How are Matched Filter (MF), Zero Forcing (ZF), and MMSE Related?

Iain Explains Signals, Systems, and Digital Comms

Подписаться 62 тыс.

Просмотров 15 тыс.

50% 1

Explains the relationships between the Matched Filter (MF), the Zero Forcing (ZF) receiver, and the Minimum Mean Square Error (MMSE) Receivers, using a digital communications example.
For the introductory material leading into this video (on the left hand side of the screen) see the following two videos:
• How are Channel Inversion and the Matched Filter Related? • How are Channel Invers...
• Signal Model for MIMO and CDMA • Signal Model for MIMO ...
* Note that I made a "typo" at the 10:45 mark, where I had a brain fade and said that (AB)^(-1) equaled B^(-1) x A^(-1) ... of course this would be true if they were transposes, instead of -1 powers. Anyway, it's not a big deal, since the end result was the same: namely that the scenario in question converged to the Zero Forcing solution. I've fixed it up in this summary sheet: drive.google.com/file/d/1vxOn...
The equations in this video are given in the following paper, and the references therein: M.R. McKay, I.B. Collings and A.M. Tulino, "Achievable Sum Rate of MIMO MMSE Receivers: A General Analytic Framework", IEEE Trans. Information Theory, Vol. 57, No. 11, pp. 396-410, January 2010.
Other Related videos: (see: iaincollings.com)
• What is a Matched Filter? • What is a Matched Filter?
• What is Pulse Shaping and the Square Root Raised Cosine? • Pulse Shaping and Squa...
• What is White Gaussian Noise (WGN)? • What is White Gaussian...
• How are sigma^2, SNR, and BER Related for the Matched Filter? • How are sigma^2, SNR, ...
• How are Correlation and Convolution Related in Digital Communications? • How are Correlation an...
• Viterbi Algorithm Explained with an Example • Viterbi Algorithm Expl...
• What is Rayleigh Fading? • What is Rayleigh Fading?
• Convolution Square with Rectangle • Convolution of Square ...
Full categorised listing of videos with PDF Summary Sheets: iaincollings.com
.

Опубликовано:

12 мар 2021

Ссылка:

Скачать:

Готовим ссылку...

Добавить в:

Мой плейлист

Посмотреть позже

Комментарии : 34

@linfangwang6724 2 года назад

I am preparing the internship interviews and I found these videos are fabulous and very suitable for reviewing .

@iain_explains 2 года назад

I'm glad to hear that the videos have been helpful. That's great. Good luck with your interviews!

@zhou6486 2 года назад

Thanks again. You are the mentor who knows what students are confused with wireless topics. Thanks, thanks, thanks.

@iain_explains 2 года назад

You are most welcome. Glad you are finding the videos helpful.

@jaypatel3233 3 года назад

Perfect explanation ! Kudos !

@iain_explains 3 года назад

Thanks. Glad you liked it.

@khaledalsoufy4075 3 года назад

great video, Thank you for your time a lot! Sir how can I compute the complexity of MF, ZF, MMSE?

@medad5413 3 года назад

Thank you!

@ravindratomar9916 2 года назад

Dear prof. how to do MRC for SIMO system when noise is correlated across the antennas.

@bobbaberson3654 2 года назад

Hi Iain, would be great if you add your usual practical wisdom at the end of this recording regarding the actual situations where these approaches are useful. Do we need rich multipath to use ZF? Or if MF is not great in dense networks (due to interference)...

@iain_explains 2 года назад

Thanks for the suggestion. I'll have to watch my video again, to remember what I said. I thought I had given that sort of intuition - but maybe that was in another of my videos. I've made 180 now, so some of them are starting to merge in my memory. In any case, in answer to your question - yes that's right: ZF needs to be able to invert the channel (needs rich multipath), and MF maximises the SNR without doing anything specific to avoid interference, so doesn't work too well in interference-limited channels.

@bobbaberson3654 2 года назад

@@iain_explains I think you are right. In the video "What is Multi-User MIMO Communications (MU MIMO)?" you mentioned that we need rich multipath for H to be invertible. But I didn't really connect that point to the ZF.

@iceinmylean3947 Год назад

Thanks for the Video! I have a question regarding zero forcing. I learned zero forcing as a precoding technique, but as I understand it that would imply that the noise is added afterwards and not affected by the channel inverse. In the video, you also applied the channel inverse to the noise, why is that?

@iain_explains Год назад

The term "zero forcing" refers to the cost function used to generate the filter. It "forces" zeros where there are poles in the system (as opposed to other cost functions, such as maximising the SNR, or maximising the Likelihood, etc). It can be used for either pre-filtering (often called "precoding") or as a receiver filter. This video might help: "How are Matched Filter (MF), Zero Forcing (ZF), and MMSE Related?" ru-vid.com/video/%D0%B2%D0%B8%D0%B4%D0%B5%D0%BE-U3qjVgX2poM.html

@CuongPhamQ 2 года назад

Dear Prof! Is H dagger equivalent to "pseudo-inverse" of H?

@iain_explains 2 года назад

No, it's the conjugate transpose.

@austinbristow5716 2 года назад

Where did the scaling factor sqrt(N_t/p) come from?

@iain_explains 2 года назад

Sorry, it's a while since I looked at the details of this. Intuitively, the power P is divided evenly amongst the transmit antennas, hence the P/N_t term (or its inverse in the filter), and the square root is because the filter is dealing with the signal, and you need to square it to get the power. The equations are in the following paper, and the references therein: M.R. McKay, I.B. Collings and A.M. Tulino, "Achievable Sum Rate of MIMO MMSE Receivers: A General Analytic Framework", IEEE Trans. Information Theory, Vol. 57, No. 11, pp. 396-410, January 2010.

@alfredogonzalez9677 11 месяцев назад

So then in the earlier video "How is Data Received?" Are all these candidates for the Matched Filter block? And the decision is dependent on the implementation ?

@iain_explains 11 месяцев назад

It's a great question. The short answer is: No. The MF block in the other video you mentioned is an analog filter, matched to the (analog) waveform of the modulation signal. The MF, ZF and MMSE filters in this video are digital filters, operating at the digital baseband.

@alalolol9949 2 года назад

Could you pls provide a detailed explaination on why ZF causes noise amplification , while MMSE not?

@iain_explains 2 года назад

If any of the eigenvalues of H are zero, then H cannot be inverted, and the ZF receiver is not defined. If the eigenvalues are very small (but not zero) then the inverse of H will have very big elements, and then the noise that goes through that inverse matrix (filter) will be amplified greatly. By adding a scaled identity matrix into the mix in MMSE, you will ensure that the smallest eigen value of (HH^(-1)+alpha I ) won't be too small, and you will always be able to invert it without getting huge values.

@alalolol9949 2 года назад

@@iain_explains thank you so much~

@pitmaler4439 5 месяцев назад

Speaking about MMSE,.the criterion to minimize is always: argmin IIy-wxII^2 ...(as scalar or vectors)...So we want to find the weight w. Why isn't it a valid solution to set y=wx to get w=y/x > so I would always get the error zero - what am I missing here? Thank you very much.

@iain_explains 5 месяцев назад

You don't get to "set y=wx". y is the measurement vector. It includes noise, so it is never going to be exactly a linear transform of x. The challenge is to find a "w" that makes wx as close to y as possible.

@tuongnguyen9391 3 года назад

I am sorry but what would be the main difference between these filter technique and equalizer technique... ?

@iain_explains 3 года назад

That's a good question. I'm planning a video on equalisation, so I'll try to remember to mention it. In any case, the difference is that equalisation refers to "undoing" the effect of inter-symbol interference (ISI), which is due to the time-dispersion of the channel. It's sometimes referred to as "self interference". In contrast, this video only considered the case where there isn't any time dispersion at the symbol rate (typical of flat fading channels, or narrow band communications, or subcarrier channels in OFDM).