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Equalization in a wideband TDMA system

Equalization in a wideband TDMA system. Three basic equalization methods Linear equalization (LE) Decision feedback equalization (DFE) Sequence estimation (MLSE-VA) Example of channel estimation circuit. DAG: Ville Kuvaja Koki Sugawara. What is ment by equalization in a TDMA system?.

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Equalization in a wideband TDMA system

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  1. Equalization in a wideband TDMA system • Three basic equalization methods • Linear equalization (LE) • Decision feedback equalization (DFE) • Sequence estimation (MLSE-VA) • Example of channel estimation circuit DAG: Ville Kuvaja Koki Sugawara

  2. What is ment by equalization in a TDMA system? To remove ISI due to multipaths Short training sequence  quick adjustment

  3. Three basic equalization methods (1) Linear equalization (LE): Performance is not very good when the frequency response of the frequency selective channel contains deep fades. Zero-forcing algorithm aims to eliminate the intersymbol interference (ISI) at decision time instants (i.e. at the center of the bit/symbol interval). Least-mean-square (LMS) algorithmwill be investigated in greater detail in this presentation. Recursive least-squares (RLS) algorithm offers faster convergence, but is computationally more complex than LMS (since matrix inversion is required).

  4. 0 fs = 1/T f Linear equalization, zero-forcing algorithm Basic idea: Raised cosine spectrum Transmitted symbol spectrum Channel frequency response (incl. T & R filters) Equalizer frequency response =

  5. Zero-Forcing Equalization Zero ISI at the receiver output B(f)H(f)E(f)=Z(f) Z(f): Nyquist spectrum e.g. raised cosine Received signal T T T  Estimate of symbol tap coefficients for equalizer E

  6. Least-mean-square (LMS) algorithm (simplification of “method of steepest descent”) for convergence towards minimum mean square error (MMSE) Real part of n:th coefficient: Imaginary part of n:th coefficient: Phase: Iteration index Step size of iteration equations

  7. LMS algorithm (cont.) After some calculation, the recursion equations are obtained in the form

  8. LMS and RLS Algorithm Minimize square error RLS uses accumulated square error of the past New coefficients at (k+1) step LMS: RLS: (stepsize 0<Δ<1)

  9. Effect of iteration step size  smaller larger  Slow acquisition Poor stability Poor tracking performance Large variation around optimum value Convergence condition 0<<2/max : eigenvalue of autocorrelation matrix of r

  10. Conventional linear equalizer of LMS type Widrow Received complex signal samples Transversal FIR filter with 2M +1 filter taps LMS algorithm for adjustment of tap coefficients T T T +  Complex-valued tap coefficients of equalizer filter Estimate of k:th symbol after symbol decision

  11. Three basic equalization methods (2) Decision feedback equalization (DFE): Performance better than LE, due to ISI cancellation of tails of previously received symbols. Decision feedback equalizer structure: Feed-back filter (FBF) Input Output Feed-forward filter (FFF) + + Symbol decision Adjustment of filter coefficients

  12. Decision feedback equalizer T T + FBF  + T T T LMS algorithm for tap coefficient adjustment FFF 

  13. Again a transversal equalizer Replicates received signal from estimated symbols Estimated symbols Filter length = CIR length T T T LMS algorithm  + k:th sample of received signal Estimated channel coefficients Channel estimation circuit Proakis, Ed.3, Section 11-3

  14. Training Sequence & Decision Directed Mode training (known) sequence weight setup decision directed mode adaptation T T T bk Weight update  +

  15. How should the length of training sequence be? At least the number of taps in the transversal filter (equalizer) all the registers are filled with data sequence the effect of each delayed component is considered at least once

  16. How does a system adapt? T T T + 

  17. Three basic equalization methods (3) Maximum Likelihood Sequence Estimation using the Viterbi Algorithm (MLSE-VA): Best performance. Operation of the Viterbi algorithm can be visualized by means of a trellis diagram with mL states, where m is the symbol alphabet size and L is the length of the overall channel impulse response (in symbol intervals). State trellis diagram Allowed transition between states State Sample time instants

  18. MLSE-VA Consider the ML of estimated symbol sequence The probability that the received signal is yk under certain symbol estimates in the past under certain channel estimate Extension to N signal sequence

  19. MLSE-VA (cont.) p goes to maximum when is minimized. Transversal filter (again!) Matched filter NW filter MLSE (VA) Channel estimation circuit

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