectiveSNR


Consider BPSK Signaling and Assume s1 = s2 = 1Time Slot 1:

Gain Pattern:

Time Slot 2:Gain Pattern:

Alamouti Scheme

⎥⎦⎤

⎢⎣⎡= φφ cos

2cos2)( 2

1kdGt

⎥⎦⎤

⎢⎣⎡= φφ cos

2sin2)( 2

2kdGt

30

210

60

240

90

270

120

300

150

330

180 0

30

210

60

240

90

270

120

300

150

330

180 0

Antenna Pattern Interpretation


Symbol Error Rate

Similar expressions have been derived for:• Polarization diversity at receiver (Maximal Ratio combining)

• One multipath (ground) bounce

• BPSK and 16-QAM signal constellations

for both Traditional Signaling and Alamouti Signaling


SER SimulationsAntenna Separation: 20’ Horizontal, 8’ VerticalAntenna Patterns: Isotropic

Simple AWGN

Channel


SER Simulations

Results Identical to Single Receive Antenna System

CircularPolarization

Diversity Reception


SER SimulationsAntenna Separation: 20’ Horizontal, 8’ VerticalAntenna Patterns: Isotropic

One Ground Bounce

(Multipath)

Prototype Testing

164

QuasonixSTC

TransmitterCombiner

Noise+

InterferenceTest Set

TelemetryReceiver

BYUSTC

DemodBERT

Laptop PC

RF1485.5 MHz

IF

70 MHz

EAFB Telemetry Lab Configuration

FastBit FB2000

AgilentStep Attenuator

8496B

Narda 4322-2

BERT

Fireberd 6000A

20 dBatten

PasternackPE7017-20

Reach TechnologiesVBERT-50S-1-R

M/A Com SMR 5550i

PasternackPE7017-20


8495B


8495B

20 dBatten

10 dBatten

10 dBatten

20 dBatten

A

(10 W)

B

(10 W)

DirectionalCoupler

SpectrumAnalyzer

−6 dB output

Agilent E4404A

Adtran 10866-6

Reference Link BER Calibration

165

RFN I/QSource

CalibratedNoise

Source

Tier-1Demod BERT

IF

70 MHz

HP 3708A

VectorGenerator

MXG Series

I

Q

RF Networks2120

HP3784ADigital Traffic Analyzer

Reference Link BER Calibration

166

10 W

10 W

Flight Tests: Airborne Configuration

167

STCTransmitter

SOQPSKTransmitter

L-bandisolator +

+÷

Channel MicrowaveL320I

3 dB

3 dB

PasternakPE 7016-3

Narda 4322-2

upper antenna

lower antenna

10 W5 W

5 W

5 W

5 W

SOQPSKTransmitter

GPS/AHRShouse keeping link antenna (separate lower antenna)

Quasonix QSX-VLT-110-105-20-6A

Quasonix


L-bandisolator


L-bandisolator


L-bandisolator


Narda 4322-2Narda 4322-2

L-bandisolator


PasternakPE 7016-3

168

C-12 Beechcraft: Airborne Platform

Antenna Locations

169

Flight Tests: Transmit Antennas

170

Lower Telemetry Antenna(behind the antenna looking forward)

Upper Telemetry Antenna(looking across the fuselage)

fuselage station = 222.25”centerline = 10” (left)waterline = 76”

fuselage station = 302””centerline = 9” (right)waterline = 145.5”

Flight Tests: Idealized Gain Patterns

171

STC FrequencyReference Link

Frequency

spectrum display

Flight Tests: Ground Station Configuration

172

LNA

Bldg 4795: “Antenna 5”EMT Model 150

5-m parabolic reflector

RHCP

multi-coupler

MU-Dell2MDP1425

T/M Receiver

1496.5 MHz

L-3/MicrodyneRCB 2000

Antenna Tracking

TCS ACU-M1

Housekeeping data logging and display

A 20 dBatten

1:4split

MU-Dell2MDA1424D-06

MU-Dell2MDA1424D-06

unity gain input-to-each-output

PC

AGC

AM

Data

Clock

to antennaservo motors

reference link1514.5 MHz

STC link1485.5 MHz

SpectrumAnalyzer

to DVD

Clk

IF

70 MHz

Test Flights: Ground Station Configuration

173

Receiver1514.5 MHz

M/A Com SMR 5550i

Tier 1Demod.

RF NetworksModel 2120

BERT

Fireberd 6000A

Data

Receiver1485.5 MHz

Microdyne 700 MR

AGC

AM

Data Acquisition

Wideband SystemsDRS 3300 (5 Msamples/s)

Clk

IF

70 MHzReceiver

1485.5 MHz

M/A Com SMR 5550i

BYUPrototype

STC Demod.BERT

Fireberd 6000A

Data

to PC data logging

Receiver1514.5 MHz

Microdyne 700 MR

AGC

AM

to PC data logging

Laptop PCfrom

splitter

National InstrumentsDAQ (20 samples/s)

Data Acquisition

AGC

AGC


174


175

STC Video Clip

176

M1: Left-Hand Turn @ 10° bank

177

M1: Test Results

178

M2: Right-Hand Turn @ 10° bank

179

M2: Test Results

180

M3: Left-Hand Turn @ 30° bank

181

M3: Test Results

182

M4: Right-Hand Turn @ 30° bank

183

M4: Test Results

184

M3 to C2 Transition

185

M3 to C2 Transition Test Results

186

C2: Cords Road West-to-East

187

C2: Test Results

188

D2: Cords Road East-to-West

189

D2: Test Results

190


STC Summary

Dual-Antenna Diversity Scheme Removes interference created by multiple transmit antennas

SNR equivalent to single antenna transmissionMulti-antenna scheme alleviates masking during maneuveringCan be used with diversity reception

Realtime hardware flight tested at Edwards AFB and showed substantial performance benefit


Forward Error CorrectionBasic premise

Insert redundant bits into transmitted streamUse known relationships between bits to correct errors

Countless schemes have been developedConvolutional code / Viterbi decoderBlock codes

BCHReed-Solomon

Low Density Parity Check (LDPC)Concatenated codes

RS / ViterbiTurbo product codes (TPC)


BER with TPC


Spectral Expansion - Tier 0


Spectral Expansion - Tier I


Sync Time with FEC


Cumulative Error Results


Does FEC help?

FEC is certainly effective in the AWGN channelReduces number of errors

FEC certainly increases the sync time of the receiving system

Increases number of errors

Net effect depends on your channelIf your channel is always in sync but has isolated one-at-a-time bit errors, FEC helpsIf your link has dropouts (due to multipath, shadowing, interference, etc.), FEC may do more harm than good


Waveform ComparisonPCM/FM (1x) SOQPSK (2x) Multi-h CPM (2.5x)

0 20 40 60 80 100 120 140 160 180 200-1

-0.8

-0.6

-0.4

-0.2

0

0.2

0.4

0.6

0.8

1

0 20 40 60 80 100 120 140 160 180 200-0.04

-0.03

-0.02

-0.01

0

0.01

0.02

0.03

0.04Eye Diagram of PCM/FM

0 20 40 60 80 100 120 140 160 180 200-1

-0.8

-0.6

-0.4

-0.2

0

0.2

0.4

0.6

0.8

1


Power Spectral Densities


Out-of-Band Power


BER Performance Comparison

1.E-07

1.E-06

1.E-05

1.E-04

1.E-03

1.E-02

1.E-01

2 3 4 5 6 7 8 9 10 11 12 13 14Eb/N0 (dB)

BER

Tier 0: Conventional Single-Symbol (1990's)

Tier 0: First Generation Multi-Symbol (2001)

Tier 0: Second Generation Multi-Symbol (2004)

Tier I (SOQPSK-TG)

Tier II (Multi-h CPM)


Bandwidth-Power Plane


Acknowledgements

Mark Geoghegan, Nova Dr. Michael Rice, Brigham Young UniversityBob Jefferis, Tybrin, Edwards AFBDr. Bernard SklarKip Temple, ARTM, Edwards AFBGene Law, NAWCWD, Pt. Mugu Vickie Reynolds, White Sands Missile Range


Questions/Comments

advanced modulation techniques for telemetry

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