Preamble Assisted Equalization for Aeronautical Telemetry

237 Pages·2017·3.86 MB·English

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Faculty Publications
2014-04-28
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AAeerroonnaauuttiiccaall TTeelleemmeettrryy ((PPAAQQ))
Michael Rice
[email protected]
Mohammad Saquib
Arlene Cole-Rhodes
Farzad Moazzami
Erik Perrins
Follow this and additional works at: https://scholarsarchive.byu.edu/facpub
Part of the Electrical and Computer Engineering Commons
BBYYUU SScchhoollaarrssAArrcchhiivvee CCiittaattiioonn
Rice, Michael; Saquib, Mohammad; Cole-Rhodes, Arlene; Moazzami, Farzad; and Perrins, Erik, "Phase 1
Final Report: Preamble Assisted Equalization for Aeronautical Telemetry (PAQ)" (2014). Faculty
Publications. 1298.
https://scholarsarchive.byu.edu/facpub/1298
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Phase 1 Final Report
Preamble Assisted Equalization
for Aeronautical Telemetry (PAQ)
Funded by the
Test Resource Management Resources Center (TRMC)
through a grant from the
Army PEO STRI Contracting Office
Contract Number W900KK-13-C-0026
Submitted by
Michael Rice (Brigham Young University)
Mohammad Saquib (University of Texas at Dallas)
Arlene Cole-Rhodes (Morgan State University)
Farzad Moazzami (Morgan State University)
Erik Perrins (University of Kansas)
April 2014
2
PAQPhase1FinalReport 3
Executive Summary
To fully leverage the benefits of a periodically inserted preamble, the preamble is used to estimate
the state of the channel. To this end the following algorithms have been developed, tested in
simulation,andportedtotheGPU-basedreal-timesystem:
1. The preamble detector, which scans the received samples searching for the presence of the
preamble. The location of the preamble in the received samples is required to use the re-
ceived samples to estimate the frequency offset, channel impulse response, and noise vari-
ance. The preamble detector works in the presence of an uncompensated frequency offset
andunknownchannel.
2. Thefrequencyoffsetestimator,whoseresultisusedtocompensateforalargefrequencyoff-
setintheRFcarrier. Thefrequencyoffsetestimatoroperatesinthepresenceofanunknown
channel.
3. The channel impulse response estimator, whose result is used by the zero-forcing and mini-
mummean-squarederrorequalizerstocomputetheequalizerfiltercoefficients. Thechannel
impulseresponseestimateisalsousedbytheCMA+AMAequalizerforinitialization.
4. Thenoisevarianceestimator,whoseresultisusedtoestimatethesignal-to-noiseratioparam-
eterincomputingtheoptimumminimummean-squarederrorequalizerfiltercoefficients.
The performance of three equalizers has been evaluated in simulation using eleven test chan-
nels derived from channel sounding experiments at Edwards AFB, CA. The equalizers are the
zero-forcing (ZF) equalizer, the minimum mean-squared error (MMSE) equalizer, and the com-
bined constant modulus algorithm, alphabet matched algorithm (CMA+AMA) equalizer. The bit
error rate performances of all three over the eleven test channels has been performed. A longi-
tudinal comparison shows that the MMSE and CMA+AMA have almost equivalent bit error rate
performance(andtheperformanceofbothissuperiortothatoftheZFequalizer). Otherequaliza-
tionoptionsarealsodiscussed(seeSection9).
Most of the hardware needed to implement the real-time demonstration system has been ac-
quired. Theseitemsincludethefollowing:
Modified L/S-band and C-band transmitters. The modification was the periodic insertion of
•
theiNETpreambleandASMfields.
Amodifiedtelemetryreceiverthatoutputsinphaseandquadraturesamplesat2samples/bit.
•
4
Two NVidia GPUs for performing the computationally complex equalization algorithms.
•
Thesecardsresideintworack-mountedhostcomputers,thathavealsobeenpurchased.
An8-channelbiterrorratetester.
•
Portable, shock-proof, racks for housing the equipment, along with the hardware, tools,
•
connectors,cables,fans,etc. necessarytosupporttheexperiments.
Because the emphasis of Phase 1 was primarily algorithmic, the report focuses on the descrip-
tion,analysis,andperformanceofthealgorithmsthatformtheequalizers. ThePhase2reportwill
provide a more detailed description of the hardware, C/C++ code, and the software architecture
usedtoimplementtheequalizationalgorithms.
PAQPhase1FinalReport 5
Contents
1 Preliminaries 7
1.1 SignalModel,Notation,andHigh-LevelSignalProcessing . . . . . . . . . . . . . 7
1.2 TestChannels . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8
2 PreambleDetector 23
2.1 TheMaximumLikelihoodPreambleDetector . . . . . . . . . . . . . . . . . . . . 26
2.2 ALow-ComplexityPreambleDetector . . . . . . . . . . . . . . . . . . . . . . . . 42
3 PAQFrequencyEstimators 55
3.1 Preliminaries . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55
3.2 ThePerrinsEstimator . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 60
3.3 TheModifiedFitzEstimator . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 62
3.4 TheModifiedLuise&ReggianniniEstimator . . . . . . . . . . . . . . . . . . . . 63
3.5 TheModifiedMengali&MorelliEstimator . . . . . . . . . . . . . . . . . . . . . 67
3.6 TheModifiedKayEstimator . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 72
3.7 SimulationResults . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 78
4 ChannelEstimator 105
4.1 DirectApplication . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 105
4.2 ImprovementstotheDirectApplication . . . . . . . . . . . . . . . . . . . . . . . 110
4.2.1 A“FullRank”PreambleSequence . . . . . . . . . . . . . . . . . . . . . . 110
4.2.2 IncludingtheASMSamplesintheChannelEstimator . . . . . . . . . . . 113
4.3 DealingWithanUnknownFrequencyOffset . . . . . . . . . . . . . . . . . . . . . 116
5 TheoreticalPerformanceBounds 123
6 SimulationResultsfortheFrequencyOffsetandChannelEstimators 131
7 Signal-to-NoiseRatioEstimator 143
7.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 143
7.2 NoiseVarianceEstimator . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 143
7.3 Signal-to-NoiseRatioEstimatorintheFieldandinSimulation . . . . . . . . . . . 153
6 Contents
8 Equalization 159
8.1 Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 159
8.2 TheZero-ForcingEqualizer . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 160
8.3 TheMinimumMean-SquaredError(MMSE)Equalizer . . . . . . . . . . . . . . . 170
8.4 CMA+AMAEqualizer . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 183
8.4.1 Background/Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . 183
8.4.2 Description . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 183
8.4.3 DiscussionandSimulationResults . . . . . . . . . . . . . . . . . . . . . . 191
8.5 LongitudinalComparisons . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 199
9 ThoughtsonOtherEqualizationTechniques 207
9.1 MaximumLikelihoodSequenceEstimation . . . . . . . . . . . . . . . . . . . . . 207
9.2 DecisionFeedbackEqualization . . . . . . . . . . . . . . . . . . . . . . . . . . . 208
9.3 AdaptiveVersionsofZFandMMSEequalizers . . . . . . . . . . . . . . . . . . . 209
9.4 FrequencyDomainEqualization(FDE) . . . . . . . . . . . . . . . . . . . . . . . 209
A SOQPSK-TGDetection 211
A.1 SOQPSK-TG:AMathematicalDescription . . . . . . . . . . . . . . . . . . . . . 211
A.2 TheSymbol-by-Symbol(SxS)Detector . . . . . . . . . . . . . . . . . . . . . . . 214
A.3 The4-StateTrellisDetector . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 217
A.4 ConcludingRemarks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 228
Bibliography 231
PAQPhase1FinalReport 7
1 Preliminaries
1.1 Signal Model, Notation, and High-Level Signal Processing
In this project, preamble and ASM fields are periodically inserted into a data bit stream. The
formatisillustratedinFigure1wheretheiNETpreamblecompriseseightrepetitionsofthe16-bit
sequenceCD98 andtheASMfieldis
hex
034776C7272895B0 . (1)
hex
These bits modulate an SOQPSK-TG carrier. After propagating through a multipath channel, the
received signal is filtered, amplified, down-converted, and sampled to produce a sample sequence
r(n). Let s(n) be the sampled version of the transmitted signal and let h(n) be the equivalent
discrete-time channel between the transmitter and receiver. The sample rate for s(n) and h(n)
is 2 samples/bit. The channel filter is assumed to have a non-causal component comprising N
1
samples and a causal component comprising N samples as illustrated in Figure 2. Consequently,
2
the channel is represented by a length-(N + N + 1) FIR filter. The relationship between the
1 2
samplesofthetransmittedsignals(n)andsamplesofthereceivedsignalr(n)is
N2
r(n) = s(n) h(n) ejω0n +w(n) = h(k)s(n k) ejω0n +w(n) (2)
∗ −
(cid:34) (cid:35)
(cid:104) (cid:105) k=(cid:88)−N1
where ω is an unknown frequency offset due to oscillator uncertainty and Doppler, and w(n) is a
0
complex-valued,zero-meandiscrete-timeGaussianrandomprocesswithautocovariancefunction
1
E w(n)w∗(n k) = σ2δ(k). (3)
2 − w
(cid:110) (cid:111)
The high-level signal processing requirements are illustrated in Figure 3. Here, the emphasis
is on the preamble detector, frequency offset estimator, and channel estimator. The equalization
algorithms are discussed more fully in Section 8. Because the frequency offset and channel are
estimated from the preamble data, the first order of business is to find the start of the samples cor-
responding to thepreamble in the receivedsample sequencer(n). This is the roleof the preamble
detector block. The received samples are stored in a data buffer and processed by the preamble
detector in parallel as shown. The preamble detector outputs the index i, which means the r(i) is
thereceivedsamplecorrespondingtothestartofthepreamble.
The received preamble samples are used to estimate the frequency offset. This estimate is
8 1 Preliminaries
data preamble ASM data …
…
6144 bits 128 bits 64 bits 6144 bits
Figure1: ThedataformatusedforthePAQproject.
performed by the frequency offset estimator block. The frequency offset ωˆ rads/sample is then
0
used to “de-rotate” the received samples stored in the first data buffer. The de-rotated samples are
storedinasecondbuffer.
ThesamplescorrespondingtothepreambleandASMfieldsinthede-rotatedsamplebufferare
usedtocomputeanestimateofthechannel. Theestimateofthechannelisusedtocomputeand/or
initializetheequalizeralgorithmasdescribedinSection8.
The signal processing flow outlined in Figure 3 shows that the preamble detector must be
able to find the preamble in the presence of an unknown frequency offset an unknown channel.
Furthermore,thefrequencyoffsetestimatormustbecapableofproducingareliableestimateinthe
presenceofanunknownchannel. Theseobservationsformthecorerequirementsforthealgorithms
describedinSections2(preambledetector)and3(frequencyoffsetestimator).
1.2 Test Channels
Toperformtheanalysisandsimulationdescribedinthefollowingsections,weusedasetofeleven
multipathchannelsderivedfromtheM4Achannelsoundingexperiments[1]. Thechannelimpulse
responseswerecomputedasfollows:
1. Resampling: Thechannel impulseresponsefrom theM4Aexperiments,h (n),was sam-
M4A
pledat200Msamples/s. Wedesirethesamechannelsampledat2samples/bitatthePAQbit
N 0 N
1 2
�
Figure 2: An illustration of the discrete-time channel of length N + N + 1 with a non-causal
1 2
componentcomprisingN samplesandacausalcomponentcomprisingN samples.
1 2
PAQPhase1FinalReport 9
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