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
• sufficient link margin (>25dB)
within FCC constraints
• reasonable excess path delay
(<20ns)
• low data rate: throughput <
1Mbps
•
•
•
•
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
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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 T  N / 2B
f
B
v t 
2-PPM
s
channel
z t 

v  t 
wt 
1
2
N
S
Detector
P
d
k
2B
sˆ
1  s     t  T  


 1  s     t  T  T / 2 
h
g
t
T /2
t
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Intersymbol Interference Aware Symbol-Wise
ML Detection with Partial Channel State Info
d
s0 ; s1
h
g
1; 1
x1
1; 1
x2
• observation vector d : one
PPM frame
• statistically independent
normal channel taps
– diagonal correlation matrices
E  h  h T    hh ; E  g  g T    gg
1; 1
x3
1; 1
x4
0
T /2
PPM frame 1
T
• maximum length of discrete
channel impulse response: T
• symbolwise -ML decision
variable with partial CSI C








 E p d x  E p d x  
3 
4 
x3 C 
x4 C 

L  ln 
 E  p d x   E  p d x  
1 
2 
x2 C 
 x1 C 

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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
d
s1
• full CSI:

C h
L  x3T  d  x1T  d
h
x1  x2
1
• instantaneous power delay profile:
  
C  abs h

 d k  x3,k
L   ln  cosh 
 2

k 1


N
h
x3  x4
1


 d k  x1,k
   ln  cosh 

 2




• average power delay profile:




C  h,k 
N /2
d k2
d k2
L 

2
2
1


/

k  N / 21
k 1 1   / h ,k
h ,k
N
0
T /2
T
• ISI metrics in paper
2
with h ,k  E  hk 


– for h,k  const : energy detector
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ED: Energy Detector
• uses the decision variable
L  d1T d1  d2T d2
– with
d1  [d1
d N / 2 ]T
d 2  [d N / 21
d N ]T
L  s1  1   [ Eh
• a unitary transformation H has
no impact on the error
performance
• we choose H such, that
H  h  [ Eh
0
0]T
• without ISI we have for s1=-1
d1  h  w1
d 2  w2
• after the unitary transformation
H we obtain the statistically
equivalent decision variable
2
0
0]T  w1  w2
2
– performance independent of
"shape" of impulse response
• excess noise due to excess
dimensions
L  s1  1 


Eh  w1,1

2

 w22,1 
N / 2 2

   w2,i  w12,i 
 i 2

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same as N/2=1
statistically independent
zero mean noise
from excess dimensions
9
MLIPDP: Instantaneous Power Delay Profile
• in the high SNR regime we
obtain the approximation
N /2


L   dk  N / 2  dk  hk
k 1
• without ISIN / 2we obtain for IPDP
L  s1  1    hk  n2,k  n1,k   hk
k 1
 for n2,k < hk
N /2

L  s1  1   hk 2  n2,k  hk  n1,k  hk
k 1

• for MLfull
• compare to MLfull
L    dk  N / 2  dk   hk
N /2
k 1
L  s1  1    hk  n2,k  n1, k   hk
N /2
k 1
   hk2  n2,k  hk  n1, k  hk 
N /2
k 1
• as L(s1=1)<0 causes a
decision error => loss for IPDP
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Performance Results without ISI
•
based on physical system
(continuous time)
–
–
•
uniform power delay profile
–
•
•
max. delay: 10ns
equivalent discrete model has
N/2=60 i.i.d. normal channel
taps
energy of each channel
realization normalized to 1
–
–
•
•
PPM frame duration T=20ns
10dB-bandwidth B10=3GHz
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
x4
d
s0 ; s1
2 Eb  2a
h
g
1; 1
2Eb  Eg  2a
x1
1; 1
x1
x2
x2
Eg
2Eb  Eg  2a
2Eb
x3
1; 1
x3
• energy per bit: Eb  h T h  g T g
• impulse crosscorrelation:
x4
1; 1
0
T /2
a  gT h
T
• decision regions adapted to ISI
• requires three correlators
• free Euclidean distance:
d 2free,1  2Eb  Eg  2a
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MLfull-Symbol-Wise Detector: ignores ISI
• decision variable
 h 
1
L  d  
 h  2 Eh
T
x2
E
 h
2
x1

x4
Eh  a
Eh  a
2 Eh
2 Eh
x3
Eh
2
– mismatched to ISI
– requires only one correlator
• free Euclidean distance:
2
E

max(
a
,0)


h
2
d free,2  2
• optimal without ISI ( g  0 )
• for a=0 and Eh=Eg: 1.8dB loss
in comparison to MLfull,ISI
Eh
• for a=0 we obtain for the loss
w.r.t the ISI aware metric
d 2free,2
d 2free,1

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Eb  Eg
Eb  12 Eg
1
14
High SNR performance of MLAPDP (ignores ISI)
• decision metric for uniform
PDP (energy detector)
PPM frame 1
s0 ; s1
N /2
h
g
1; 1
x1
1; 1
x2
1; 1
x3
1; 1
x4
0
T /2
L   d k2 N / 2  dk2
k 1
• without additive noise we
obtain e.g. for s1= -1
L  s1  1, s0  1  h T h  g T g
=> ISI causes error floor
T
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MLSE : Maximum Likelihood Sequence Estimator
• uses two decision variables
per PPM frame
N /2
L1   dk2 and L2 
k 1
• very limited instantaneous CSI
required:
hT h
N

k  N / 21
dk2
gT g
– energy detector: L=L2-L1
hT g
• simplified branch metrics
• simple two-state trellis:
L1; L2   h T h ; g T g
s0  1

0; h T h
s0  1
h

T

h; gT g
2
h  g ; gT g

2

– 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)
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Performance Results: Weak ISI
•
based on physical system
(continuous time)
–
–
•
uniform power delay profile
–
•
•
•
•
PPM frame duration T=20ns
10dB-bandwidth B10=3GHz
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)
–
–
•
uniform power delay profile
–
•
•
ED not applicable due to 10%
error floor
MLSE removes error floor
MLIPDP,ISI almost as robust to
ISI as MLfull,ISI
–
•
max. delay: 17ns
energy of each channel
realization normalized to 1
–
•
PPM frame duration T=20ns
10dB-bandwidth B10=3GHz
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 MLsymbol 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
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