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Does zero-forcing equalizer need known channel impulse response?

You need an estimate of the channel to receive the sequence but the zero-forcing equalizer does not need the channel response as an input. The zero forcing equalizer estimates the channel response. … In high-SNR the MMSE equalizer will converge to be the same as a zero-forcing equalizer, so has better performance over all conditions. …
Dan Boschen's user avatar
1 vote

LMS algorithm: Training and tracking phase

As a reference for the implementation of the LMS Equalizer, see Rappaport "Wireless Communications Principles and Practice" p. 376, with the further notations in my graphic below. … The bars over variables represent arrays of $M$ samples, which is the length of the equalizer filter. …
Dan Boschen's user avatar
1 vote

Fequency Domain Oversampling - decimating when going back to time domain

Multiplying by your equalizer in frequency is identical to convolving in time the original time domain waveform with the Fourier transform of your equalizer fucntion, and therefore will delay this waveform … With knowledge of the channel and specific equalizer function, the delay can be determined. …
Dan Boschen's user avatar
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Fractionally spaced equalizer - LMS algorithm

The switch between training and tracking would then have to change from a fractional spaced equalizer to a baud rate equalizer if implemented as shown. … (1D array like) num_taps: length of equalizer (positive integer) alpha: damping coefficient, typically < 0.01 (positive float) shift: number of samples to shift dominant equalizer tap to …
Dan Boschen's user avatar
1 vote
Accepted

Frequency-specific Delay?

Yes it does exist and these are called "all-pass" filters in that over the band of interest the magnitude does not change (other than a possible fixed gain at all frequencies) but modify the phase res …
Dan Boschen's user avatar
1 vote
Accepted

Equalization with FSK

The LMS equalizer would perform equally well for "non-linear" modulations such as FSK. This is because the modulation itself does not come into play. … We are using a linear equalizer to compensate for linear (multi-path) channel distortions. …
Dan Boschen's user avatar
3 votes
Accepted

Requirements on Signal Spectrum for Fractionally Spaced Equalization

As far as equalizer performance and possible limitations I provide two key points below about the span of the equalizer and the number of samples per symbol to use. … A linear equalizer will cause noise enhancement on these null locations leading to degraded performance (and a non-linear equalizer such as a decision feedback equalizer may be a better choice). …
Dan Boschen's user avatar
1 vote

Least Squares Solution Using the DFT vs Wiener-Hopf Equations

This is not a complete answer but a companion simulation to the other answers showing that the two approaches when used for a practical application are not identical as concluded in some of the other …
Dan Boschen's user avatar