How are BER and SNR Related for PSK and QAM?

Explains how to calculate the Bit Error Rate (BER) for BPSK and the Symbol Error Rate (SER) for QAM, and discusses the relationship between them.
Note that the SNR plotted on the horizontal axis of the figure, is the 'SNR per bit'. I have updated the Summary Sheet at iaincollings.com to make this clear. drive.google.com/file/d/1_3B-...
Related videos: (see: iaincollings.com)
• What is Gaussian Noise? • What is Gaussian Noise?
• What is Noise Power in Communication Systems? • What is Noise Power in...
• How are Bit Error Rate (BER) and Symbol Error Rate (SER) Related? • How are Bit Error Rate...
• How are sigma^2, SNR, and BER Related for the Matched Filter? • How are sigma^2, SNR, ...
• What is a p.d.f.? • What is a Probability ...
• What is SNR and Eb/No? • What are SNR and Eb/No?
• What is a Matched Filter? • What is a Matched Filter?
• What is Power Spectral Density (PSD)? • What is Power Spectral...
Full categorised list of all videos with Summary Sheets: iaincollings.com
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[@Timmay08TOTHELIMIT]

Prof Iain Collings is that you? Legend of a lecturer mate!

[@taniaguillot2580]

I just watched the 14 videos of this series and understand comms so much better now after 3 months of taking the subject and not knowing whats going on. I have the final exam in 2 weeks so thank you so much for the help!

[@iain_explains]

Glad the videos helped! Good luck in your exam.

[@fadilhabibidanufane9593]

Excellent explanation! For someone like me who's doing research on wireless communication with next to zero background in information theory, your videos are heaven's gifts. Can't wait to learn about more advanced concepts, perhaps polar codes or Non-orthogonal multiple access ;)

[@iain_explains]

Thanks. Glad the videos are helpful! I've added your two suggestions to my "to-do" list (which is getting quite long).

[@AbuSous2000PR]

The ending is amazing. Many thx Prof.

[@iain_explains]

Thanks. I'm glad yo liked it.

[@aetrew5499]

Thanks for the video, much appreciated.

[@iain_explains]

Glad it was helpful!

[@euqinuykcaj]

Hi, I'm going to enroll at next spring as a ECE graduate student, and I am appreciated for you channel which helps me a lot for picking up so many knowledge that I do not have. Thanks again!

[@iain_explains]

I'm so glad! Thanks for your comments. It's great to hear. Good luck with your future studies.

[@ana-rl1mw]

Great explanation, thanks prof. !

[@iain_explains]

You are welcome!

[@falguni.bonaparte]

Thanks Sir!

[@falcon-xm3uo]

Thanks for the excellent video series - very clear. Can you plz make a video on Signal to Quantization Noise Ratio (SQNR)? Thanks

[@iain_explains]

Thanks for the suggestion, I've added it to the "to do" list.

[@igorpetrov6683]

Excellent explanation !

[@iain_explains]

Glad you liked it!

[@mickey11324]

You are amazing. keep the great work ! thank you !

[@iain_explains]

Thanks. I'm glad you like the videos.

[@mattsymington487]

Does the BPSK graph represent what you’d see on a spectrum analyzer? Great video btw helped me learn a lot more about my job

[@iain_explains]

Spectrum analysers show you the "spectrum". ie. the signal in the frequency domain. Glad you liked the video. Perhaps this one will help to understand the frequency domain a bit more: "How are Data Rate and Bandwidth Related?" kzbin.info/www/bejne/kHO2p4CYhJWghrM

[@soumyaneogy9522]

Thanks for the excellent video . As always you made an awesome video and with utmost clarity . I had one question . I am unable to understand that while plotting the graph at 1:14 in your video why the gaussian noise is shifted with mean of +A . The gaussian noise must have a zero mean as you mentioned . So my question is about why the pdf is shifted by +A .

[@iain_explains]

It is the (conditional) probability density function for the output of the channel - not the p.d.f. of the noise. Check out this video for more insights (starting at the 9:06 mark): kzbin.info/www/bejne/jmPGe2usdshjg7c

[@youcefboukezzoula4479]

Good presentation

[@iain_explains]

Glad you think so!

[@MagicGirlsOnly]

Another banger!

[@iain_explains]

Glad you found it useful.

[@NathanBi]

Good video! Here is a question: At the time 8:31 in your video, you mentioned that BER for BPSK and QPSK are not the same. However, some text book say that the BER are the same for BPSK and QPSK. I wonder the intrinsic principle of this question.

[@iain_explains]

Great question. It's something that often confuses people. You've given me the idea that I should add this as a topic for a future video. To be precise, I didn't say that the BER are not the same. I said that the SER are not the same. There's a difference. In summary, a BPSK symbol exactly corresponds to a bit, so BER = SER for BPSK. But for QPSK, each symbol corresponds to 2 bits, and so the BER and SER are not the same. For QPSK, the SER is higher than the BER, since when you make symbol errors in QPSK, often only 1 of the 2 corresponding bits is in error.

[@stringstoparadise2392]

hello sir, @13:50 why in psk we need not to worry about the amplitude of the received waveform after all its the amplitude of the I/q components which is deciding the phase of the received symbol (like in qpsk I=SQRT(Eb/2), q=SQRT(Eb/2) ) where phase = arctan(q/i) Eb=Ac^2*T/2 which is depending upon the amplitude of the received signal

[@iain_explains]

I'm not sure exactly what you're asking, but yes of course you would like to have a system with a strong signal amplitude, so in that sense you "care" are it - but that's not what I meant. What I meant was that you can tolerate errors in the amplitude estimate and yet still detect the data correctly, because all of the data symbols have the same amplitude. This would not be possible if you were using a modulation format that encoded some of the data into the amplitude, such as in QAM, ASK, and APSK.

[@TheBartona]

Great Video! However, you define SNR as A^2/N_0. Shouldn't this be A^2/(N_0/2*BW) as N_0 is the noise power spectral density, not the noise power itself?

[@iain_explains]

Ah yes, this is a very common cause for confusion. I'm going to make a couple of videos to explain this in more detail, so keep a look out for them in the next week or so on the channel. The problem comes from the fact that bandwidth hasn't even been mentioned at all! Technically, non-band-limited white noise has infinite power, so if we are going to consider signals with finite energy, sent over infinite bandwidth channels, then the SNR would be zero. To get around this, many textbooks implicitly define SNR to be "Signal Power to Noise Power Spectral Density" (or in other words, noise power per unit bandwidth), but they often don't make this explicit, or try to explain it. Hopefully my upcoming videos on this topic will help.

[@nikhilv3231]

Hi Sir, could you make videos on How pulse shaping affects the wave form of a Phase modulated Signal(BPSK/QPSK). When there is no pulse shaping is present, the Envelope of the Signal happens to be Constant and only the phase is affected. But for the case when the message is shaped using any pulses other than ON_OFF keying (say a Raised Cosine Pulse), will the envelope of the Signal will still remain a constant.

[@iain_explains]

Good question. I've added it to my "to do" list. In short though, PSK does not need to have the same amplitude for the entire symbol period (ie. it can have pulse shaping applied, to reduce the bandwidth). The important thing is that all the symbols have the same magnitude at the output of the matched filter in the receiver - so that it is immune to nonlinearities in the receiver amplifier (ie. all symbols are affected to the same degree). There is a modulation scheme that has a constant modulus for the entire symbol period (CPM) but it requires a much more complex receiver.

[@georgepalafox5967]

Hi Professor! Excellent explanation. I now have a better understanding in regards to when it is better to use PSK vs QAM. Q: why do we care about 10^-6 or higher BER? It's one but effort every 1M or higher bits. Doesn't seem like something noticeable. Why not go with 10^-4 and and conserve EBNO? I guess perhaps a better question would be what applications require extremely low BER? Thanks.

[@iain_explains]

It's a great question. Most applications wouldn't be overly affected by 1 error in a million, but some would - for example, financial records transfer, etc. In any case, even 1 error in a million will cause the TCP layer to request a re-transfer of that frame.

[@eswnl1]

I wonder why this graph uses SER vs SNR and the other graph in the other video is BER vs Eb/No? Is it to do with SER and SNR being connected to bandwidth while the other graph isn’t?

[@iain_explains]

This video might help: "What are SNR and Eb/No?" kzbin.info/www/bejne/mH-8p4uoa9mtjrM

[@edwinr4378]

Thank u sir

[@iain_explains]

You're welcome.

[@balcofono666]

Could you cover APSK Vs QAM?

[@iain_explains]

Thanks for the suggestion, I've added it to my "to do" list.

[@tuongnguyen9391]

I have a question Does the receiver actually know the SNR. Recall that SNR is signal power over noise power. It is quite easy to measure to signal power given the appropriate apparatus but how can we measure noise power ?

[@iain_explains]

That's an excellent question. The noise power can be estimated from measuring the "received signal" when there is no signal being transmitted. The received signal power is only really able to be estimated by measuring the received signal when known training data is being transmitted, and averaging over many training symbols in order to "average out" the noise.

[@cr1901]

Is the SNR for 16-QAM worst-case, where you're choosing two symbols out of the constellation with the minimum amplitude 50% of the time? Or are you calculating SNR based on equal probability (1/16) for all symbols in the constellation? For instance, I see "PAM4 has an SNR 9.5dB worse than NRZ for an equivalent amplitude" in a number of references. But this calculation only works for unipolar PAM4, where you're only sending either 0 or A/3 50% of the time, compared to NRZ sending 0 or A 50% of the time: 10*log(A^2/2) - 10*log(A^2/18) = 10*log(9) = 9.54 Any other probability for symbols {0, A/3, 2A/3, A} (or different DC bias, for that matter) will give a different SNR reduction compared to NRZ {0, A} 50% of the time.

[@iain_explains]

SNR is the ratio of the power of the signal, divided by the power of the noise. So yes, the power of the signal is a function of the probabilities of each symbol in the constellation being sent. In general it is assumed that the data is sufficiently compressed (or random) such that each constellation point is equally likely.

[@SADEEM-ART]

4:14 This constellation diagram for QAM or QPSK?

[@iain_explains]

4-QAM is the same as QPSK.

[@lutzvonwangenheim9682]

hey lain @ 13:50 you have made a statement that we don't have to bother about amplitude in case of 16 psk why is it so . can you spread some light on this ? and why you have made the statement that 64 QAM is better in case of AWGN CHANNEL and why not in case of RAYLEIGH FADING whwere as in both cases amplitude is being affected

[@iain_explains]

All the symbols in PSK have the same amplitude, so all you need to do to detect them at the receiver, is to track the phase. You don't need an accurate estimate of the channel gain. For QAM, you need to estimate the channel gain accurately, since not all symbols have the same amplitude. And I think you're confusing the AWGN channel - it does not affect the gain - as the name indicates, it only adds noise.

[@lutzvonwangenheim9682]

@@iain_explains but its not like that even to make a correct estimate of the phase we need an correct estimate of I and Q component at the receiver which also requires a estimated correct gain of the channel to do so as phase is arctan(I/q)

[@iain_explains]

Yes, but that doesn't mean you need accurate estimates of I and Q. As long as I and Q are both "inaccurate in the same way" - which is what happens in non-linear amplifiers. In other words, you only need the _ratio_ of I and Q to be accurate.

[@DrDeuteron]

How does the algo know I am simulating q am and psk at work? My work computer and phone has no connection to me irl, for…reasons

[@mohammedbenlamlih8957]

Excellent explanation. Another lesson to learn from this video: PPT slides is NOT the best way to teach. White board is the way to go. Thanks again.

[@iain_explains]

Glad it was helpful! And yes, I made a decision back in 2018 when I started making these videos, that I wanted to focus on the ideas, and not on wiz-bang video production and animated graphics technologies, which quite often distract from the message. For example, I'm determined never to make a video where I'm writing on a glass wall 😉

[@mandarmoksha]

I wish you were my professor in my bachelor's and master's. Do nt mean to demean the great work but I feel there will b good response to donation/contribution if you setup one...

[@iain_explains]

Thanks for the suggestion. I'll give it some thought.

[@streetvendour1287]

Do anyone know how to calculate SER or is it the same as BER

[@iain_explains]

This video should help: "How are Bit Error Rate (BER) and Symbol Error Rate (SER) Related?" kzbin.info/www/bejne/mqaQpHiufrqJY7s and you might like to check out other videos on the channel, that are listed in categorised order here: iaincollings.com

[@gopalsolanki1519]

Shouldn’t SNR be A^2/(No/2). Noise variance I thought was No/2.

[@iain_explains]

Hopefully this video might help: "What is Noise Power in Communication Systems?" kzbin.info/www/bejne/laLRZYWwgteLeMU