Communication Technology Laboratory Wireless Communication Group 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
19
Embed
Communication Technology Laboratory Wireless Communication Group Partial Channel State Information and Intersymbol Interference in Low Complexity UWB PPM.
This document is posted to help you gain knowledge. Please leave a comment to let me know what you think about it! Share it to your friends and learn new things together.
Transcript
Communication Technology LaboratoryWireless Communication Group
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
2 Communication Technology LaboratoryWireless Communication Group
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
3 Communication Technology LaboratoryWireless Communication Group
Wireless Body Area Network
• sufficient link margin (>25dB) within FCC constraints
• reasonable excess path delay (<20ns)
• low data rate: throughput < 1Mbps
• 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
4 Communication Technology LaboratoryWireless Communication Group
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
5 Communication Technology LaboratoryWireless Communication Group
Discrete System Model
2-PPM channel v t z t
v t
12 1
1 / 2
s t T
s t T T
t
Detector
w t
s s S
P
2
k
B
N
d
Bf
observationwindow / 2T N B
h
g
/ 2T
t
6 Communication Technology LaboratoryWireless Communication Group
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
/ 2T T0
0 1;s s
1; 1
1; 1
1; 1
1; 1
h
g
PPM frame 1
;T Thh ggE h h E g g
1x
2x
3x
4x
d
3 4
1 2
3 4
1 2
lnx C x C
x C x C
E p d x E p d xL
E p d x E p d x
d
7 Communication Technology LaboratoryWireless Communication Group
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
8 Communication Technology LaboratoryWireless Communication Group
Special Case: Decision Metrics without ISI
• full CSI:
• instantaneous power delay profile:
• average power delay profile:
– for : energy detector
/ 2T T0
1s
1
1
h
3, 1,
2 21
ln cosh ln coshN
k k k k
k
d x d xL
3 1T TL x d x d
1 2x x
3 4x x
C h
C abs h
h
2 2/ 2
2 2/ 2 1 1, ,
2
,
1 / 1 /
with
N Nk k
k N kh k h k
h k k
d dL
E h
• ISI metrics in paper
,h kC
,h k const
d
9 Communication Technology LaboratoryWireless Communication Group
• 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
ED: Energy Detector
• 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
1 1 2 2T TL d d d d
1 1 / 2
2 / 2 1
[ ]
[ ]
TN
TN N
d d d
d d d
[ 0 0]ThH h E
2 2
1 1 21 [ 0 0]ThL s E w w
2
21,1
/ 22 22
2
,
,
,
1
1
12
1
N
i
h
ii
w
w
L s
E w
w
same as N/2=1
statistically independent zero mean noisefrom excess dimensions
1 1
2 2
d h w
d w
10 Communication Technology LaboratoryWireless Communication Group
• without ISI we obtain for IPDP
• for MLfull
• as L(s1=1)<0 causes a decision error => loss for IPDP
/ 2
1 2, 1,1
2,
/ 22
1 2, 1,1
1
for <
1
N
k k k kk
k k
N
k k k k kk
L s h n n h
n h
L s h n h n h
MLIPDP: Instantaneous Power Delay Profile
• in the high SNR regime we obtain the approximation
• compare to MLfull
/ 2
/ 21
N
k N k kk
L d d h
/ 2
/ 21
N
k N k kk
L d d h
/ 2
1 2, 1,1
/ 22
2, 1,1
1N
k k k kk
N
k k k k kk
L s h n n h
h n h n h
11 Communication Technology LaboratoryWireless Communication Group
Performance Results without ISI
• based on physical system (continuous time)
– PPM frame duration T=20ns
– 10dB-bandwidth B10=3GHz
• 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
– MLfull performance same as AWGN
– emphasizes impact of PDP
• minor improvement with IPDP• ED performance sufficient
12 Communication Technology LaboratoryWireless Communication Group
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
13 Communication Technology LaboratoryWireless Communication Group
MLfull,ISI-Symbol-Wise Detector: Considers ISI
• energy per bit:• impulse crosscorrelation:
• free Euclidean distance:
2 bE
2 2b gE E a 2 2bE a
gE1x
2x
3x
4x
2 2b gE E a
T TbE h h g g
Ta g h
2,1 2 2free b gd E E a
/ 2T T0
0 1;s s
1; 1
1; 1
1; 1
1; 1
h
g
1x
2x
3x
4x
d
• decision regions adapted to ISI• requires three correlators
14 Communication Technology LaboratoryWireless Communication Group
MLfull-Symbol-Wise Detector: ignores ISI
• decision variable
– mismatched to ISI
– requires only one correlator
• free Euclidean distance:
• for a=0 we obtain for the loss w.r.t the ISI aware metric
2hE
1
2T
h
hL d
Eh
4x
2h
h
E a
E
2hE
2x
2h
h
E a
E
1x
3x
2
2,2
max( ,0)2 h
freeh
E ad
E
2,2
2 12,1
1free b g
free b g
d E E
d E E
• optimal without ISI ( )
• for a=0 and Eh=Eg: 1.8dB loss in comparison to MLfull,ISI
0g
15 Communication Technology LaboratoryWireless Communication Group
• decision metric for uniform PDP (energy detector)
• without additive noise we obtain e.g. for s1= -1
High SNR performance of MLAPDP (ignores ISI)
/ 22 2
/ 21
N
k N kk
L d d
1 01, 1 T TL s s h h g g
=> ISI causes error floor
/ 2T T0
0 1;s s
1; 1
1; 1
1; 1
1; 1
h
g
PPM frame 1
1x
2x
3x
4x
16 Communication Technology LaboratoryWireless Communication Group
MLSE : Maximum Likelihood Sequence Estimator
• uses two decision variables per PPM frame
– energy detector: L=L2-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)
/ 22 2
1 21 / 2 1
and N N
k kk k N
L d L d
0 1s
0 1s
1 2; ;T TL L h h g g
2
2; Th g g g
0; Th h
;T Th h g g
T
T
T
h h
g g
h g
17 Communication Technology LaboratoryWireless Communication Group
Performance Results: Weak ISI
• based on physical system (continuous time)
– PPM frame duration T=20ns
– 10dB-bandwidth B10=3GHz
• uniform power delay profile– max. delay: 14ns
• energy of each channel realization normalized to 1