# Need information about following channel model

The following research paper is for blind channel equalization and the author has modeled the channel as 7 tap weights

https://ieeexplore.ieee.org/document/1096877

On page 3 it has shown the channel tap weights which they have used it. I want to know information about the channel? Is it the multipath fading channel or what kind of channel they are using? If somebody can help? and can I simulate the following channel in MATLAB,if yes then how?

The channel impulse response is given in figure below:

• Can you just post the information for your question directly? The link you gave requires a login to then get to the paper to see what you are asking. – Dan Boschen Oct 26 '18 at 22:52
• Here is the URL to download: link – Faizan Zaheer Oct 29 '18 at 4:31
• I also updated the post with channel impulse response – Faizan Zaheer Oct 29 '18 at 4:36

## 1 Answer

The channel impulse response represent the weighted gains and phases at different delays, so yes this is a multipath channel. You can simulate the channel (in Matlab as you requested, what I show below was done in Octave with compatible results) by first creating the complex channel weights:

channel = [c1, c2, c3, c4, c5, c6, c7];


where $$c1 = -.005 - j0.004$$, $$c2 = 0.009 + j0.030$$, etc

The following are examples of inspecting and using the channel:

filter

Use the filter command to determine the complex baseband received signal from the complex baseband transmitted signal (analytic signal):

rx = filter(channel, 7, tx)


Where rx is the received signal and tx is the transmitted signal. The denominator factor of 7 is somewhat arbitrary and is just a scaling.

freqz

Use the freqz command to plot the magnitude and phase frequency response of the channel.

freqz(channel)


The horizontal axis is normalized angular frequency from DC to $$2\pi$$ where $$2\pi$$ represents the sampling rate used. (So if the tx data was sampled at 1 MHz for example, the right side of the plot would be 1 MHz). Because it is a complex spectrum the full frequency range from DC to the sampling rate is unique as shown.

grpdelay

Use the grpdelay command to determine the group delay of the channel, which is the delay of the signal in time or in samples at each frequency. In the phase vs frequency plot above it appears the channel may be linear phase, however a group delay plot (group delay is $$d\phi/d\omega$$) would give us a better indication since it will remove the linear trend.

grpdelay(channel, 1, 512, 'whole');
xlabel('Normalized Frequency (rad/sample)')
ylabel('Delay (samples)')
title('Group Delay')


From the above results we see that the channel distortion is not significant or challenging both in magnitude (+/- a few dB) and group delay (+/- half a sample), in comparison to a highly frequency selective channel that would have deep nulls throughout the passband magnitude response. The delay distortion is more pronounced if a lower sampling rate is used, so depends on how many samples per symbol there are (The delay can be converted to seconds by dividing by the sampling rate).

See this post on implementing an LMS Equalizer to compensate for this channel in the receiver (using the Wiener-Hopf equations): Compensating Loudspeaker frequency response in an audio signal .

For "blind" equalization using this approach, I would use receiver decisions to recreate the expected transmitted signal (including any pulse shaping etc). I did not read your reference link but you could do that as a comparison if that wasn't the technique used directly. A comparison should include performance under lower SNRs.