What is a Constellation Diagram?
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- Опубліковано 4 жов 2024
- Explains the Constellation Diagram in Digital Communications and how it relates to real transmitted signals.
Note that the "average power" term at the bottom is actually the average energy (it would be the average power if I'd included at 1/T term). It's just a scaling of T between the two, so sometimes the final equation for the measured signal y_k is written with P's (Power) and sometimes with E's (Energy). Depending on which is put there, the variance of the noise term n_k is either N_0 (for the Power version) or N_0W (for the energy version). This video has more details: "What are SNR and Eb/No?" • What are SNR and Eb/No?
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For a non-engineer doing research about 5G and telecom, these videos have been a god-sent. Thank you so very much.
That's great to hear. I'm so glad you've found the videos to be helpful.
I am a RF Radio System Engineer in Ericsson. I like your radios and thanks for your sharing !!!!! Great explanation for every detailed sub aspects of the whole communication system!
Thanks for your nice comment. I'm glad you like the level of detail I put into the videos.
UA-cam algorithm is truly messed up. So much crap just floats on top with hundreds of thousands of views and golden channels like yours become hard to find. But I am so glad that i finally found it. I hope more people subscribe to you. BTW great video and explained really clearly,
Thanks for your comment. I'm glad you like the videos.
Cant agree more .
You make the hard stuff that blows our mind off as simple as drinking water
Thumbs up as usual 👍🏼🫡
That's great to hear. Glad you like the explanations.
Thank you, easy and concise, some things I just can’t understand from the textbook
Glad you found it helpful.
@@iain_explains 00he 00years were 0in to 00⁰000
Your video made me so clear to understand how QAM works! Thank you very much!!!
That's great. I'm glad you found the video helpful.
Great explanation but if you make all the topics and if you order the lectures in a playlist according to any standard textbook(proakis or haykin) it will be really helpful.
It sounds like you haven't discovered my web page yet. iaincollings.com
Very clear explanation, thank you so much!!!
Glad it was helpful!
Hungrily waiting for your videos on binary phase shift keying, code division multiple access cdma, binary offset carrier wave modulation
I've got this video on CDMA: "How does DS CDMA Work?" ua-cam.com/video/U_uOrrLBKz4/v-deo.html plus others comparing the standards, like this one: "Mobile Standards Evolution: FDMA, TDMA, CDMA, OFDMA" ua-cam.com/video/bm53RpK-S2k/v-deo.html Have you seen my webpage? I has all the videos listed in categories. iaincollings.com
Thanks! You are making a good video. And good explain and make complex things simple, accessible and understandable. It would be nice if there was a video about EVM and MER. And about the influence of various factors on the EVM (for example phase noise)
Thank s, I'm glad you like the videos. And thanks for the topic suggestions, I've added them to my "to do" list.
thank u sir
Great job!
Thanks. I'm glad you liked the video.
very helpful sir. Thank you.
Happy to help
Thank you so much mister, easy and clear 🤍🤍👏
You are very welcome. I'm glad you liked it.
Thank you for this video. What is the difference between a constellation diagram and an IQ plot? Best
The Constellation Diagram is plotted on an IQ plot. The output of the demodulator will be a trace on the IQ plot. If you only sample that trace at the symbol times, then you get the output constellation diagram.
Best Explanation Since my graduation.
Thanks.
@@iain_explains
Will you be doing any video on Maximum Likelihood Estimation?
Have you seen this video on my channel: "What are Maximum Likelihood (ML) and Maximum a posteriori (MAP)?" ua-cam.com/video/9Ahdh_8xAEI/v-deo.html
@@iain_explains
Yes I did. I bookmarked it and liked it too. Thankyou for great work and remarkable presentation style and insights.
great video..appreciated..
Glad you liked it
Greetings sir!
What a wonderful explanation!
Just curious as to why the normalization factor is square root of average power of all symbols and not just the average power?
Looking forward
Power = (voltage)^2 / resistance , and the constellation diagram is essentially showing voltage (normalised for a unit resistor).
Thank you !
You're welcome!
Just a correction (If i remeber it correctly!!!). It is φ not Θ since it is phase which in greek is φάση.
No, not true. I could have used any symbol I liked. It didn't even need to be a greek letter. I could have made up my own symbol. It is just a label. In any case I think it is better to focus on the content and understanding. That's much more important.
Thank you sir! I was reading that book of Goldsmith and felt like it was written in alien's language. You save me!
I'm glad the video helped. Have you seen my webpage with a full categorised listing of all the topics? iaincollings.com
I understand why @8:45 the integration is the same for all I but the amplitude is not so clear. For QAM vs 16 QAM would be: (18+18+18+18)=72 vs 4x(2+10+10+18)/16=10. I assumed the amp for QAM is (sqr (3^2+3^2)).
@Iain Explains Signals, Systems, and Digital Comms it would be great if you take a look at this question.
Thank you for explaining!
I have a question in 10:30. My english skill is not good so i don't understand the 'h' and 'root p' in equation.
Could you tell me more detail about that..?
The 'h' is the channel gain (which will be a complex number with magnitude between 0 and 1), and the "root p" is the square root of the transmit power.
Thank youuuu sooo much professor. Love you.
You are very welcome
damn finally a useful video, thanks !
Glad you found it helpful. If you're looking for other useful videos, you might like the others on my channel. You can find a categorised list here: iaincollings.com
Hello Sir, Please make a video on OQPSK and MSK !!
Thanks for the suggestion, I've added them to my "to do" list.
Thank You Iain, for making learning easier :)
Is this factor 'sqrt(p)' that you have used to normalize the X_k, is the average power of all possible symbols?
What is it mathematically?
Yes, p is the average power. To calculate it, you simply add up the powers of all the symbols and divide by the number of symbols. In the 16-QAM example shown, it is (1^2 + 2*(3^2+1^2)+(3^2+3^2))/4 ... you only need to work out the powers of the 4 symbols in the top right quadrant and divide by 4, since the constellation is symmetric ... and I've just used Pythagoras to calculate the powers of each constellation point.
Good day. I have a remark related to "terminology". Why do you speak about mean power of the costellation when you write the integral. A^2*T = E. It should be mean energy, isn't it?
Power and Energy are related by a constant, T (the time duration of the symbol), so it's just a simple scaling between the two.
For sure. I think wordplay happens because transmitting and receiving constellations should be considered separately and may even have different measured units. What do you think about it?
sir @ 7:04 whether it would be energy as we are transmitting the signal for only Tb duration and signal which we are sending is energy signal i think ??
anyhow a great video sir now i can visualize the waveforms thanks for this
Sorry, I'm not sure what you mean by "energy signal". But in any case, I'm glad you found the video helpful.
Sir Thank you for sharing the knowledge. I am from electrical background and I am now exploring digital communication. Can you please explain is it possible to plot constellation diagram for passband communication with out using filters as figure 6.8, page 359 ,fourth edition of Simon Haykin shows that we don't need filter to extract data?
I don't have the book handy, but I'm guessing you're referring to a correlation receiver with a mixer and a sampler. That's just a different way to implement the matched filter.
Okay Thank you Sir.@@iain_explains
so can we say The larger the SNR, the more constellation points can be used in a symbol ?
Yes, assuming you're wanting to keep the same bit error rate.
at 10:06 in your video you say "so this gives you a power of 1 " . [1] I did not understand this part . [2] how does that scaling of dividing by square root of average power is making the comparison across different constellation easy ?
There is always a limit on the transmit power (due to either government regulations or simple battery limitations in the device). To choose which modulation format to use, we need to make sure they are compared under the same power constraints. It is not acceptable to add more constellation points at the outside of a constellation (ie. to use a higher modulation order, and thus send more data per symbol) without scaling back all the points so that the overall average power remains the same.
The phase at 1:17 is 90 not 0 and at 1:23 it is 270 not 180 . Right?
Sorry, but the video is correct. cos(0) = 1. Also cos(2pi f t) is the Real part of e^(j 2pi f t), and so it is along the horizontal axis (theta = 0).
Sir, nice video, sir I have one doubt, constellation diagrams is used to demodulate the symbol?
The constellation diagram is used to visualise all the symbols. It shows where the decision boundaries could be placed in a demodulator to decide which symbol was sent.
Hi Iain, thanks for the nice video. One question: Are the carrier frequency fc and the symbol duration time T related to each other? Looking on the plot at 1:11 , I can see that fc equals to 2/T. So I guess in general we can pick fc as an integer multiple of 1/T. But is there any reason for doing so?
In general yes, the maths all works best when we pick fc as an integer multiple of 1/T, but in practice it's not necessary. In passband communications, the carrier frequency is so much higher than the bandwidth, that the fractional extra part of the "final" wavelength in the symbol has negligible effect compared to all the other "whole" wavelengths in the symbol (if you know what I mean).
@@iain_explains Thanks so much for the answer !
sir, can we plot a frequency variation signal's like MFSK using the constellation diagram?
like making the x axis for 'a' frequency and the y axis for the '2a' frequency ...... and how can we find the absolute value for the vector in this case?
Yes, that's right. Each symbol (frequency) in FSK is orthogonal to the others, so each constellation point can be represented by a point on an orthogonal vector (in a multi-dimensional space). Then it's just the same as for any other constellation diagram (except in higher dimensions). The decision boundaries are still equidistant between each neighbouring pair of points.
@@iain_explains
Ok, thank you.
I am bit confused in the part where average power is defined (around time 8:00). If value is integrated over time would not be an average energy (at least dimensionally)?
The term "average power" means "averaged over the different possible constellation points (transmission signals)" assuming that the data is equally likely 1's and 0's (ie. assuming that each constellation point is equally likely.)
@@iain_explains thanks for the reply but my doubt is not about the fact that we are "averaging" but rather on the quantity we are averaging. I see we are integrating over given time (the period) the square of signal value; so it looks to me we are averaging an energy rather than power. Could you please clarify to me this point? Thanks
Ah, sorry, I see now. Yes, I should have called it energy (sorry about that). It's just a scaling of T between the two, so sometimes the final equation is written with P's (Power) and sometimes with E's (Energy). Depending on which is put there, the variance of the noise term n_k is either N_0 (for the Power version) or N_0W (for the energy version). This video has more details: "What are SNR and Eb/No?" ua-cam.com/video/bNYvXr6tzXQ/v-deo.html
ECE 485, UofA.
could you please tell me, how the pulse shaping will come into the picture with constellation?
If you've seen my video on pulse shaping ("Pulse Shaping and Square Root Raised Cosine" ua-cam.com/video/Qe8NQx4ibE8/v-deo.html) then you'll know about pulse shaping of a single real-valued data sequence. Then this video on how to send complex baseband signals will show you how to extend to the complex-valued data sequence case: "How are Complex Baseband Digital Signals Transmitted?" ua-cam.com/video/0lkRJgnywkg/v-deo.html
I have doubt in constellation points. How it works?
See: "What is a Constellation Diagram?" ua-cam.com/video/kfJeL4LQ43s/v-deo.html
@@iain_explains ❤️ got it sir
sir can you please tell me the difference between the average power and transmitted power i mean i am not able to figure out the difference , are they same?
and secondly @10:07 what do you mean by unity power (Xk/sqrt(p'))= 1?
"Transmitted power" is the power at the output of the transmit amplifier that is connected to the UTP/Coax cable (for wireline channels), or as it goes into the antenna (for wireless), or laser (for optical channels). Typically the "average" value is quoted. "Instantaneous power" goes up and down at the carrier frequency, since it is defined as being the square of the voltage. If you want to compare two different modulation formats, you need to make sure you are doing a fair comparison, and so you scale the constellations (ie. the actual transmit waveforms) so that they have the same average power. The clearest way is to scale them to unity (ie. so the power equals 1).
@@iain_explains ok I got it now thankyou sir for looking into it
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