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 ∗ The University of Hong Kong, Hong Kong Email: gongpu@ece.ualberta.ca WCNC’10

Outline ■ Introduction Outline Introduction ■ Previous Results Previous Results Problem Formulation Proposed Solution Performance Analysis Simulation Results ■ Problem Formulation Conclusion ■ Proposed Solution ■ Performance Analysis ■ Simulation Results ■ Conclusion 2

Introduction ■ Two-way relay networks (TWRN) can enhance the overall communication rate [Boris Rankov, 2006], [J.Ponniah, 2008]. Outline Introduction Previous Results Problem Formulation Proposed Solution Performance Analysis Simulation Results ✎☞ ✎☞ ✎☞ Conclusion ✲ ✛ T 1 h 1 R h 2 T 2 ✍✌ ✍✌ ✍✌ ✛ ✲ f 1 f r f 2 Figure 1: System configuration for two-way relay network. 3

Previous Results ■ Most existing works in TWRN assumed perfect synchronization and channel state information Outline Introduction (CSI). Previous Results Problem Formulation Proposed Solution ■ Channel estimation problems in Performance Analysis Simulation Results amplify-and-forward (AF) TWRN are different from Conclusion 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. 4

Joint CFO and Channel Estimation Problems in TWRN ■ With CFOs, the orthogonality between subcarriers will be destroyed in TWRN. Outline Introduction Previous Results Problem Formulation ■ Even with completed estimation, data detection is Proposed Solution Performance Analysis not simple as circular convolution no longer exists. Simulation Results Conclusion ■ 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. 5

Signals at Relay ■ The relay R will down-convert the passband signal by e −  2 πf r t and obtain Outline Introduction 2 Previous Results � Γ ( N + L ) [ f i − f r ] H ( N ) Problem Formulation r zp = zp [ h i ] s i + n r , (1) Proposed Solution i =1 Performance Analysis Simulation Results Conclusion where Γ ( K ) [ f ] = diag { 1 , e j 2 πfT s , . . . , e j 2 πf ( K − 1) T s } and   0 x 0 . . .   . . ... s i, 0  . .  . .   s i, 1     ... H ( K ) s i = F H ˜   zp [ x ] �   s i = . x P x 0     . .     . . ...   . . s i,N − 1 . .   0 . . . x P � �� � K columns ■ Next, R adds L zeros to the end of r and scales it by the factor of α zp to keep the average power constraint. 6

Signals at Terminal T 1 ■ T 1 will down-convert the passband signal by e −  2 πf 1 t and get Outline y zp = α zp Γ ( N +2 L ) [ f r − f 1 ] H ( N + L ) [ h 1 ] r zp + n 1 Introduction zp Previous Results = α zp Γ ( N +2 L ) [ f r − f 1 ] H ( N + L ) [ h 1 ] Problem Formulation zp Proposed Solution   Performance Analysis 2 � Simulation Results Γ ( N + L ) [ f i − f r ] H ( N ) × zp [ h i ] s i   Conclusion j =1 + α zp Γ ( N +2 L ) [ f r − f 1 ] H ( N + L ) [ h 1 ] n r + n 1 (2) zp � �� � n e ■ Next, using the following equalities � � H ( K ) zp [ x ] Γ ( K ) [ f ] = Γ ( K + P ) [ f ] H ( K ) Γ ( K ) [ − f ] x (3) , zp and � � Γ ( K + P ) [ f ] H ( K ) zp [ x ] = H ( K ) Γ ( P +1) [ f ] x Γ ( K ) [ f ] . (4) zp 7

Signals at Terminal T 1 ■ y zp can be rewritten as Outline y zp = α zp H ( N + L ) [ Γ ( L +1) [ f r − f 1 ] h 1 ] H ( N ) zp [ h 1 ] s 1 + n e Introduction zp Previous Results + α zp Γ ( N +2 L ) [ f 2 − f 1 ] H ( N + L ) [ Γ ( L +1) [ f r − f 2 ] h 1 ] × H ( N ) zp [ h 2 ] Problem Formulation zp Proposed Solution (5) Performance Analysis Simulation Results Conclusion ■ We further note that H ( N + L ) [ x 1 ] H ( N ) zp [ x 2 ] = H ( N ) zp [ x 1 ⊗ x 2 ] zp where ⊗ denotes the linear convolution. ■ Hence y zp is finally written as � � y zp = α zp H ( N ) ( Γ ( L +1) [ f r − f 1 ] h 1 ) ⊗ h 1 s 1 + n e zp � �� � a zp � � + α zp Γ ( N +2 L ) [ f 2 − f 1 ] H ( N ) ( Γ ( L +1) [ f r − f 2 ] h 1 ) ⊗ h 2 s 2 , (6) zp � �� � � �� � v b zp where a zp , b zp are the (2 L + 1) × 1 equivalent channel vectors and v is the equivalent CFO. 8

Joint CFO and Channel Estimation ■ We then obtain Outline y = S 1 a + ΓS 2 b + n e . (7) Introduction Previous Results Problem Formulation Proposed Solution ■ Since S 1 is a tall matrix, it is possible to find a matrix J such Performance Analysis that J H S 1 = 0 . Simulation Results Conclusion ■ Left-multiplying y by J H gives J H y = 0 + J H ΓS 2 b + J H n e (8) . � �� � � �� � n G ■ Joint CFO estimation and channel estimation y H JG ( G H G ) − 1 G H J H y , v = arg max ˆ (9) v ˆ b =( G H G ) − 1 G H J H y , (10) 1 ( y − ˆ ΓS 2 ˆ 1 S 1 ) − 1 S H a =( S H ˆ b ) . (11) 9

Performance Analysis ■ At high SNR, the perturbation of the estimated CFO can be approximated by Outline Introduction g ( v 0 ) ˙ Previous Results ∆ v � ˆ v 0 − v 0 ≈ − (12) g ( v 0 ) } , Problem Formulation E { ¨ Proposed Solution Performance Analysis Simulation Results where g ( v ) = y H JG ( G H G ) − 1 G H J H y . Conclusion ■ The NLS estimation of CFO is unbiased and its MSE is σ 2 E { ∆ v 2 } = ne (13) . 2 b H ˙ G H [ I − G ( G H G ) − 1 G H ] ˙ Gb ■ The channel estimation ˆ b is unbiased and its MSE is MSE { b } = ( G H G ) − 1 G H ˙ Gbb H ˙ G H G ( G H G ) − 1 E { ∆ v 2 } + σ 2 ne ( G H G ) − 1 . (14) 10

Simulation Results −3 Outline 10 v numerical MSE N=16 Introduction v theoretical MSE N=16 Previous Results v numerical MSE N=32 Problem Formulation −4 10 v theoretical MSE N=32 Proposed Solution Performance Analysis Simulation Results −5 Conclusion 10 CFO MSE −6 10 −7 10 −8 10 −9 10 0 5 10 15 20 25 30 SNR (dB) Figure 2: Numerical and Theoretical MSEs of CFO versus SNR 11

Simulation Results 0 Outline 10 a numerical MSE N=16 Introduction a numerical MSE N=32 Previous Results b numerical MSE N=16 Problem Formulation b theoretical MSE N=16 Proposed Solution b numerical MSE N=32 Performance Analysis −1 10 b theoretical MSE N=32 Simulation Results Channel Estimation MSE Conclusion −2 10 −3 10 −4 10 0 5 10 15 20 25 30 SNR (dB) Figure 3: Numerical and Theoretical MSEs of Channel Estimation versus SNR 12

Conclusion Outline Introduction 1. Adapt ZP -based OFDM transmission scheme. Previous Results Problem Formulation Proposed Solution Performance Analysis 2. Suggest joint estimation method of CFO and Simulation Results Conclusion channels. 3. Performance analysis: prove unbiasedness and give closed-form MSE expression. 13

Conclusion Outline Introduction 1. Adapt ZP -based OFDM transmission scheme. Previous Results Problem Formulation Proposed Solution Performance Analysis 2. Suggest joint estimation method of CFO and Simulation Results Conclusion channels. 3. Performance analysis: prove unbiasedness and give closed-form MSE expression. Problem: How to obtain individual frequency and channel parameters? (Globecom 2010) 13

Outline Introduction Previous Results Problem Formulation Proposed Solution Performance Analysis Simulation Results Questions and discussion? Conclusion Email: gongpu@ece.ualberta.ca 14