<< Chapter < Page Chapter >> Page >

To see what these figures mean, consider the eight plots contained in [link] and [link] . The first plot is the received signal, which containsthe transmitted signal corrupted by the sinusoidal interferer and the white noise. After the equalizer design,this received signal is passed through the equalizer, and the output is shown in the plot entitled“optimal equalizer output.” The equalizer transforms the data in the received signal into two horizontal stripes.Passing this through a simple sign device recovers the transmitted signal. Without the equalizer, the sign function would be applied directly to the receivedsignal, and the result would bear little relationship to the transmitted signal. The width of these stripes is related to the cluster variance. The difference between thesign of the output of the equalizer, and the transmitted data is shown in the plot labelled “decision device recovery error.”This is zero, indicating that the equalizer has done its job. The plot entitled “combined channel and optimal equalizer impulseresponse” shows the convolution of the impulse response of the channel with the impulse response of the equalizer.If the design was perfect and there was no interference present, one tap of thiscombination would be unity and all the rest would be zero. In this case, the actual design is close to this ideal.

The plots in [link] show the same situation, but in the frequency domain. The zeros of the channel aredepicted in the plot in the upper left. This constellation of zeros corresponds tothe darkest of the frequency responses drawn in the second plot. The T -spaced equalizer, accordingly, has a primarily highpass character, as can be seenfrom the dashed frequency response in the upper right plot of [link] . Combining these two gives the response in the middle.This middle response (plotted with the solid line) is mostly flat, except for a largedip at 1 . 4 radians. This is exactly the frequency of the sinusoidal interferer, and this demonstrates the second majoruse of the equalizer; it is capable of removing uncorrelated interferences.Observe that the equalizer design is given no knowledge of the frequency of the interference, nor even thatany interference exists. Nonetheless, it automatically compensates for the narrow band interference by buildinga notch at the offending frequency. The plot labelled“channel-optimum equalizer combination zeros” shows the zeros of the convolution of the impulse response of thechannel and the impulse response of the optimal equalizer. Were the ring of zeros at a uniform distance from the unitcircle, then the magnitude of the frequency response would be nearly flat.But observe that one pair of zeros (at ± 1 . 4 radians) is considerably closer to the circle than all the others. Since the magnitude ofthe frequency response is the product of the distances from the zeros to the unit circle,this distance becomes small where the zero comes close. This causes the notch. If this kind of argument relating the zeros of the transfer function to the frequency response ofthe system seems unfamiliar, see Appendix [link] .

Get Jobilize Job Search Mobile App in your pocket Now!

Get it on Google Play Download on the App Store Now




Source:  OpenStax, Software receiver design. OpenStax CNX. Aug 13, 2013 Download for free at http://cnx.org/content/col11510/1.3
Google Play and the Google Play logo are trademarks of Google Inc.

Notification Switch

Would you like to follow the 'Software receiver design' conversation and receive update notifications?

Ask