Clipping Noise Cancellation Based on Compressed Sensing for Visible Light Communication Presented by Jian Song jsong@tsinghua.edu.cn Tsinghua University, China 1
Contents 1 Technical Background 2 System Model 3 Proposed Solutions 4 Simulation Results 5 Conclusions 2
Contents 1 Technical Background 2 System Model 3 Proposed Solutions 4 Simulation Results 5 Conclusions 3
Technical Background Asymmetrically clipped optical OFDM (ACO-OFDM) Hermitian symmetry (real-valued) Only the odd subcarriers in the frequency domain are occupied (non-negative) Clipping noise nonlinear transfer characteristics of LEDs generate the self-interference deteriorates the performance 4
Technical Background Proposed scheme to reconstruct clipping noise compressed sensing Taking advantage of the time-domain sparsity of the clipping noise Using sparsity adaptive matching pursuit (SAMP) greedy algorithm partially aware support a coarse estimation of the clipping noise location improve the accuracy and robustness, complexity is also lower 5
Contents 1 Technical Background 2 System Model 3 Proposed Solutions 4 Simulation Results 5 Conclusions 6
System Model The transmitter block diagram of the OFDM systems Mapping Serial to Parallel IFFT Add Cyclic Prefix Parallel to Serial Clipping Operation D/A Converter The transmitted symbol The ACO-OFDM signal X = (0, X1,0, X2, XN/2 1,0, XN/2 1,,0, X1 ) xx AAAAAA,nn = xx nn, xx nn 0, 0, xx nn < 0. NN 1 xx nn = XX kk exp kk=0 jj2ππππππ NN XX kk = 2XX AAAAAA,kk 7
System Model The transmitter block diagram of the OFDM systems Mapping Serial to Parallel IFFT Add Cyclic Prefix Parallel to Serial Clipping Operation D/A Converter The clipped signal xx AAAAAA,nn = xx AAAAAA,nn, xx AAAAAA,nn AA ttt, AA ttt, xx AAAAAA,nn > AA ttt, xx AAAAAA,nn = xx AAAAAA,nn + cc nn XX AAAAAA,kk = XX AAAAAA,kk + CC kk 8
System Model The proposed receiver block diagram of the OFDM systems A/D Converter y Y Maximum FFT Likelihood X Estimation + Reliable Observation CS Reconstruc -tion c C FFT + Maximum Likelihood Estimation The received symbol Compressed Sensing Model Y = X + Z = X + C + Z k ACO, k k ACO, k k k The initial decision Xˆ k = arg min 2 Yk s, s χ Xˆ Xˆ Xˆ Y = X + C+ Z = C+ ( X + Z) 2 2 2 The final decision Xˆ = arg min 2 ( Y Cˆ ) s, s χ k k k 9
Contents 1 Technical Background 2 System Model 3 Proposed Solutions 4 Simulation Results 5 Conclusions 10
Proposed Solutions Compressed Sensing Model Measurement vector Sensing matrix φ unknown vector c = Xˆ Xˆ Y = C+ ( X + Z) = C+ θ 2 2 Y = S( Y Xˆ / 2) = SC + Sθ = SFc + Sθ =Φ c + η Selection matrix S y = SCˆ φ = S F select a series of reliable tones 11
Proposed Solutions Compressed Sensing Model Y = SFc + Sθ =Φ c + η Measurement vector Sensing matrix φ unknown vector c RIP (restricted isometry property) = N kn, + 2 2 N 2 j π π k( n+ ) j kn N 2 N F = e = e = F kn, Φ mn, = Φ N RIP doesn t hold mn+, 2 y = SCˆ φ = S F needs to be reconsidered! 12
Proposed Solutions The Transformation of CS Problem Φ = [A, A], c = [c ;c ] 1 2 Y = SFc + Sθ =Φ c + RIP η c, 1 Y = Φc + η Y = [A, A] + η = Ac + η c= c1 c2 c 2 c1,n = 0,c2,n = c, if c > 0, c1,n = c, c2,n = 0, if c 0. the clipping noise c 0 13
Proposed Solutions Problem Y =Φ c+ η Solution CS method clipping noise is variable and unknown SAMP (sparsity adaptive matching pursuit) not require the sparsity level to be known partially aware support PAS-SAMP 14
Proposed Solutions priori information 1.2 partial support 0.8 1 { n y 2 } n λt (0) Π = > 0.6 Facilitate the CS recovery process 0.4 0.2 0 0 10 20 30 40 50 60 70 15
Proposed Solutions The priori information initial support set Complexity the testing sparsity level (0) T K + j s T j s Adaptivity 16
Contents 1 Technical Background 2 System Model 3 Proposed Solutions 4 Simulation Results 5 Conclusions 17
Simulation Results 16-QAM,N=256,Ath=1.5 Sparse level K =10 At the target BER=10-3 PAS-SAMP outperforms SAMP 0.2dB the gap to worst case is 1.5dB 18
Simulation Results 64-QAM,N=1024,Ath=1.8 Sparse level K =20 At the target BER=10-3 PAS-SAMP outperforms SAMP 0.3dB the gap to worst case is 1.6dB 19
Contents 1 Technical Background 2 System Model 3 Proposed Solutions 4 Simulation Results 5 Conclusions 20
Conclusions Clipping noise cancellation for ACO-OFDM systems based on compressed sensing with partially aware support Apply CS to clipping noise cancellation in ACO-OFDM systems Solves the RIP problem that the sensing matrix for ACO-OFDM systems Improve the accuracy and robustness of the proposed scheme Computational complexity is lower 21
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Jian Song Tsinghua University, China