SLIDE 1
Outline
Outline Introduction Previous Results Problem Formulation Proposed Solution Performance Analysis Simulation Results Conclusion 2
Joint CFO and Channel Estimation for ZP-OFDM Modulated Two-Way Relay - - PowerPoint PPT Presentation
Joint CFO and Channel Estimation for ZP-OFDM Modulated Two-Way Relay - - PowerPoint PPT Presentation
Joint CFO and Channel Estimation for ZP-OFDM Modulated Two-Way Relay Networks Gongpu Wang , Feifei Gao , Yik-Chung Wu , and Chintha Tellambura University of Alberta, Edmonton, Canada, Jacobs University, Bremen, Germany
SLIDE 2
SLIDE 3
Introduction
Outline Introduction Previous Results Problem Formulation Proposed Solution Performance Analysis Simulation Results Conclusion 3
■ Two-way relay networks (TWRN) can enhance the
- verall communication rate [Boris Rankov, 2006],
[J.Ponniah, 2008].
T1 ✍✌ ✎☞ T2 ✍✌ ✎☞ R ✍✌ ✎☞ ✲ ✛ ✲ ✛ h1 h2 f1 fr f2
Figure 1: System configuration for two-way relay network.
SLIDE 4
Previous Results
Outline Introduction Previous Results Problem Formulation Proposed Solution Performance Analysis Simulation Results Conclusion 4
■ Most existing works in TWRN assumed perfect
synchronization and channel state information (CSI).
■ Channel estimation problems in
amplify-and-forward (AF) TWRN are different from those in traditional communication systems.
■ Flat-fading and frequency-selective channel
estimation and training design for AF TWRN has been done in [Feifei Gao, 2009].
■ Our paper will focus on joint frequency offset (CFO)
and channel estimation for AF-based OFDM-Modulated TWRN.
SLIDE 5
Joint CFO and Channel Estimation Problems in TWRN
Outline Introduction Previous Results Problem Formulation Proposed Solution Performance Analysis Simulation Results Conclusion 5
■ With CFOs, the orthogonality between subcarriers
will be destroyed in TWRN.
■ Even with completed estimation, data detection is
not simple as circular convolution no longer exists.
■ How to estimate the mixed CFOs and channels and
how to faciliate data detection?
■ We introduce some redundancy and modify the
OFDM TWRN system to facilitate both the joint estimation and detection.
SLIDE 6
Signals at Relay
Outline Introduction Previous Results Problem Formulation Proposed Solution Performance Analysis Simulation Results Conclusion 6
■ The relay R will down-convert the passband signal by e−2πfrt
and obtain rzp =
2
- i=1
Γ(N+L)[fi − fr]H(N)
zp [hi]si + nr,
(1) where Γ(K)[f] = diag{1, ej2πfTs, . . . , ej2πf(K−1)Ts} and si = FH˜ si = si,0 si,1 . . . si,N−1 H(K)
zp [x]
x0 . . . . . . ... . . . xP ... x0 . . . ... . . . . . . xP
- K columns
■ Next, R adds L zeros to the end of r and scales it by the
factor of αzp to keep the average power constraint.
SLIDE 7
Signals at Terminal T1
Outline Introduction Previous Results Problem Formulation Proposed Solution Performance Analysis Simulation Results Conclusion 7
■ T1 will down-convert the passband signal by e−2πf1t and get
yzp =αzpΓ(N+2L)[fr − f1]H(N+L)
zp
[h1]rzp + n1 =αzpΓ(N+2L)[fr − f1]H(N+L)
zp
[h1] ×
2
- j=1
Γ(N+L)[fi − fr]H(N)
zp [hi]si
+ αzpΓ(N+2L)[fr − f1]H(N+L)
zp
[h1]nr + n1
- ne
(2)
■ Next, using the following equalities
H(K)
zp [x] Γ(K)[f] = Γ(K+P )[f]H(K) zp
- Γ(K)[−f]x
- ,
(3) and Γ(K+P )[f]H(K)
zp [x] = H(K) zp
- Γ(P +1)[f]x
- Γ(K)[f].
(4)
SLIDE 8
Signals at Terminal T1
Outline Introduction Previous Results Problem Formulation Proposed Solution Performance Analysis Simulation Results Conclusion 8
■ yzp can be rewritten as
yzp =αzpH(N+L)
zp
[Γ(L+1)[fr − f1]h1]H(N)
zp [h1] s1 + ne
+ αzpΓ(N+2L)[f2 − f1]H(N+L)
zp
[Γ(L+1)[fr − f2]h1] × H(N)
zp [h2]
(5)
■ We further note that H(N+L)
zp
[x1]H(N)
zp [x2] = H(N) zp [x1 ⊗ x2]
where ⊗ denotes the linear convolution.
■ Hence yzp is finally written as
yzp =αzpH(N)
zp
- (Γ(L+1)[fr − f1]h1) ⊗ h1
- azp
s1 + ne + αzpΓ(N+2L)[f2 − f1
v
]H(N)
zp
- (Γ(L+1)[fr − f2]h1) ⊗ h2
- bzp
s2, (6) where azp, bzp are the (2L + 1) × 1 equivalent channel vectors and v is the equivalent CFO.
SLIDE 9
Joint CFO and Channel Estimation
Outline Introduction Previous Results Problem Formulation Proposed Solution Performance Analysis Simulation Results Conclusion 9
■ We then obtain
y = S1a + ΓS2b + ne. (7)
■ Since S1 is a tall matrix, it is possible to find a matrix J such
that JHS1 = 0.
■ Left-multiplying y by JH gives
JHy = 0 + JHΓS2
G
b + JHne
n
. (8)
■ Joint CFO estimation and channel estimation
ˆ v = arg max
v
yHJG(GHG)−1GHJHy, (9) ˆ b =(GHG)−1GHJHy, (10) ˆ a =(SH
1 S1)−1SH 1 (y − ˆ
ΓS2ˆ b). (11)
SLIDE 10
Performance Analysis
Outline Introduction Previous Results Problem Formulation Proposed Solution Performance Analysis Simulation Results Conclusion 10
■ At high SNR, the perturbation of the estimated CFO can be
approximated by ∆v ˆ v0 − v0 ≈ − ˙ g(v0) E{¨ g(v0)}, (12) where g(v) = yHJG(GHG)−1GHJHy.
■ The NLS estimation of CFO is unbiased and its MSE is
E{∆v2} = σ2
ne
2bH ˙ GH[I − G(GHG)−1GH] ˙ Gb . (13)
■ The channel estimation ˆ
b is unbiased and its MSE is MSE{b} = (GHG)−1GH ˙ GbbH ˙ GHG(GHG)−1E{∆v2} + σ2
ne(GHG)−1.
(14)
SLIDE 11
Simulation Results
Outline Introduction Previous Results Problem Formulation Proposed Solution Performance Analysis Simulation Results Conclusion 11 5 10 15 20 25 30 10
−9
10
−8
10
−7
10
−6
10
−5
10
−4
10
−3
SNR (dB) CFO MSE v numerical MSE N=16 v theoretical MSE N=16 v numerical MSE N=32 v theoretical MSE N=32
Figure 2: Numerical and Theoretical MSEs of CFO versus SNR
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Simulation Results
Outline Introduction Previous Results Problem Formulation Proposed Solution Performance Analysis Simulation Results Conclusion 12
5 10 15 20 25 30 10
−4
10
−3
10
−2
10
−1
10 SNR (dB) Channel Estimation MSE a numerical MSE N=16 a numerical MSE N=32 b numerical MSE N=16 b theoretical MSE N=16 b numerical MSE N=32 b theoretical MSE N=32
Figure 3: Numerical and Theoretical MSEs of Channel Estimation versus SNR
SLIDE 13
Conclusion
Outline Introduction Previous Results Problem Formulation Proposed Solution Performance Analysis Simulation Results Conclusion 13
- 1. Adapt ZP-based OFDM transmission scheme.
- 2. Suggest joint estimation method of CFO and
channels.
- 3. Performance analysis: prove unbiasedness and
give closed-form MSE expression.
SLIDE 14
Conclusion
Outline Introduction Previous Results Problem Formulation Proposed Solution Performance Analysis Simulation Results Conclusion 13
- 1. Adapt ZP-based OFDM transmission scheme.
- 2. Suggest joint estimation method of CFO and
channels.
- 3. Performance analysis: prove unbiasedness and
give closed-form MSE expression. Problem: How to obtain individual frequency and channel parameters? (Globecom 2010)
SLIDE 15
Outline Introduction Previous Results Problem Formulation Proposed Solution Performance Analysis Simulation Results Conclusion 14