How are Channel Inversion and the Matched Filter (MF) Related?

Explains how Channel Inversion and the Matched Filter (MF) are related in digital communications.
Related videos: (see iaincollings.com)
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Full categorised listing of videos with PDF Summary Sheets: iaincollings.com
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[@amalgeevarghese6867]

Thanks a lot Iain! This channel is such a gem for Communication & Signal Processing engineers!

[@iain_explains]

Glad you like them!

[@明简-z9w]

Dear professor, I'd like to ask a question. In the case of inversion, you said when h near to zero (less than 1) then the noise will become larger, so we use MF method, although the noise will not increase, h* multiple h will let the signal become smaller when h

[@iain_explains]

Yes, when h

[@linn8007]

Every time I want to learn about some knowledge points, I find related videos in ur channel. Thank u soooo much sir

[@iain_explains]

I'm so glad to hear it. That's what I'm aiming for. A collection of videos that answer people's questions, before they know they're going to ask them.

[@linn8007]

@@iain_explains Sir you are doing a great job. thank you.

[@ayaelmai7677]

Dear Professor, Thank you for your videos, they really help so much. I have a small question about the matched filter. In a previous video introducing the matched filter you mentioned that the impulse response of the matched filter was similar to the one at the transmit filter. However here you multiplied by the conjugate of the channel. This had me slightly confused. Could you please clarify ? Thank you again for your amazing videos!!!

[@iain_explains]

Great question. It's often overlooked. The Matched Filter is "matched" to whatever came before it in the transmission "chain". More specifically, in linear transmission systems, it is "matched" to the convolution of the transmit filter and the channel "filter". In the case of the previous video you refer to, I was considering the case where the channel was AWGN, which is flat across the band - and therefore didn't have any "filtering" action. In the case of this CI-MF video, it is dealing with non-flat channels, and also it is considering the digital signal, after it has come out of the detector (where the "transmitter matching" took place).

[@CuongPhamQ]

I have the feeling that I am returning to university. Amazing Professor

[@iain_explains]

I hope it's a good feeling. 😁

[@tianyuez]

Dear Professor, thanks for your video as always. May I ask one question, in this video, the channel h is multiplied with the input x, but in another video of yours "What is a Matched Filter", the "transmitter filter" s(t) is convolved with the input x(t). So why sometimes we use multiplication and other times we use convolution? Is this have anything to do with the channel delay spread, i.e., if the delay spread is large, we use convolution, if it is small, we use multiplication? And if I take this question one step further, is multiplication a special case of convolution mathematically? Many thanks!

[@iain_explains]

Yes, exactly. The channel acts as a linear filter in most communication systems (wireless, DSL twisted pair, coax, PCB track, ...), and so the operation is a convolution. But if the delay spread is shorter than a symbol period, then the convolution reduces to just a multiplication (only one "tap" in the filter).

[@tianyuez]

@@iain_explains Thank you very much for your reply! Now I understand the concept more clearly.

[@iain_explains]

Great. 😁

[@salvatorecardamone7717]

These videos really are a fantastic resource -- thanks a lot, Iain! Great stuff!

[@iain_explains]

Thanks for your comment. Glad you like them!

[@sankMRT]

Thank you very much for the clarification. One quick question is, how can we compare h*/|h| equalization with what you have discussed here. If the noise is complex Gaussian, multiplying with h*/|h| will not have any impact on the statistical properties of the noise distribution. However, x will be linearly-scaled within the signal direction (fading). Kindly let me know your thoughts.

[@iain_explains]

Yes, in this scalar case, it is just a rotation and scaling, so both the signal and the noise are rotated and scaled equally. The difference comes when there is structure in the noise. This happens, for example, when there is interference from other users, or other spatial channels in the case of MIMO. I've got a video coming up on the channel on this.

[@sankMRT]

@@iain_explains Thank you very much. If I understand you correctly, you are referring to the colored noise case right? I am looking forward to that video.

[@bobbaberson3654]

Thanks for the nice video. It is not very clear why h*h maximizes the SNR. The inversion is very clear however I can't visualize why the complex conjugate multiplication helps.

[@iain_explains]

Perhaps this video will help: "What is a Matched Filter?" kzbin.info/www/bejne/eZqQdp2fgq-iaas

[@malini50]

Hi Iain. When you say y = hx + n I presume it is fading channel and hence the presence of h?

[@iain_explains]

It doesn't need to be fading. All channels attenuate the signal (UTP, Coax, Fibre, Wireless, ...)

[@tianyuez]

Dear Professor, may I ask a slightly unrelated question about radar? To the best of my knowledge, matched filtering can be also applied to radar: since the "channel" h is supposed to be estimataed (ranging reflectors in the space), we convolve the reflected signal y with the transmitted signal x*. But the question is I cannot make an analogy in terms of inversion, i.e., I've never seen people "invert" the transmitted signal and convolve it with the reflected signal to estimate the channel h. Is it possible for you to shed some light on why the difference? Many thanks!

[@iain_explains]

It depends on the aim. In radar, the aim is to locate and identify targets. The targets are essentially parameters in the overall "channel". So radar is not trying to "invert" (or remove/cancel) the channel. This is different to data communications, where the aim is to extract the transmitted signal from the received signal, and in this case it is helpful to "invert" (or remove/cancel) the channel.

[@tianyuez]

@@iain_explains Dear Professor, thanks a lot for your reply, But that's not what I asked. For radar: we want to get the channel h, can we "invert" the transmitted signal x (instead of inverting h as in your reply)? Though I think it's possible mathematically, I've never seen people do this. Thanks again!

[@iain_explains]

Well, yes, that's basically what's being done in many/most channel estimation schemes. For example when using Least Squares to estimate channel parameters. See the following video. The example at the top right of the page shows an equivalent case, where the "data" corresponds to the d values, and the "channel" corresponds to the beta values. "What is Least Squares Estimation?" kzbin.info/www/bejne/eIuch5-jotqiqq8

[@tianyuez]

@@iain_explains Thanks again, professor! The pseudo-inverse, yeah!😁😄

[@badalsoren2947]

sir, in case of matched filter case when the complex conjugate is multiplied it says that the constillation is moved to the other location what does it actually means other location its not clear

[@iain_explains]

It means that the complex coefficient of the received waveform will be +/-conj(h)h rather than +/-1 (in this binary case).

[@ngolisaoran8166]

nice video

[@tuongnguyen9391]

So there will be Zero Forcing in the future :)

[@iain_explains]

Well spotted :-) It'll be on the channel on Sunday.