Communication Technology Laboratory

1
Partial Channel State Information and Intersymbol
Interference in Low Complexity UWB PPM Detection

• T. Zasowski, F. Troesch, A. Wittneben
• 12. MCM of COST 289
• October 30-31, 2006

has been published in part at ICUWB, September
2006, Waltham/Boston, USA
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Outline

• Introduction
• Motivation
• Intersymbol Interference aware ML symbol
  detection with partial channel state information
• Performance without Intersymbol Interference
• MLfull, MLIDPD, MLAPDP
• Performance with Intersymbol Interference
• MLfull,ISI, MLIDPD,ISI, MLAPDP,ISI
• Energy detector with MLSE
• Conclusions

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Wireless Body Area Network

• ultra low power consumption
• low duty cycle, i.e. high peak data rate
  (50Mbps) ISI
• low complexity modulation and detection
• robustness to synchronization errors

• 2-PPM impulse radio
• single pulse per bit
• symbol-wise (energy) detector
• Goal get intuition on the impact of partial CSI
  in the presence of ISI

• sufficient link margin (gt25dB) within FCC
  constraints
• reasonable excess path delay (lt20ns)
• low data rate throughput lt 1Mbps

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Partial Channel State Information

• full CSI
• (discrete) channel impulse response known at the
  receiver
• instantaneous power delay profile (IPDP)
• only magnitude of the real channel taps known at
  RX
• measured after squaring device of energy detector
  receiver
• average power delay profile (APDP)
• average power of each channel tap known at RX
• no CSI
• average energy of channel impulse response known
  at RX

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Discrete System Model
observation window
f
2-PPM
channel

Detector
S
P
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Intersymbol Interference Aware Symbol-Wise ML
Detection with Partial Channel State Info

• observation vector one PPM frame
• statistically independent normal channel taps
• diagonal correlation matrices
• maximum length of discrete channel impulse
  response T
• symbolwise -ML decision variable with partial CSI
  C

PPM frame 1
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Outline

• Introduction
• Motivation
• Intersymbol Interference aware ML symbol
  detection with partial channel state information
• Performance without Intersymbol Interference
• MLfull, MLIDPD, MLAPDP
• Performance with Intersymbol Interference
• MLfull,ISI, MLIDPD,ISI, MLAPDP,ISI
• Energy detector with MLSE
• Conclusions

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Special Case Decision Metrics without ISI

• full CSI
• instantaneous power delay profile
• average power delay profile
• for energy detector

• ISI metrics in paper

9
ED Energy Detector

• after the unitary transformation H we obtain the
  statistically equivalent decision variable
• performance independent of "shape" of impulse
  response
• excess noise due to excess dimensions

• uses the decision variable
• with
• a unitary transformation H has no impact on the
  error performance
• we choose H such, that
• without ISI we have for s1-1

same as N/21
statistically independent zero mean noise from
excess dimensions
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MLIPDP Instantaneous Power Delay Profile

• without ISI we obtain for IPDP
• for MLfull
• as L(s11)lt0 causes a decision error gt loss for
  IPDP

• in the high SNR regime we obtain the
  approximation
• compare to MLfull

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Performance Results without ISI

• based on physical system (continuous time)
• PPM frame duration T20ns
• 10dB-bandwidth B103GHz
• uniform power delay profile
• max. delay 10ns
• equivalent discrete model has N/260 i.i.d.
  normal channel taps
• energy of each channel realization normalized to
  1
• MLfull performance same as AWGN
• emphasizes impact of PDP

• minor improvement with IPDP
• ED performance sufficient

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Outline

• Introduction
• Motivation
• Intersymbol Interference aware ML symbol
  detection with partial channel state information
• Performance without Intersymbol Interference
• MLfull, MLIDPD, MLAPDP
• Performance with Intersymbol Interference
• MLfull,ISI, MLIDPD,ISI, MLAPDP,ISI
• Energy detector with MLSE
• Conclusions

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MLfull,ISI-Symbol-Wise Detector Considers ISI

• energy per bit
• impulse crosscorrelation
• free Euclidean distance

• decision regions adapted to ISI
• requires three correlators

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MLfull-Symbol-Wise Detector ignores ISI

• decision variable
• mismatched to ISI
• requires only one correlator
• free Euclidean distance
• for a0 we obtain for the loss w.r.t the ISI
  aware metric

• optimal without ISI ( )
• for a0 and EhEg 1.8dB loss in comparison to
  MLfull,ISI

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High SNR performance of MLAPDP (ignores ISI)

• decision metric for uniform PDP (energy detector)
  
• without additive noise we obtain e.g. for s1 -1

PPM frame 1
gt ISI causes error floor
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MLSE Maximum Likelihood Sequence Estimator

• uses two decision variables per PPM frame
• energy detector LL2-L1
• simple two-state trellis

• very limited instantaneous CSI required
• simplified branch metrics
• the noise is modelled as normally distributed
  with nonzero mean
• potentially removes error floor of ED with ISI
• note operates with bit clock (as opposed to
  sample rate)

17
Performance Results Weak ISI

• based on physical system (continuous time)
• PPM frame duration T20ns
• 10dB-bandwidth B103GHz
• uniform power delay profile
• max. delay 14ns
• energy of each channel realization normalized to 1

• ISI aware metrics substantially improve
  performance
• MLAPDP,ISI essentially blanks ISI segment of PPM
  frame
• MLSE close to MLAPDP,ISI even though max. delay
  is not known
• no error floor

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Performance Results Strong ISI

• based on physical system (continuous time)
• PPM frame duration T20ns
• 10dB-bandwidth B103GHz
• uniform power delay profile
• max. delay 17ns
• energy of each channel realization normalized to 1

• ED not applicable due to 10 error floor
• MLSE removes error floor
• MLIPDP,ISI almost as robust to ISI as MLfull,ISI
• ISI aware metric very efficient
• MLSE and MLAPDP,ISI again have similar
  performance

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Summary and Conclusions

• we derived the intersymbol interference aware
  ML-symbol decision metrics for partial CSI
• full CSI (MLfull MLfull,ISI)
• instantaneous power delay profile (MLIPDP
  MLIPDP,ISI)
• average power delay profile (MLAPDP MLAPDP,ISI)
• MLAPDP,ISI removes the ISI induced error floor of
  the ED
• MLfull and MLIPDP are suprisingly robust to ISI
• MLSE performs similar to MLAPDP,ISI
• overall the MLSE seem the most attractive
  compromise between complexity and performance in
  our application