Adaptive linear equalizer

Adaptive linear equalizer

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  ADAPTIVE LINEAR EQUALIZER By R.SOPHIA JEANNE [email protected]
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  What is adaptivelinear equalization? The equalizers are designed to be adjustable to the channel response and for time variant channels to be adaptive to the time variations in the channel response . Typically employed in high-speed communication systems, which do not use differential modulation schemes or frequency division multiplexing
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  Cont… The equalizer isthe most expensive component of a data demodulator and can consume over 80% of the total computations needed to demodulate a given signal Adaptive equalizers compensate for signal distortion attributed to inter-symbol interference (ISI), which is caused by multipath within time-dispersive channels
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  Time nature ofadaptive linear equalizer Adaptive filter assumes that the channel is time variant and tries to design an equalizer filter whose coefficients are also time variant according to the change of the channel and also try to eliminate ISI and additive noise at each time . The implicit assumption of adaptive equalizer is that the channel is varying slowly.
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  Linear vs. non-linearequalizer techniques Two general categories linear nonlinear equalization Linear: No feedback path to adapt the equalizer , the equalization is linear. Non linear fed back to change the subsequent outputs of the equalizer the equalization is non-linear.
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  Types of linearequalizers Zero-forcing: Designs E(z) so that the ISI is totally removed Minimum mean square error: designs E(z) to minimize mean square error MSE = 𝑘 𝜀2 𝑘 = 𝑘(𝑐 𝑘 − 𝑐(𝑘))2
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  Basic idea: zeroforcing equalizer Raised cosine spectrum Transmitted symbol spectrum Channel frequency response (incl. T & R filters) Equalizer frequency response =        Z f B f H f E f 0 ffs = 1/T  B f  H f  E f  Z f
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  Zero forcing equalizer
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  The overall responseat the detector input must satisfy Nyquist’s criterion for no ISI Zero-Forcing Equalizer
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  Cont…. • Suppose thereceived pulse in a PAM system is p(t), which suffers ISI • This signal is sampled at times t=nT to give a digital signal pn=p(nT) • We wish to design a digital filter HE(z) which operates on pn to eliminate ISI • Zero ISI implies that the filter output is only non-zero in response to pulse n at sample instant n, i.e. the filter output is the unit pulse dn in response to pn
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  MMSE equalizer
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  Basic idea: MMSEEQUALIZER The aim is to minimise 2 kJ E e ˆ ˆ k k k k ke z b b z  (or depending on source EqualizerChannel kz ˆ kb ke  r k s k + Estimate of k:th symbol Input to decision circuit  z k  ˆb k Error
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  Cont…. MMSE formulation HE(z) xn yn an -E[(.)2] For a ‘fixed’ equaliser E[(.)2] is minimised by adjusting the coefficients of HE(z). Effectively we have a trade off between noise enhancement and ISI.
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  Cont…. The solution hasthe form, o E NzP zH   )( 1 )( – equaliser needs knowledge of the noise PSD – If No=0, the solution is the same as the ZFE – When noise is present the ZFE solution is modified to make a trade-off between ISI and noise amplification Where P(z) is the Z transform of the channel pulse response and No is the noise
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  Advantages and disadvantagesof adaptive linear equalizer Advantages: Optimal approximation for the Channel- once calculated it could feed the Equalizer taps. Disadvantges: Heavy processing( due to matrix inversion which itself is a challenge) Not adaptive ( calculated periodically which is not good for varying channels)
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  Applications of adaptiveequalizer Noise cancellation Hands- free earphones Aircraft headphones