Vincent Savaux - An Iterative and Joint Estimation of SNR and Frequency Selective Channel for OFDM Systems

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1. 06/06/2012 1 SEMINAIRE SCEE 26 avril 2012 Supélec, campus de Rennes Présentation : Vincent Savaux April 17‐20, 2012 Poznań, Poland An Iterative and Joint Estimation of SNR and An Iterative and Joint Estimation of SNR and Frequency Selective Channel for OFDM Systems Authors : Vincent Savaux , Yves Louët , Moïse Djoko‐Kouam and Alexandre Skrzypczak Speaker: Vincent Savaux, PhD student 1,2 1 1 2 ECAM Rennes – Louis de Broglie, Rennes Campus, France 1 SUPELEC, Rennes Campus , France 2
2. 06/06/2012 2 An Iterative and Joint Estimation of SNR and Frequency Selective Channel for OFDM Systems 1. Background  System Model  Estimation Methods 2. Proposed Method  Presentation of the Algorithm  Convergence of the Algorithm 3 3. Simulation Results 4. Conclusion 1.Background System Model In the frequency domain, the received OFDM symbol is: DFT size = 0 0 + Matrix of the emitted OFDM symbol Frequency channel response AWGN Vector of the received OFDM symbol 4 with : zero mean Gaussian process : number of paths of the channel : path delay ,
3. 06/06/2012 3 1.Background Estimation Methods ‐ Signal to noise ratio (SNR, noted ) , with the second moment‐order of the received signal [1]: estimated thanks to the subtraction of two consecutive received signal vectors [2]: estimated thanks to the subspace properties of the estimated covariance matrix of the received signal 5 G. Ren, H. Zhang, and Y. Chang, “SNR Estimation Algorithm Based on the Preamble for OFDM Systems in Frequency Selective Channels,” IEEE Transactions on Communications, vol. 57, no. 8, August 2009. X. Xu, Y. Jing, and X. Yu, “Subspace‐Based Noise Variance and SNR Estimation for OFDM Systems,” in IEEE Mobile Radio Applications Wireless Communication Networking Conference, March 2005, pp. 23 –26. [1] [2] Our solution: estimated thanks to the MMSE criterion 1.Background Estimation Methods ‐ Noise estimation MMSE criterion performed on the pilot (index ) ‐ = 2 2 6 In practice: approximation of MMSE criterion The noise variance estimation depends on the channel estimation quality
4. 06/06/2012 4 1.Background Estimation Methods ‐ Channel estimation Least square (LS) estimator: Linear minimum mean square error (LMMSE) estimator: , with the frequency covariance matrix of the channel For the noise variance estimation: 7 LS estimator: not adapted for the noise variance estimation leads to LMMSE estimator: efficient estimator, adapted for the noise variance estimation requires nevertheless an estimation of the noise variance 2.Proposed Method Presentation of the Algorithm We suppose pilots as requires Problem: , and requires Solution an iterative algorithm LMMSE channel estimation Solution: an iterative algorithm MMSE noise variance estimation SNR estimation At each iteration , we do 8 ,
5. 06/06/2012 5 2.Proposed Method Presentation of the Algorithm LMMSE h l MMSE noise variance estimation SNR estimation Initialization of the Algorithm: If , the LMMSE estimation is equivalent to the LS one: channel estimation 9 The initialization is chosen so that 2.Proposed Method Convergence of the Algorithm ‐ noise variance From the theoretical expression of the MMSE noise variance estimation: eigenvalues of C b l i ith After some mathematical developments: One example of f(x) 10 Convergence by solving with Solution: the fixed point theorem
6. 06/06/2012 6 2.Proposed Method Convergence of the Algorithm Solution: the fixed point theorem applied to the function One example of f(x) is upper and lower bounded: , so is strictly growing has at least one fixed point with the number of paths of the channel 11 is monotonous converges to a fixed point of p Unicity of convergence soon published 2.Proposed Method Convergence of the Algorithm ‐ channel estimation Thanks to Noise variance estimation converges converges Estimated values 12 Channel estimation What about the speed of convergence and the bias of the estimator ? Real values
7. 06/06/2012 7 3.Simulation Results Perfect covariance matrix: Approximate covariance matrix: Case 1: Case 2: Convergence of the algorithm Parameters: : 148 carriers Channel: US Consortium from DRM standard (4 paths channel) Convergence of the algorithm 13 High speed of convergence: 3 iterations Low bias : <2% for SNR=0 dB and <5 % for SNR=10 dB 3.Simulation Results Comparison of SNR estimation with other methods Ren’s method: requires 2 pilots by preamble Xu’s method: requires 1 pilot by preamble Our method: requires 1 pilot by preamble Case 1: perfect covariance matrix Case 2: approximation of the covariance matrix 14 Good trade‐off between efficiency and number of pilot required for the estimation
8. 06/06/2012 8 3.Simulation Results Channel estimation 15 Proof by simulation of the convergence of the channel estimation Gap between perfect estimation and Case 2 <0.5 dB (<0.1 dB in Case 1) 4.Conclusion • New algorithm for joint estimation of SNR and multipath channel • Proof of convergence of the algorithm • Good quality of channel and SNR estimations with high speed of convergence • Improvement of the trade‐off between the number of required pilots and quality of estimation, compared with existing methods in literature • Further works and publications : ‐Unicity of convergence of the algorithm 16 ‐Development of a practical solution with an estimated frequency channel covariance matrix
9. 06/06/2012 9 Thank you for your attention Questions ? … 17