Low-Complexity Channel Estimation for Wireless OFDM Systems

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. Outline -- Introduction -- Radio channel model -- Pilot-assisted OFDM system -- Blind OFDM system

3. Introduction • 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 • Channel estimator must satisfy 3 requirements: • rely on the least possible training overhead • achieve performance close to optimal • be of the least possible computational complexity

4. Baseband OFDM system

5. Channel model • 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 : -- 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. Channel frequency response (CFR) • Example of CFR of the considered fading channel : (max. delay spread) (RMS delay spread) (max. Doppler freq.)

7. Block of N subsymbols CP Last Ncpsub- symbols repeated Ncsub- symbols Frequency-domain block processing • Nd data subsymbols are transmitted in block of Nd+P+Ncpsubsymbols, with P pilot subsymbols and a cyclic prefix of length NcpL - 1 (L = expected CIR length) • Receiver processes blocks in frequency domain by taking FFT of each received block • Typically the size of the processing block N = Nd+P is 5 to 10 times Ncp OFDM time-frequency grid Temporal block structure Frequency (subcarriers) N Time (OFDM symbols / blocks)

8. Pilot-assisted system • 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 • Interpolation of pilots in frequency is performed to get CFR estimate in the full band Pilot subcarrier Data subcarrier Frequency (subcarriers) N Time (OFDM symbols)

9. Design definition of the constrained estimator • Anticipated CIR length • Number of pilot subcarriers • 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. 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 : • For the equipowered ( ) and equispaced ( , ) pilot subcarriers (optimal training structure) we have:

11. Flow chart of the CLS scheme

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

13. Low-complexity CMMSE design-form • Applying the matrix inversion identities, one can show that • For the equipowered and equispaced pilot subcarriers:

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 • 2 practical approaches are possible: • robust mode, when (similar to the CLS scheme) • recursive mode (dynamic estimation of and )

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. Recursive CMMSE estimator (cont.) • Let then • For the equipowered and equispaced pilot subcarriers:

17. Flow chart of the recursive CMMSE • Initial settings: • During the initialisation period, until the reliable estimate of is obtained, estimator operates in the robust mode (as CLS), i.e.

18. Optimisation of pilots • 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. Theoretical/simulation results • System configuration: (subcarriers), (pilots), (CP length), 16QAM Average PDR set to optimal calculated for • Channel model: (modelled CIR length), (modelled Doppler spread)

20. MSE & BER performance (case 1) Channel – non-sample-spaced: 2-path UPDP,

21. MSE performance (case 2) Channel – sample-spaced: Exponential PDP,

22. Impact of the number of pilot subcarriers on the system performance Channel – sample-spaced: Exponential PDP,

23. Dependence of SNR gain at equaliser’s output on PDR CMMSE estimator used Channel – non-sample-spaced: 2-path UPDP,

24. Blind system • Minimises training overhead to just one pilot subcarrier (reference phase acquisition) • 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 • The optimal data detection involves an exhaustive search across the lattice of MD points (M – modulation constellation size), yielding a vector of D detected subsymbols satisfying

25. Simulation results • System configuration: (total subcarriers), (detectable subcarriers), (CP length), QPSK, equi-powered subcarriers CLS channel estimation based on detected subsymbols • Channel model: 2-path uniform PDP with

26. MSE & BER performance

27. Problems to investigate • 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 transmit power distribution between the detectable subcarriers and others • Combine blind algorithm with optional time-domain interpolation to improve performance • Determine whether the blind receiver is more efficient than the pilot-assisted one

28. Published work [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. 6th 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. 5th 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.

29. Experimental OFDM model in Simulink

30. ….… egolovins@crg.ee.uct.ac.za