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Effective Synchronization Scheme for Impulse Radio Ultra Wideband Systems
適用於脈衝無線電超寬頻系統之有效率的同步機制
東海大學．電機工程學系溫志宏 教授
Page 2
Outline
What’s Ultra Wideband?
Symbol-Differential UWB System
Frame-Differential UWB System
Proposed Synchronization Scheme
Performance Analysis
Simulation Results
Conclusion
Page 3
What is ultra-wideband?
Ultra wideband (UWB)Bandwidth is wider than 500 MHz
Fractional bandwidth is greater than 0.2
Time hopping impulse radio (TH-IR) UWBBased on transmitting very short and low power pulses
Pulses are transmitted in the frames based on the specific pseudo random (PN) time hopping code ( ) assigned for each users
t
, 0k cTC , 1-fNk cTC , 1k cTC
frametime
symbol time
1
0
fN
k, j jc
Page 4
Symbol-Differential UWB System
Page 5
Symbol-Differential UWB System
The transmitted signal of the symbol differential scheme
, with a is any M-ary PAM symbol.
: the transmitted pulse energy.
: the normalized pulse.
: the number of frames in one symbol.
: the frame duration
: the time hopping code.
: the chip duration
1
0 0
( ) ( ) ( ( ) ),fN
p f f j ci j
s t E d i w t iN j T c T
pE
( )w t
fN
fT
jc
cT
2( ) ( 1)i
d i a
Page 6
2
0
( ; ) : ( ) ( )sT
sy K r t r t T dt
1
1( ) ( 1) ( 2 )
Kk
sk
r t r t kTK
0[0, )
arg max ( ; )sT
y K
1
1( ) ( 1) ( (2 1) )
Kk
s sk
r t T r t k TK
Architecture of Symbol-Differential Receiver
Delay
Delay
sT
2
0( .)
sTd t
1
1( 1) .
K k
kK
Controller
Timing Synchronization Block
to symbol demodulator
( )r t ( )r t
K: pair of symbol
0
( ) ( )L
l ll
h t t
( ) ( ) ( ) ( )r t s t h t n t
Page 7
2 sT 4 sT 6 sT 8 sT 10 sT0
2 sT 4 sT 6 sT 8 sT 10 sT0
2 sT 4 sT 6 sT 8 sT 10 sT0
2 sT 4 sT 6 sT 8 sT 10 sT0
2 sT 4 sT 6 sT 8 sT 10 sT0
Synchronization algorithm(Timing with Dirty Template; TDT)
+1 +1 -1 -1 +1 +1 -1 -1 +1 +1 -1 -1 +1 +1 -1 -1sT
+1+1
+1+1
+1+1
+K+K
+1-1
+1-1
+1-1
+K-K
+1-1
+1+1 +1-1
1
K
+1+1
+1+1
+1+1
+K+K
+1-1
+1-1
+1-1
+K-K
+1-1
+1+1 +1-1
1
K
+1
+1
+1
+K
-1
-1
-1
-K
-1
+1 -1
1
K
+1-1
+1-1
+1-1
+K-K
-1 -1
-1 -1
-1 -1
-K -K
-1+1
+1-1 -1 -1
1
K
+1-1
+1-1
+1-1
+K-K
-1 -1
-1 -1
-1 -1
-K -K
-1+1
+1-1 -1 -1
1
K
1
1( ) ( 1) ( 2 )
Kk
sk
r t r t kTK
1
1( ) ( 1) ( (2 1) )
Kk
s sk
r t T r t k TK
sT sT sT sT sT sT sT sT sT sT
Page 8
Symbol-differential 需花費的時間：
4[(2 2) ] (7.17 8.9) 102 2
fsf f s
TTT N K T K ns
1 1 1
[2 ( 1) 2 ] [(2 2) ]N N N
s s sn n n
KT n T n K T
sTN
( 1) [(2 2) ]2 s
NN N K T
[(2 2) ]2 2
ss
TN K T
6[(2 2) ] (2.5 3.1) 102 2
s cc c f s
T TT N N K T K ns
Ex:
, 32, 35, 1s f f f c c f c cT N T N N T N N T ns
Page 9
Frame-Differential UWB System
Page 10
Signal Model
Data symbol , where is the data symbol index.
Each information bit is modulated by BPSK.
A known random polarity sequence is differentially modulated on the monocycle pulses, where is the pulse index within a symbol.
Each pulse is differentially modulated by both BPSK and random polarity sequence, the differentially modulated pulse-polarities are obtained as and .
{ 1, 1}id i
{ 1, 1}jb {0,1,2, , 1}fj N
, 1 ,i j i j i ja a d b 1,0 , 1 1f fi i N i Na a d b
Page 11
1D 2D 3D0D
The time shifts between pulses are defined as and . Here, we let for .
,0 1ia ,1 ,0 0i i ia a d b
,2 ,1 1i i ia a d b,3 ,2 2i i ia a d b
1,0 ,3 3i i ia a d b
= -1= -1
= 11,1 1,0 1 0i i ia a d b
11
0j 1j 2j 3j 0j
isymbol
symbol 1i
1j
, 1 ,j i j i jD t t 1 1,0 , 1f fN i i ND t t
j kD D j k
, 1 ,i j i j i ja a d b 1,0 , 1 1f fi i N i Na a d b 0 3 0 1 0 2 ,c c 0 3 1 1 -1 1b b 4,f cN N 1 1,id 1,id Ex
:
Page 12
The transmitted signal of this UWB system can be expressed as:
: the symbol index
: the frame index
: the pulse-polarity
: the frame duration
: the chip duration
: the transmitted pulse waveform
1
,0
( ) ( ( ) ),fN
i j f f j ci j
s t a w t iN j T c T
,i ja
( )w t
fT
cT
ij
Page 13
1j 0j 2fj N 1fj N
0D 1D 1fND 2fND
0D2D 3fND
Frame-Differential Receiver
1 1( 1)s cnT n c T
Delay1fND
( )r t
Decisionand
ControlLogic
Delay2fND
Delay
0DDelay
3fND
Delay
0DDelay
1fND
Delay
1D
1
1
(.)SIW
dt
Delay2fND
Delay2fND
Delay3fND
Delay1fND
Delay4fND
0
0
(.)SIW
dt
1
1
(.)N f
N f
SIWdt
1fNb 2fNb 3fNb 0b
3fNb 4fNb 1fNb
1fNb 2fNb 1b0b
2fNb
0z
1z
1fNz
Integrated & Dumped
Integrated & Dumped
Integrated & Dumped
0 0( 1)s cnT n c T
1 1( 1)f fN s N cnT n c T
s f f f c cT N T N N T j kD D for j k
Page 14
Frame-differential 需花費的時間：
1 1 1
[( 1) ] ( )N N N
s sn n n
n T n T
( )2 2s
NN T
(1 ) ( )2 s
NN N T
fTN
4[ ] 4 102 2
f cc c s
T TT N T ns
Ex:
, 32, 35, 1s f f f c c f c cT N T N N T N N T ns
35 [ ] 8 105 2 2
fc cc s
TN TT T ns
Page 15
Proposed Synchronization Scheme
Parallel signal acquisition with shared loop delay line (PS-SLD)
Page 16
1fNz 1
1
(.)N f
N f
SIWdt
1
1
(.)SIW
dt
0
0
(.)SIW
dt
Proposed Receiver Architecture
0DDelay
1DDelay
2DDelay
1fND
Delay
0DDelay
1DDelay
1fND
Delay
0b
1b
1fNb
0z
1z
( )r t
Decisionand
ControlLogic
s f f f c cT N T N N T j kD D for j k
0 ( )x t
1( )x t
1( )fNx t
0 ( )l t
1( )l t
1( )fNl t
0 ( )y t
1( )y t
1( )fNy t
1j 0j 2fj N 1fj N
0D 1D 1fND 2fND
0D2D 3fND
Page 17
0 ( )x t
sp
0D
0( )r t D
0 ( )l t
3 0D Dsp
0 ( )y t0 0( ) ( )x t l t 0 0( ) ( )x t l t
2 ssp T sp1 c ssp c T T 1 3c ssp c T T
: 開始積分時間: 接收起始點 : 開始有值輸出
( )r t
[0 1 0 2]c [5 3 6 2]D 4c fN N
sp
接地的時間接收資料的時間
Page 18
1D
1( )r t D
1( )x t
sp
1( )l t
0 1D Dsp
: 開始積分時間: 接收起始點 : 開始有值輸出
( )r t
[0 1 0 2]c [5 3 6 2]D 4c fN N
sp
1( )y t1 1( ) ( )x t l t 1 1( ) ( )x t l t
2 ssp T sp2 c ssp c T T 2 3c ssp c T T
接地的時間接收資料的時間
Page 19
2D
2( )r t D
2 ( )x t
sp
sp 1 2D D2 ( )l t2 ( )l t
1 2D Dsp
2 ( )y t2 2( ) ( )x t l t 2 2( ) ( )x t l t
2 ssp T sp3 c ssp c T T 3 3c ssp c T T
: 開始積分時間: 接收起始點 : 開始有值輸出
( )r t
[0 1 0 2]c [5 3 6 2]D 4c fN N
sp
接地的時間接收資料的時間
Page 20
3D
3( )r t D
3( )x t
sp
3( )l t
2 3D Dsp
3( )y t
3 3( ) ( )x t l t
2 ssp T sp
3 3( ) ( )x t l t
0 c ssp c T T 0 3c ssp c T T
: 開始積分時間: 接收起始點 : 開始有值輸出
( )r t
[0 1 0 2]c [5 3 6 2]D 4c fN N
sp
接地的時間接收資料的時間
Page 21
0 ( )y t0 0( ) ( )x t l t 0 0( ) ( )x t l t
2 ssp T sp1 c ssp c T T 1 3c ssp c T T
接地的時間接收資料的時間
1( )y t1 1( ) ( )x t l t 1 1( ) ( )x t l t
2 ssp T sp2 c ssp c T T 2 3c ssp c T T
接地的時間接收資料的時間
2 ( )y t2 2( ) ( )x t l t 2 2( ) ( )x t l t
2 ssp T sp3 c ssp c T T 3 3c ssp c T T
接地的時間接收資料的時間
3( )y t
3 3( ) ( )x t l t
2 ssp T sp
3 3( ) ( )x t l t
0 c ssp c T T 0 3c ssp c T T
接地的時間接收資料的時間
mod( 1, )(2 1) ( 1)fs j N csp n T n c T
(2 2) ( 1)ssp n T n mod( 1, )[ (2 1) ( 1) ]
fs j N cMax sp n T n c T SIW
: 開始積分時間: 接收起始點 : 開始有值輸出[0 1 0 2]c [5 3 6 2]D 4c fN N
積分器開始積的時間 :
開始接地的時間 :
開始接收資料的時間 :
Page 22
Proposed synchronization scheme 需花費的時間：
1 1 1
[( 1) 2 ] (2 )N N N
s sn n n
n T n T
(2 )2 2
fs
TN T
(1 ) (2 )2 s
NN N T
fTN
4[2 ] 7.9 102 2
f cc c s
T TT N T ns
Ex:
, 32, 35, 1s f f f c c f c cT N T N N T N N T ns
45 [2 ] 1.6 105 2 2
fc cc s
TN TT T ns
Page 23
Performance Analysis
Page 24
Signal Model
Transmitted signal of the k-th user
i : the symbol index
j : the frame index
: symbol duration
1
, , ,0
1 -1
, , ,0 ,0 0
( )
( ( ) )
( )
f
f
N
k i j f f k j ci j
N j
k i j s k c k pi j p
k t a w t iN j T c T
a w t iT c T D
s
-1
, ,0
, 1 , 0( ) N Nf f
k p k pp
f ck p k pD DT c c T and
s f fT N T
• : modulus N ffN
Page 25
The multipath channel corresponding to every user k is modeled as a tap delay line with taps
: amplitudes of multipath signals
: delays of multipath signals, and is defined
: the propagation delay of the first arrival signal
, ,0
( ) ( )kL
k k l k k ll
h t t
,0 0k
[0, )k sT
, 0
kL
k l l
, 0
kL
k l l
1kL
Page 26
Received signal
where
1
0
1
0
11 -1
, , , ,0 ,0 0 0
1 -1
, , , ,0 , ,0 0 0
( )
( ) ( ) ( ) ( )
( ) ( )
( )
u
u
fu
f k
N
k kk
N
i k
NN j
k i j k i k pi k j p
N L j
k i j k l s k c k p k k lj l p
n t
r t s t h t n t
a v t D n t
a w t iT c T D
-1
, , , ,0 , ,0 0
( ) ( )kL j
k i j k l s k c k p k k ll p
v t w t iT c T D
Page 27
Autocorrelation output
1
1,
1 1,
1 1 1
,
,
,
,
,
1 1 1
1 1
, ,1
11 -1
, ,0 ,0 0 0
, ,
,
( ) ( ) ( )
( ) ( )
( )
f f
f fuk q w
k q
k q w
k q
k q w
N N Nf f fk q
N f
N q N q
k km q p m
N NN jT
k i k i k pm q k j p
T
k q k q
T
m m p
jmi
y
b r t r t D t D
b a v t D n t
z n t dt
dt
2
2 2 2
2 2 2
2 2 2
1
11 -1
, , ,0 ,, ,0 0 0
1
,1
, ( ) ( )
( )
fu
f
N Nf f
N f
q
NN j
k i k i k pk kk j p
N q
kp m
j m mi
p
a v t D D n t D
t D dt
1 1
, , ,1
( )( ) ( ) ( )f f
N N Nf f f
N q
m q
N q
k q m k m k pp m
b r ty t r t D t D
, ,, ( 1)k q s k q cwhere i T c T n
Page 28
the desired signal terms can be extracted with indexes ,
, , ,
1 2k k k
1 ( 1) fi i m N 2 fi i m N 1 1j m 2j m
,
,,
1 1
, ,0 , ,0, , ,, ( 1) , 1 , ,0 0
( ) ( )f
k q w
f fN N N NN Nf f f fk q f fk q
N q m mT
k i k im k p k m k pk i m N m k i m N mm q p p
nz b a v t D a v t D D
,
,
1
,1
1
, ,0 1
12, ,0, ( 1) , 1 , ,
, ( 1) ,
( )
( ) ( )
f
f
N Nf f
N f
fk q w
f fN N Nf k qf f
fN f
N q
kp m
N qm
k p k pp p m
p
N qT
k im k i m N m k i m N mm q
m k i m N m
t D dt
v t D t D
n
b a a n
b a
dt
,
,
,
,
1
,0
12, ,01 , ,
12
, , , 1 , 1 , ,0 ,0
( )
( ) ( 1) ( )
f
N f
fk q w
fN N k qf f
k q w
k q
N q
k pp
N qT
k ik i m N mm q
qT
f k i k i k i k i k i s k pp
v t D
n
a n
N q d d d q d v t T D dt
dt
Page 29
Let , and
Since , and
, , 1 1k i k id d -1
, , , ,0 , ,0 0
( ) ( )kL j
k i j k l s k c k p k k ll p
v t w t iT c T D
,
,
21
, , ,0 ,0 0
, ( ) ( ) k
k q w
k qf
L qT
k l s k p s k k k ll p
k q Nz w t T D iT c T dt nn
1
, ,0 ,0
q
k p k c f k q cp
D c T qT c T
,
,
( 1)
,( 1)0
2
, ,
, ,
, ( )
( )
( ( 1)
)
(
ks k q c w
s k q cf
f
Li T c T n T
k l s fi T c T nl
k q c k k l
k l f k k l
k q N
N
z w t i T qT
c T dt n
w t n qT
n
0
0
2
)k
wL
T
l
ndt
, ,( 1)k q s k q ci T c T n
Page 30
Assuming
If is neglected, then exhibits a maximum when
The estimated propagation delay is given by
n
1 2, , 1 20( ) ( ) 0,
wT
f k k l f k k lw t n qT w t n qT dt for each l l
2 2, ,0
0, ( ) ( )
kw
f
LT
k l k l f kl
k q Nz w t n qT nn dt
,k qz n k fqT n
,1], [0, [0, 1]
, arg max , :i f
fk q i
n N q N
Tn q z n where N
k fqT n
Page 31
Probability of detection (PD)
The probability of detection is denoted as
Assuming and are target indexes, and represents the inaccuracy between the declared symbol boundary and the true symbol boundary The pdf of based on each determined is given as The probability of detection (PD) for every and based on a determined is given as
*
* * * * *,, ,
( , ) Pr Pr [ ] max [ ]d k qk q q nP q n q q and n n z n z n
* *: s fT q T n
, [ ]k qz n
, ( | )q nf z
* *
* *
* *,,
( , ) ( , )
( , | ) ( | ) ( | )z
q nq nq n q n
p q n f z f x dx dz
*q*n
*q *n
Page 32
Let ,where and satisfy
Assuming that is uniformly distributed over interval of
0,
* *1 * *
1
* *2 * *
2
,,0( , ) ( , )
.,( , ) ( , )
0
* * * *1 20
1 ( | ) ( | )
( | ) ( | )
1( )
1 ( , | ) ( , | )
z
q nq nq n q n
z
q nq nq n q n
d d
f z f x dx dz
f z f x dx dz d
P P d
p q n p q n d
(Eq. 1)
* * * *1 2( ) : ( , | ) ( , | )dP p q n p q n *
1n* *
1
* *2
0
0
s f
s f
T q T n
T q T n
*2n
Page 33
Lower bound of PD
Through the central limit theorem, can be treated as Gaussian distributed
where
* *1* *
1
* *2* *
2
,,0( , ) ( , )
,,( , ) ( , )
1: ( | ) ( | )
( | ) ( | ) (Eq. 2)
z
d d q nq nq n q n
z
q nq nq n q n
P P f z f x dxdz
f z f x dxdz d
, [ ]k qz n
* *1
* ** *1
1
* *2
* ** *2
2
, ,
2 20( , ) ( , ) , ,
, ,
2 2( , ) ( , ) , ,
( | ) ( | )1
( | ) ( | )
( | ) ( | ) (Eq. 3)
( | ) ( | )
q n q nd
q n q n q n q n
q n q n
q n q n q n q n
m z m zP Q
z z
m z m zQ d
z z
2, , , ,( | ) is mean of [ ], and ( | ) is variance of [ ] q n k q q n k qm z z n z z n
Page 34
Simulation results
Page 35
Parameters
Under UWB CM1 with (1/, 1/, , )=(42.9, 0.4, 7.1, 4.3)
32, 35, 35 , 1 , 35f c f c wN N T ns T ns and T ns
, , , k p k q for each p qD D
Page 36
Theoretical results
For the simulation result, wT
- 15 - 10 - 5 0 5 10 15 20
0
0.2
0.4
0.6
0.8
1
Pro
bab
ility
of
det
ectio
n (P
D)
SNR (dB)
Simulation resultEq. (1), Monte Carlo methodEq. (2), Monte Carlo methodEq. (3), Monte Carlo method
Page 37
Probability of Detection (PD)
Shift step size: wT
-15 -10 -5 0 5 10 15 20
0
0.2
0.4
0.6
0.8
1
Probability of detection (PD)
SNR (dB)
PS-SLD, single userPS-SLD, single user(averaging over 8 symbols)
TDT, Prop. 4, K=1, single user
TDT, Prop. 4, K=8, single user
PS-SLD, 5 usersTDT, Prop. 4, K=8, 5 users
Page 38
Normalized Mean Square Error (MSE)
Shift step size:wT
-15 -10 -5 0 5 10 15 2010
-4
10-3
10-2
10-1
Nor
mal
ized
MSE
SNR (dB)
PS-SLD, single user
TDT, Prop. 4, K=1, single userPS-SLD, 5 users
TDT, Prop. 4, K=8, 5 users
Page 39
Normalized MSE
Shift step size: 1ns
-15 -10 -5 0 5 10 15 2010
-5
10-4
10-3
10-2
10-1
Nor
mal
ized
MSE
SNR (dB)
PS-SLD, single user
TDT, Prop. 4, K=1, single userPS-SLD, 5 users
TDT, Prop. 4, K=8, 5 users
Page 40
Conclusion
PS-SLD has a higher hardware complexity than the TDT scheme The performance of PS-SLD in both PD and MSE is better than that of TDT, especially in multi-user environmentsThe synchronization speed of PS-SLD is also faster than that of TDT algorithm
Uncertain region is bounded within one frame duration, and is only
of that of the TDT
1fN
Page 41
Appendix
Proof of Eq. 3
* *
* *
* * * *
* *
* *
,,
,
,,
,
, ,,
,,
2
,
( | ) ( | )
( | )( | ) 1
( | )
( | )( | ) ( | )
( | )
( | ) ( | )1
( |
z
q nq n
q n
q nq n
q n
q n q nq n
q nq n
q n
f z f x dxdz
z m zf z Q dz
z
z m zf z dz f z Q dz
z
m z m zQ
z
* *
* *
, ,
2 2 2, , ,
( | ) ( | )
) ( | ) ( | ) ( | )
q n q n
q n q n q n
m z m zQ
z z z
* * * *1 2
* * * ** * * *1 2
1 2
, ,, ,
2 2 2 20( , ) ( , ) ( , ) ( , ), ,, ,
( | ) ( | ) ( | ) ( | )1
( | ) ( | ) ( | ) ( | )
T q n q nq n q nd
q n q n q n q nq n q nq n q n
m z m z m z m zP Q Q d
T z z z z
