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Zero-forcing equalizer
open-in-new
<h2 id="algorithm">Algorithm</h2> <p>If the channel response (or <a href="/facts/Transfer_function/slDsh1lH">channel transfer function</a>) for a particular channel is H(s) then the input signal is multiplied by the <a href="/facts/Multiplicative_inverse/yczdYyCw">reciprocal</a> of it. This is intended to remove the effect of channel from the received signal, in particular the <a href="/facts/Intersymbol_interference/6oGRSogt">intersymbol interference</a> (ISI). </p><p>The zero-forcing equalizer removes all ISI, and is ideal when the channel is noiseless. However, when the channel is noisy, the zero-forcing equalizer will amplify the noise greatly at frequencies <i>f</i> where the channel response H(j2π<i>f</i>) has a small magnitude (i.e. near zeroes of the channel) in the attempt to invert the channel completely. A more balanced linear equalizer in this case is the <a href="/facts/Minimum_mean-square_error/hI2lqEMh">minimum mean-square error</a> equalizer, which does not usually eliminate ISI completely but instead minimizes the total power of the noise and ISI components in the output. </p> <h2 id="references">References</h2> <ol> <li id="fn:1"><p>Jon Mark and Weihua Zhuang (2003). "Ch. 4". Wireless Communications and Networking. Prentice Hall. p. 139. ISBN 0-13-040905-7. <a href="0-13-040905-7" target="_blank">0-13-040905-7</a> <a href="#fnref:1" class="footnote-back-ref">↩</a></p></li> <li id="fn:2"><p>Jon Mark and Weihua Zhuang (2003). "Ch. 4". Wireless Communications and Networking. Prentice Hall. p. 143. ISBN 0-13-040905-7. <a href="0-13-040905-7" target="_blank">0-13-040905-7</a> <a href="#fnref:2" class="footnote-back-ref">↩</a></p></li> </ol>