1. Low-Complexity Channel Estimation for Wireless OFDM Systems Eugene Golovins Neco Ventura egolovins@crg.ee.uct.ac.za neco@crg.ee.uct.ac.za

2. E. Golovins UCT-COE Seminar26/07/2007 - 2 - Outline -- Introduction -- Radio channel model -- Pilot-assisted OFDM system -- Blind OFDM system

3. E. Golovins UCT-COE Seminar26/07/2007 - 3 - Introduction OFDM has been found efficient in reducing severe effects of the frequency-selective fading (inherent to the urban and indoor radio channels) OFDM has been found efficient in reducing severe effects of the frequency-selective fading (inherent to the urban and indoor radio channels) High-capacity subcarrier modulation techniques (e.g., QAM) require accurate estimation of the channel frequency response (CFR) for coherent detection at the receiver High-capacity subcarrier modulation techniques (e.g., QAM) require accurate estimation of the channel frequency response (CFR) for coherent detection at the receiver Channel estimator must satisfy 3 requirements: Channel estimator must satisfy 3 requirements: rely on the least possible training overhead rely on the least possible training overhead achieve performance close to optimal achieve performance close to optimal be of the least possible computational complexity be of the least possible computational complexity

4. E. Golovins UCT-COE Seminar26/07/2007 - 4 - Baseband OFDM system

5. E. Golovins UCT-COE Seminar26/07/2007 - 5 - Channel model Two kinds of impairments in the fading channel: Two kinds of impairments in the fading channel: -- dispersion (frequency selectivity) – due to multipath propagation -- time variability (Doppler effect) – due to the relative motion of TX and RX antennas Adopted model – quasi-static approximation of the WSSUS process : Adopted model – quasi-static approximation of the WSSUS process : -- channel response does not change on the interval of one OFDM symbol -- multipath response is comprised of an arbitrary number of the statistically independent path-gains, delayed at fixed time intervals -- inter-symbol variation of the path-gains is governed by the Doppler random process with Jakes’s spectrum

6. E. Golovins UCT-COE Seminar26/07/2007 - 6 - Channel frequency response (CFR) Example of CFR of the considered fading channel : Example of CFR of the considered fading channel : (max. Doppler freq.) (max. delay spread) (RMS delay spread)

7. E. Golovins UCT-COE Seminar26/07/2007 - 7 - Frequency-domain block processing N d data subsymbols are transmitted in block of N d +P+N cp subsymbols, with P pilot subsymbols and a cyclic prefix of length N cp  L - 1 (L = expected CIR length) N d data subsymbols are transmitted in block of N d +P+N cp subsymbols, with P pilot subsymbols and a cyclic prefix of length N cp  L - 1 (L = expected CIR length) Receiver processes blocks in frequency domain by taking FFT of each received block Receiver processes blocks in frequency domain by taking FFT of each received block Typically the size of the processing block N = N d +P is 5 to 10 times N cp Typically the size of the processing block N = N d +P is 5 to 10 times N cp N cp Last N cp sub- symbols repeated N c N c sub- symbols Block of N subsymbols CP Frequency (subcarriers) Time (OFDM symbols / blocks) OFDM time-frequency grid Temporal block structure N

8. E. Golovins UCT-COE Seminar26/07/2007 - 8 - Pilot-assisted system Channel estimator operates only in 1D (across freq. domain) computing channel distortions for each OFDM symbol separately Channel estimator operates only in 1D (across freq. domain) computing channel distortions for each OFDM symbol separately Known pilot sequence is transmitted on a small fraction of subcarriers (P) to train the estimator Known pilot sequence is transmitted on a small fraction of subcarriers (P) to train the estimator Interpolation of pilots in frequency is performed to get CFR estimate in the full band Interpolation of pilots in frequency is performed to get CFR estimate in the full band Frequency (subcarriers) Time (OFDM symbols) N Pilot subcarrier Data subcarrier

9. E. Golovins UCT-COE Seminar26/07/2007 - 9 - Design definition of the constrained estimator Anticipated CIR length Anticipated CIR length Number of pilot subcarriers Number of pilot subcarriers Received subsymbols at the pilot positions: Received subsymbols at the pilot positions: contains reference values of P pilot subsymbols is the selection matrix that is needed to extract pilot samples of the CFR is the zero-padding matrix (from L up to N) is the WGN vector at the pilot subcarriers is the CIR vector (to be found)

10. E. Golovins UCT-COE Seminar26/07/2007 - 10 - Constrained Least Squares (CLS) estimator Minimise the quadratic difference between the received pilot subsymbols and the reference pilot values being affected by the assumed CFR model: Minimise the quadratic difference between the received pilot subsymbols and the reference pilot values being affected by the assumed CFR model: For the equipowered () and equispaced (, ) pilot subcarriers (optimal training structure) we have: For the equipowered () and equispaced (, ) pilot subcarriers (optimal training structure) we have:

11. E. Golovins UCT-COE Seminar26/07/2007 - 11 - Flow chart of the CLS scheme

12. E. Golovins UCT-COE Seminar26/07/2007 - 12 - Constrained linear Minimum MSE (CMMSE) estimator Minimise MSE between the CFR estimate and the assumed CFR model with respect to Q : Minimise MSE between the CFR estimate and the assumed CFR model with respect to Q : Computation of is of large complexity if P is big. Can we design the CMMSE estimator in the transform-domain form ? Computation of is of large complexity if P is big. Can we design the CMMSE estimator in the transform-domain form ? is the design CFR correlation matrix is the design CIR correlation matrix is the design setting for the WGN variance

13. E. Golovins UCT-COE Seminar26/07/2007 - 13 - Low-complexity CMMSE design-form Applying the matrix inversion identities, one can show that Applying the matrix inversion identities, one can show that For the equipowered and equispaced pilot subcarriers: For the equipowered and equispaced pilot subcarriers:

14. E. Golovins UCT-COE Seminar26/07/2007 - 14 - What if the parameters are not known ? Generally the true CIR correlation matrix and the true are not known, therefore the optimum CMMSE design (, ) is hardly achievable Generally the true CIR correlation matrix and the true are not known, therefore the optimum CMMSE design (, ) is hardly achievable 2 practical approaches are possible: 2 practical approaches are possible: robust mode, when (similar to the CLS scheme) robust mode, when (similar to the CLS scheme) recursive mode (dynamic estimation of and ) recursive mode (dynamic estimation of and )

15. E. Golovins UCT-COE Seminar26/07/2007 - 15 - Recursive CMMSE estimator is the precision matrix of the CIR+noise mixture described as Substitute with is an estimate of obtained for the ith OFDM symbol is an estimate of for the (i-1)th OFDM symbol

16. E. Golovins UCT-COE Seminar26/07/2007 - 16 - Recursive CMMSE estimator (cont.) Letthen Letthen For the equipowered and equispaced pilot subcarriers: For the equipowered and equispaced pilot subcarriers:

17. E. Golovins UCT-COE Seminar26/07/2007 - 17 - Initial settings: Initial settings: During the initialisation period, until the reliable estimate of is obtained, estimator operates in the robust mode (as CLS), i.e. During the initialisation period, until the reliable estimate of is obtained, estimator operates in the robust mode (as CLS), i.e. Flow chart of the recursive CMMSE

18. E. Golovins UCT-COE Seminar26/07/2007 - 18 - Optimisation of pilots To achieve the best CFR estimation accuracy under the total transmit power constraint: To achieve the best CFR estimation accuracy under the total transmit power constraint: -- pilot subcarriers must be equipowered and equispaced in the band -- pilot-to-data (PDR) power ratio for the CLS and CMMSE (worst- case CIR correlation) estimators with one-tap equalisation is determined as Pilot subcarrier Data subcarrier

19. E. Golovins UCT-COE Seminar26/07/2007 - 19 - Theoretical/simulation results System configuration: System configuration: (subcarriers), (pilots), (CP length), 16QAM (subcarriers), (pilots), (CP length), 16QAM Average PDR set to optimal calculated for Channel model: Channel model: (modelled CIR length), (modelled Doppler spread) (modelled CIR length), (modelled Doppler spread)

20. E. Golovins UCT-COE Seminar26/07/2007 - 20 - MSE & BER performance (case 1) Channel – non-sample-spaced: 2-path UPDP,

21. E. Golovins UCT-COE Seminar26/07/2007 - 21 - MSE performance (case 2) Channel – sample-spaced: Exponential PDP,

22. E. Golovins UCT-COE Seminar26/07/2007 - 22 - Impact of the number of pilot subcarriers on the system performance Channel – sample-spaced: Exponential PDP,

23. E. Golovins UCT-COE Seminar26/07/2007 - 23 - Dependence of SNR gain at equaliser’s output on PDR CMMSE estimator used Channel – non-sample-spaced: 2-path UPDP,

24. E. Golovins UCT-COE Seminar26/07/2007 - 24 - Blind system Minimises training overhead to just one pilot subcarrier (reference phase acquisition) Minimises training overhead to just one pilot subcarrier (reference phase acquisition) Detection is performed on a portion of subcarriers Detection is performed on a portion of subcarriers (D  L + 1 ) Detected subsymbols are fed forward to the channel estimation and interpolation algorithm (e.g., CLS, CMMSE) to get CFR Detected subsymbols are fed forward to the channel estimation and interpolation algorithm (e.g., CLS, CMMSE) to get CFR The optimal data detection involves an exhaustive search across the lattice of M D points (M – modulation constellation size), yielding a vector of D detected subsymbols satisfying The optimal data detection involves an exhaustive search across the lattice of M D points (M – modulation constellation size), yielding a vector of D detected subsymbols satisfying

25. E. Golovins UCT-COE Seminar26/07/2007 - 25 - Simulation results System configuration: System configuration: (total subcarriers), (detectable subcarriers), (total subcarriers), (detectable subcarriers), (CP length), QPSK, equi-powered subcarriers (CP length), QPSK, equi-powered subcarriers CLS channel estimation based on detected subsymbols Channel model: Channel model: 2-path uniform PDP with

26. E. Golovins UCT-COE Seminar26/07/2007 - 26 - MSE & BER performance

27. E. Golovins UCT-COE Seminar26/07/2007 - 27 - Problems to investigate Use a reduced-complexity suboptimal blind detection algorithm, e.g. V-BLAST, instead of computationally prohibitive exhaustive search Use a reduced-complexity suboptimal blind detection algorithm, e.g. V-BLAST, instead of computationally prohibitive exhaustive search Optimise D value to allow for fast operation and satisfactory performance Optimise D value to allow for fast operation and satisfactory performance Optimise transmit power distribution between the detectable subcarriers and others Optimise transmit power distribution between the detectable subcarriers and others Combine blind algorithm with optional time-domain interpolation to improve performance Combine blind algorithm with optional time-domain interpolation to improve performance Determine whether the blind receiver is more efficient than the pilot-assisted one Determine whether the blind receiver is more efficient than the pilot-assisted one

28. E. Golovins UCT-COE Seminar26/07/2007 - 28 - [1]E. Golovins, and N. Ventura. “Comparative analysis of low complexity channel estimation techniques for the pilot-assisted wireless OFDM systems,” in Proc. Southern African Telecommun. Networks and Applications Conf. (SATNAC), Sep. 2006. [2]E. Golovins, and N. Ventura. “Optimisation of the pilot-to-data power ratio in the MQAM-modulated OFDM systems with MMSE channel estimation,” to appear in Proc. Southern African Telecommun. Networks and Applications Conf. (SATNAC), Sep. 2007. [3]E. Golovins, and N. Ventura, “Design and performance analysis of low-complexity pilot-aided OFDM channel estimators,” in Proc. 6 th IEEE Intern. Workshop on Multi-Carrier and Spread Spectrum (MC-SS), May 2007. [4]E. Golovins, and N. Ventura, “Modified order-recursive least squares estimator for the noisy OFDM channels,” in Proc. 5 th IEEE Commun. and Netw. Services Research Conf. (CNSR), May 2007. [5]E. Golovins, and N. Ventura, “Low-complexity constrained LMMSE estimator for the sparse OFDM channels,” to appear in Proc. IEEE Africon 2007 Conf., Sep. 2007. Published work

29. E. Golovins UCT-COE Seminar26/07/2007 - 29 - Experimental OFDM model in Simulink

30. E. Golovins UCT-COE Seminar26/07/2007 - 30 - ….… egolovins@crg.ee.uct.ac.za