communication technology laboratory wireless communication group partial channel state information...

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


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


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


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


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


Outline






• Conclusions


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


• 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


• 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


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


Outline






• Conclusions


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


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


• 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


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


Performance Results: Weak ISI






• 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


Performance Results: Strong ISI






• 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


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

communication technology laboratory wireless communication group partial channel state information...

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isi isi aware metric

weak isi

strong isi

isi note

isi energy detector

isi aware metrics

isi induced error floor