Timing Synchronization in Ultra-Wideband Systems with ... - IEEE Xplore
264
IEEE COMMUNICATIONS LETTERS, VOL. 11, NO. 3, MARCH 2007
Timing Synchronization in Ultra-Wideband Systems with Delay Line Combination Receivers Hsi-Chou Hsu and Jyh-Horng Wen
Abstract— This paper proposes a novel non-data aided timing synchronization algorithm designated as ”timing with delay line combination” (TDLC), to improve the synchronization speed of differential impulse radio ultra-wideband systems. Continuously integrating the combinative output signal provided by the proposed ”frame-differential delay line” (FDL), it is found that the integration output exhibits a sharp rising or falling transition at the moment that the first signal per symbol arrives. By accurately detecting the time of the rising or falling edge, the symbol boundary can be simply derived. The proposed scheme achieves timing synchronization within a single symbol duration. Index Terms— Synchronization, timing acquisition, differential transmitted reference (DTR), impulse radio (IR), ultra-wideband (UWB).
I. I NTRODUCTION NE of the critical challenges in designing UWB receivers is the synchronization issue. In most instances, the channel information is not known exactly during the synchronization phase. It has been shown that differential transmitted reference (DTR) receivers [1] can resolve the problem of energy collection without any channel information. In a similar approach to that adopted in the DTR receivers, ”timing with dirty templates” (TDT) algorithms employ symbol-long segments of the received signals as ”templates” in the correlation operation [2]. The synchronization criterion of TDT algorithms exploits the fact that the cross-correlation of these ”dirty templates” exhibits a unique maximum at the correct symbol time. However, although TDT algorithms are blind in the sense that they do not require TH code, they are inoperable in multi-user environments in which other users employ the same training pattern. This paper proposes a novel non-data aided (NDA) synchronization algorithm designated as the ”timing with delay line combination” (TDLC) algorithm. In contrast to TDT algorithms, which rely on acquiring a maximum integration output by testing all of the candidate time offsets (τ ), the synchronization criterion of the TDLC algorithm is based on detecting the sharpest rising or falling edge of the continuous integration output of the combinative output signal provided by the frame-differential delay line (FDL) during one symbol period. The TDT algorithm requires 2K × Ni symbol periods for each round, where K is the number of pairs of symbollong received segments required for reliable estimation and Ni is the number of candidate time offsets. However, the
O
Manuscript received October 29, 2006. The associate editor coordinating the review of this letter and approving it for publication was Dr. Philippe Ciblat. The authors are with the Institute of Electrical Engineering, National Chung Cheng University, Chia-Yi, Taiwan (email: [email protected]). Digital Object Identifier 10.1109/LCOMM.2007.061765.
proposed TDLC algorithm requires just one symbol period per round. Therefore, the TDLC algorithm is superior to the TDT algorithms in terms of its synchronization speed. The present simulation results also demonstrate that the TDLC algorithm achieves a higher probability of detection (PD) than the TDT algorithms in both multipath and multi-user environments. II. S IGNAL M ODEL The transmitted signal from the kth user is given by f −1 ∞ N
sk (t) =
(dk,i )j w(t − iTs − jTf − ck,j Tc ), (1)
i=−∞ j=0
where k is the user index; i is the symbol index; j is the frame index; dk,i ∈ {+1, −1} is the data sequence for the kth active user; w(t) is the transmitted pulse waveform; Ts is the symbol Nf −1 duration; Tf is the pulse repetition time; {ck,j }j=0 is the time hopping (TH) code; and Tc is the chip duration. Each symbol is transmitted in Nf successive frames with one pulse per frame and the jth transmitted pulse of the ith symbol is modulated by (dk,i )j . As discussed in [3], let Dk,p indicate the time offset between the pth and the (p+1)th transmitted pulses from the kth user, where Dk,p = Tf + (ck,mod(p+1,Nf ) − ck,mod(p,Nf ) ) × Tc for p ∈ [0, Nf − 1]. Eq. (1) can then be rewritten as f −1 ∞ N
sk (t) =
(dk,i ) w(t−iTs −ck,0 Tc − j
−1
Dk,p ), (2)
p=0
i=−∞ j=0
where
j−1
Dk,p = 0 is defined.
p=0
The multipath channel corresponding to each user k is modeled as a tap delay line with Lk taps, whose amplitudes Lk k {αk,l }L l=1 and delays {τk,l }l=1 are invariant over one symbol duration. The channel impulse response is given by hk (t) =
Lk
αk,l δ(t − τk,l ),
(3)
l=1
where τk,1 is the propagation delay of the first arrival signal. The aggregated waveform for all of active users has the form r(t) =
N u −1
sk (t) ∗ hk (t) + n(t)
k=0
=
N u −1
f −1 Lk ∞ N
(dk,i )j αk,l w(t − iTs − ck,0 Tc
k=0 i=−∞ j=0 l=1
−
j−1 p=0
c 2007 IEEE 1089-7798/07$25.00
Dk,p − τk,l ) + n(t)
HSU and WEN: TIMING SYNCHRONIZATION IN ULTRA-WIDEBAND SYSTEMS WITH DELAY LINE COMBINATION RECEIVERS N f −1
where
265
D0,p = 0 is defined.
p=Nf
The DLC receiver introduces a delay time Tw . Note that the value of Tw should be designed appropriately in order to optimize the performance of the proposed synchronization (k) algorithm. Generally, it is reasonable to assume Tw ≤ Tmds , (k) where Tmds = τk,Lk −τk,1 is the maximum delay spread under the channel impulse response hk (t) . Subtracting z(t − Tw ) from z(t) gives α(t) = z(t) − z(t − Tw )
Nf −1
=
Nf −1
r(x −
t−Tw
m=0
Nf −1
t
D0,p ) × r(x −
p=m
D0,p )dx.
p=m+1
(7)
Substituting Eq. (5) into Eq. (7), yields
Nf −1
Fig. 1.
α(t) =
Block diagram of DLC receiver for the 0th user.
{
t−Tw
m=0
Nf −1 ∞
Nu −1
t
k1 =0 i1 =−∞ j1 =0 Nf −1
j1 −1
=
−
Nf −1
N u −1
∞
vk,i,j (t) + n(t),
(4)
p=0
×{
r(t) =
(dk,i ) vk,i,0 (t −
k=0 i=−∞ j=0
j
j−1
Dk,p ) + n(t). (5)
=
0 Nf −1 t m=0
0
Nf −1
r(x −
p=m
Nf −1
D0,p ) × r(x −
m=0 i=−∞
D0,p )dx,
p=m+1
(6)
Dk2 ,p
Nf −1
D0,p )}dx.
(8)
p=m+1
∞
Nf −1
m−1
t
(d0,i )m v0,i,0 (x −
t−Tw
D0,p −
p=0 m
× (d0,i )m+1 v0,i,0 (x −
i=−∞
The delay line combination (DLC) receiver proposed in this study is derived from the differential IR-UWB system presented in [3]. However, in the current DLC receiver, the delay elements are arranged in a cascade rather than in parallel. This sequence of delay elements is designated as the ”frame-differential delay line” (FDL). The delays in the FDL are denoted by Dk,Nf −1 , Dk,Nf −2 , ..., Dk,0 , sequentially. As shown in Fig. 1, the active user is indexed as 0, and y(t) is the combinative output signal of the Nf tap branches of the FDL. The continuous integration output of y(t) is given by t y(x)dx z(t) =
j2 −1
p=0
D0,p ) + n(x −
∞
= (Nf )
III. T IMING WITH D ELAY L INE C OMBINATION (TDLC) A LGORITHM
D0,p )}
p=m
Extracting the desired terms with indexes k1 = k2 = 0, i1 = i2 , j1 = m , and j2 = m + 1 from Eq. (8) gives α(t) =
p=0
(dk2 ,i2 )j2 vk2 ,i2 ,0 (x −
p=m+1
Nf −1
∞
p=m
Nf −1 ∞
−
p=0 Nf −1
D0,p ) + n(x −
Nf −1
Lk k Dk,p −τk,l ) . Since {αk,l }L l=1 and {τk,l }l=1 are in-
variant over one symbol duration, vk,i,j (t) = (dk,i )j vk,i,0 (t − j−1 Dk,p ) . Eq. (4) can be rewritten as
Nf −1
k2 =0 i2 =−∞ j2 =0
l=1
N u −1
Nu −1
where Nu is the total number of active users; n(t) is the addiLk tive Gaussian noise, and vk,i,j (t) = (dk,i )j αk,l w(t−iTs − j−1
Dk1 ,p −
p=0
k=0 i=−∞ j=0
ck,0 Tc −
(dk1 ,i1 )j1 vk1 ,i1 ,0 (x
t
t−Tw
D0,p )
p=m
Nf −1
D0,p −
p=0
(d0,i )
D0,p )dx + Ψ(t)
p=m+1
2 v0,i,0 (x − Ts )dx + Ψ(t),
(9)
where Ψ(t) denotes the noise and interference terms. If Ψ(t) is ignored, |α(t)| exhibits a local maximum when t − Tw = (i + 1)Ts + τ0,1 + c0,0 Tc for each symbol index i. Therefore, the true symbol boundary, i.e. (i+1) tsymbol = (i + 1)Ts + τ0,1 , can be determined by detecting the time at which |α(t)| exhibits its local maximum during each symbol period. Assuming that the time at which |α(t)| exhibits its local (i+1) maximum is denoted by tmax and is estimated in accordance with the criterion t(i+1) max = arg
max (|α(t)|),
ti
IEEE COMMUNICATIONS LETTERS, VOL. 11, NO. 3, MARCH 2007
Timing Synchronization in Ultra-Wideband Systems with Delay Line Combination Receivers Hsi-Chou Hsu and Jyh-Horng Wen
Abstract— This paper proposes a novel non-data aided timing synchronization algorithm designated as ”timing with delay line combination” (TDLC), to improve the synchronization speed of differential impulse radio ultra-wideband systems. Continuously integrating the combinative output signal provided by the proposed ”frame-differential delay line” (FDL), it is found that the integration output exhibits a sharp rising or falling transition at the moment that the first signal per symbol arrives. By accurately detecting the time of the rising or falling edge, the symbol boundary can be simply derived. The proposed scheme achieves timing synchronization within a single symbol duration. Index Terms— Synchronization, timing acquisition, differential transmitted reference (DTR), impulse radio (IR), ultra-wideband (UWB).
I. I NTRODUCTION NE of the critical challenges in designing UWB receivers is the synchronization issue. In most instances, the channel information is not known exactly during the synchronization phase. It has been shown that differential transmitted reference (DTR) receivers [1] can resolve the problem of energy collection without any channel information. In a similar approach to that adopted in the DTR receivers, ”timing with dirty templates” (TDT) algorithms employ symbol-long segments of the received signals as ”templates” in the correlation operation [2]. The synchronization criterion of TDT algorithms exploits the fact that the cross-correlation of these ”dirty templates” exhibits a unique maximum at the correct symbol time. However, although TDT algorithms are blind in the sense that they do not require TH code, they are inoperable in multi-user environments in which other users employ the same training pattern. This paper proposes a novel non-data aided (NDA) synchronization algorithm designated as the ”timing with delay line combination” (TDLC) algorithm. In contrast to TDT algorithms, which rely on acquiring a maximum integration output by testing all of the candidate time offsets (τ ), the synchronization criterion of the TDLC algorithm is based on detecting the sharpest rising or falling edge of the continuous integration output of the combinative output signal provided by the frame-differential delay line (FDL) during one symbol period. The TDT algorithm requires 2K × Ni symbol periods for each round, where K is the number of pairs of symbollong received segments required for reliable estimation and Ni is the number of candidate time offsets. However, the
O
Manuscript received October 29, 2006. The associate editor coordinating the review of this letter and approving it for publication was Dr. Philippe Ciblat. The authors are with the Institute of Electrical Engineering, National Chung Cheng University, Chia-Yi, Taiwan (email: [email protected]). Digital Object Identifier 10.1109/LCOMM.2007.061765.
proposed TDLC algorithm requires just one symbol period per round. Therefore, the TDLC algorithm is superior to the TDT algorithms in terms of its synchronization speed. The present simulation results also demonstrate that the TDLC algorithm achieves a higher probability of detection (PD) than the TDT algorithms in both multipath and multi-user environments. II. S IGNAL M ODEL The transmitted signal from the kth user is given by f −1 ∞ N
sk (t) =
(dk,i )j w(t − iTs − jTf − ck,j Tc ), (1)
i=−∞ j=0
where k is the user index; i is the symbol index; j is the frame index; dk,i ∈ {+1, −1} is the data sequence for the kth active user; w(t) is the transmitted pulse waveform; Ts is the symbol Nf −1 duration; Tf is the pulse repetition time; {ck,j }j=0 is the time hopping (TH) code; and Tc is the chip duration. Each symbol is transmitted in Nf successive frames with one pulse per frame and the jth transmitted pulse of the ith symbol is modulated by (dk,i )j . As discussed in [3], let Dk,p indicate the time offset between the pth and the (p+1)th transmitted pulses from the kth user, where Dk,p = Tf + (ck,mod(p+1,Nf ) − ck,mod(p,Nf ) ) × Tc for p ∈ [0, Nf − 1]. Eq. (1) can then be rewritten as f −1 ∞ N
sk (t) =
(dk,i ) w(t−iTs −ck,0 Tc − j
−1
Dk,p ), (2)
p=0
i=−∞ j=0
where
j−1
Dk,p = 0 is defined.
p=0
The multipath channel corresponding to each user k is modeled as a tap delay line with Lk taps, whose amplitudes Lk k {αk,l }L l=1 and delays {τk,l }l=1 are invariant over one symbol duration. The channel impulse response is given by hk (t) =
Lk
αk,l δ(t − τk,l ),
(3)
l=1
where τk,1 is the propagation delay of the first arrival signal. The aggregated waveform for all of active users has the form r(t) =
N u −1
sk (t) ∗ hk (t) + n(t)
k=0
=
N u −1
f −1 Lk ∞ N
(dk,i )j αk,l w(t − iTs − ck,0 Tc
k=0 i=−∞ j=0 l=1
−
j−1 p=0
c 2007 IEEE 1089-7798/07$25.00
Dk,p − τk,l ) + n(t)
HSU and WEN: TIMING SYNCHRONIZATION IN ULTRA-WIDEBAND SYSTEMS WITH DELAY LINE COMBINATION RECEIVERS N f −1
where
265
D0,p = 0 is defined.
p=Nf
The DLC receiver introduces a delay time Tw . Note that the value of Tw should be designed appropriately in order to optimize the performance of the proposed synchronization (k) algorithm. Generally, it is reasonable to assume Tw ≤ Tmds , (k) where Tmds = τk,Lk −τk,1 is the maximum delay spread under the channel impulse response hk (t) . Subtracting z(t − Tw ) from z(t) gives α(t) = z(t) − z(t − Tw )
Nf −1
=
Nf −1
r(x −
t−Tw
m=0
Nf −1
t
D0,p ) × r(x −
p=m
D0,p )dx.
p=m+1
(7)
Substituting Eq. (5) into Eq. (7), yields
Nf −1
Fig. 1.
α(t) =
Block diagram of DLC receiver for the 0th user.
{
t−Tw
m=0
Nf −1 ∞
Nu −1
t
k1 =0 i1 =−∞ j1 =0 Nf −1
j1 −1
=
−
Nf −1
N u −1
∞
vk,i,j (t) + n(t),
(4)
p=0
×{
r(t) =
(dk,i ) vk,i,0 (t −
k=0 i=−∞ j=0
j
j−1
Dk,p ) + n(t). (5)
=
0 Nf −1 t m=0
0
Nf −1
r(x −
p=m
Nf −1
D0,p ) × r(x −
m=0 i=−∞
D0,p )dx,
p=m+1
(6)
Dk2 ,p
Nf −1
D0,p )}dx.
(8)
p=m+1
∞
Nf −1
m−1
t
(d0,i )m v0,i,0 (x −
t−Tw
D0,p −
p=0 m
× (d0,i )m+1 v0,i,0 (x −
i=−∞
The delay line combination (DLC) receiver proposed in this study is derived from the differential IR-UWB system presented in [3]. However, in the current DLC receiver, the delay elements are arranged in a cascade rather than in parallel. This sequence of delay elements is designated as the ”frame-differential delay line” (FDL). The delays in the FDL are denoted by Dk,Nf −1 , Dk,Nf −2 , ..., Dk,0 , sequentially. As shown in Fig. 1, the active user is indexed as 0, and y(t) is the combinative output signal of the Nf tap branches of the FDL. The continuous integration output of y(t) is given by t y(x)dx z(t) =
j2 −1
p=0
D0,p ) + n(x −
∞
= (Nf )
III. T IMING WITH D ELAY L INE C OMBINATION (TDLC) A LGORITHM
D0,p )}
p=m
Extracting the desired terms with indexes k1 = k2 = 0, i1 = i2 , j1 = m , and j2 = m + 1 from Eq. (8) gives α(t) =
p=0
(dk2 ,i2 )j2 vk2 ,i2 ,0 (x −
p=m+1
Nf −1
∞
p=m
Nf −1 ∞
−
p=0 Nf −1
D0,p ) + n(x −
Nf −1
Lk k Dk,p −τk,l ) . Since {αk,l }L l=1 and {τk,l }l=1 are in-
variant over one symbol duration, vk,i,j (t) = (dk,i )j vk,i,0 (t − j−1 Dk,p ) . Eq. (4) can be rewritten as
Nf −1
k2 =0 i2 =−∞ j2 =0
l=1
N u −1
Nu −1
where Nu is the total number of active users; n(t) is the addiLk tive Gaussian noise, and vk,i,j (t) = (dk,i )j αk,l w(t−iTs − j−1
Dk1 ,p −
p=0
k=0 i=−∞ j=0
ck,0 Tc −
(dk1 ,i1 )j1 vk1 ,i1 ,0 (x
t
t−Tw
D0,p )
p=m
Nf −1
D0,p −
p=0
(d0,i )
D0,p )dx + Ψ(t)
p=m+1
2 v0,i,0 (x − Ts )dx + Ψ(t),
(9)
where Ψ(t) denotes the noise and interference terms. If Ψ(t) is ignored, |α(t)| exhibits a local maximum when t − Tw = (i + 1)Ts + τ0,1 + c0,0 Tc for each symbol index i. Therefore, the true symbol boundary, i.e. (i+1) tsymbol = (i + 1)Ts + τ0,1 , can be determined by detecting the time at which |α(t)| exhibits its local maximum during each symbol period. Assuming that the time at which |α(t)| exhibits its local (i+1) maximum is denoted by tmax and is estimated in accordance with the criterion t(i+1) max = arg
max (|α(t)|),
ti
