Bit error probability

[sonaiko]

I have been going through some graphs, and I have a question about the graphs that shows the Error vs Eb/No.

Now Eb is Energy per bit.
Error is number of errors.
What is No? is it the Gaussian white noise of zero mean?
Why the Eb/No axis is measured in dB? what is the reference here?

for example the error probability graph for the NRZ digital data looks like a low pass filter graph. But somehow I just cannot understand it very well. Does that mean if my bit has more energy there is less probability to have an error? why? (a pic is shown).
so No is constant?

Does this graph give me any information about the bit rate? like if I have a faster bit rate ill have more error?

 

[Pommie]

That graph appears to show that the louder you shout the fewer errors you will have.

 

[philba]

Actually, the x axis is SNR (signal to noise ratio), not signal. This should be intuitive. The stronger your signal is with respect to the noise, the lower the error rate.

Think about having a conversation on a busy street vs in a quiet room. Clearly the quiet room makes the words easier to understand and you get fewer errors. On the noisy street, you have to raise your voice to be heard properly. You have thus increased your SNR and decreased the error rate.

 

[Willbe]

Does this graph give me any information about the bit rate?

I'd say no, which implies that the bit error prob. is independent of the bit rate and only dependent on the S/N ratio.

 

[sonaiko]

Actually, the x axis is SNR (signal to noise ratio), not signal. This should be intuitive. The stronger your signal is with respect to the noise, the lower the error rate.

Think about having a conversation on a busy street vs in a quiet room. Clearly the quiet room makes the words easier to understand and you get fewer errors. On the noisy street, you have to raise your voice to be heard properly. You have thus increased your SNR and decreased the error rate.

Ok this explanation makes it sound easy. But..
How do I calculate No? I mean, if I am generating my digital signal, and I want to calculate the energy Eb, I just integrate my bit over the interval. But how would I know my No so then I would know on which point im standing on the x-axis?

Also why dB? what is the reference here?

 

[Mikebits]

You to need to compute your system noise figure.

**broken link removed**

 

[goonsvondoom]

Bit Rate and BER

The graph only addresses the relationship between SNR and BER, apparently without regards to factors such as frequency of carrier, type of modulation, bit rate, signal strength with regards to parameters of the Tx and Rx, BER mitigating factors such as forward error correction (FEC) algorithms, modulation error ratio and/ or error vector magnitude, etc. For instance, all things being equal, a QAM16 modulation scheme uses four constellation points in each quadrant each point (or "symbol") represents four bits. 16 bits in one complete cycle. Each symbol is represented by two signals separated 90 degrees in phase. The two signals are interpreted as the real and imaginary parts (respectively) that make a complex number. Basically the two signals are vectors whose phase and amplitude represent the phase angle and magnitude, from this we can calculate a resultant vector that gives us our symbol. QAM64 uses 16 constellation points in each quadrant with each symbol representing 16 bits with 64 bits in one complete cycle. The higher the QAM the more rapidly the two signals must shift amplitude or phase. Also, each respective position for becomes closer and there for possibly less distinguishable from another. Symbols may be interpreted by the Rx as being an adjacent symbol. Higher QAMs at the same frequencies can transmit more data but a higher BER will result from the same amount of noise. I hope this helps. I'd be glad to elaborate further if needed.

 

[goonsvondoom]

dB answer for sonaiko

To answer your question why dB? and what the reference is... dB is commonly used to represent a difference between two power levels. It is a logarithmic unit of measurement that allows exponential changes to be represented as linear. dB by itself is dimensionless. +/- 3dB indicates that the power level has increased or decreased by 1 power. For instance if voltage A was 10V and was increased by 3 dB it would be 100V. A 6 dB increase would give you 1000V. There is no reference point with regards to dB by itself. However other measurements exist. For example dBmV is commonly used to measure RF. O dBmV = 1mV. Different numbers that serve as references for different measurements derived from the dB are chosen with different factors in mind but are all arbitrary to a certain extent. Here's a formula for dB ---- dB = 10Log(v1/v0) Where v0 is your start power and v1 is your end power. It's 10Log because a decibel is 1/10 of a Bel. Some measurements use 20Log, but I don't recall why.

 

[sonaiko]

Thank you goonsvondoom for ur good information.

I still need a clue how to calculate my No if I know my Eb so I can know on which point on the x-axis I am standing..

 

[goonsvondoom]

What exactly are you measuring?

What are you trying to measure and what tools do you have access to (such as meter, scope, etc.)? To measure BER you'd need a highly specialized meter. To measure SNR measure peak signal and peak noise. There are a few different methods I can think of but I need to know exactly what you're working with. What medium is the signal traveling on? Is what you're doing a scientific experiment or are you designing or troubleshooting a device... or something else? Please give more details.

 

[sonaiko]

What are you trying to measure and what tools do you have access to (such as meter, scope, etc.)? To measure BER you'd need a highly specialized meter. To measure SNR measure peak signal and peak noise. There are a few different methods I can think of but I need to know exactly what you're working with. What medium is the signal traveling on? Is what you're doing a scientific experiment or are you designing or troubleshooting a device... or something else? Please give more details.

I am just simulating right now i have no tools. I could simulate gaussian white noise (which is some random data with mean zero) and add it to my digital data using C programming language. Now I moved into simulating into verilog so I can apply the whole thing into FPGA.

So, using C, I can know Eb by integrating my digital signal squared over one period. How can I know my No of my bit? coz im adding the noise in a complete random manner.

So I need a way to know No so I can simply divide Eb/No and know which point I am in on the x-axis. Unless u have a better way ofcourse..

 

[goonsvondoom]

I am just simulating right now i have no tools. I could simulate gaussian white noise (which is some random data with mean zero) and add it to my digital data using C programming language. Now I moved into simulating into verilog so I can apply the whole thing into FPGA.

So, using C, I can know Eb by integrating my digital signal squared over one period. How can I know my No of my bit? coz im adding the noise in a complete random manner.

So I need a way to know No so I can simply divide Eb/No and know which point I am in on the x-axis. Unless u have a better way ofcourse..

Ok, so if I understand what you're saying, all data in the program is merely simulated (I'm still wondering what it's simulating a baseband signal like in a digital circuit or is it a broadband signal like RF transmission or Microwave?). I think (and correct me if I'm wrong) but the problem you're having is that since the SNR is measured in dB (therefore doesn't have a reference) you're not sure what to use for the noise or SNR. You said that you know the value of Eb by integrating the simulated digital signal squared over one period. Could you give me the specific detail of that calculation (when you say digital signal I'm not sure whether you're referring to it's amplitude, frequency, BER?). Also I'm not sure what any element (all the ones I'm familiar with at least) of a digital signal squared over one period would give you, unless this is something you've devised that's related the program calculating data in a certain manner. Let me give you an example, let's suppose we have a broadband transmission (RF). The medium that it's transmitted across has a noise floor which at a minimum (a medium at absolute zero I believe is 100% noise free) is equal to the noise created by the naturally occurring electron activity. A piece of coaxial cable, like you would find as a run between a satellite dishes LNB and the IF receiver, has a noise figure around -53dBmV. There is always a small amount of noise that is generated by the equipment and if there are any faults the system, outside noise can leak in. In one of my previous posts last evening I mentioned that 0dBmV = 1mV. This is the formula used to arrive at that number 10Log(1mV/1mV) = 0dBmV -- and 10Log(5nV/1mV) = -53.01dBmV -- Let's say the IF receiver requires an input of -10dBmV and +10dBmV. If our signal is 0dBmV and our noise floor is at -50dBmV our SNR would be 50dBmV. The point of all this is you need to make a determination of what normal signal is. You should also pick a number that represents the baseline noise. Determining normal signal level is easy with a broadband signal because the carrier is a sinusoidal wave form but with a baseband signal there are two normal states (high and low), with their own voltages respectively. If this is the case the problem you're working with is different then what I just described but at least a portion of the info will carry over. If you can tell me what type of signal you're simulating, what it's normal level(s) are and the scenario that's being simulated I might be able to get you a better answer. I took C++ class last year and I'm curious about the program. Is the purpose of the program to tell the user about the signal characteristics or is the program something that will run in something like an embedded system and the code needs to be fit to deal with possible BER impairments?

 

[Mickster]

goonsvondoom,

whilst you obviously know your subject, the current posting format is a little difficult to read for some.

Breaking the content into readable paragraphs makes it less likely that someone who could benefit from your experience may skip over it.

Regards.

 

[goonsvondoom]

Yeah, I thought about that. Usually I'd type something like this in word. Next time I post that long I'll make it more readable. Thanks.

 

[sonaiko]

goonsvondoom,

Thanks for the help.

Actually im simulating digital baseband signals for RF transmittion. You can read more about my system here. Also if u can make a suggestion there about what i need that would be amazing.

My digital levels are 5, -5. I added simple White Gaussian Noise before I generate my digital signal so im actually receiving values like 4.9, 4.8, 4.7, 5.1,5.2 ... etc when HIGH (3.5 ~ 6) and -4.9,-4.8, -5.2 .. etc when LOW. (-3.5 ~ -6).

Now u know that, my transmission medium is the wireless RF.

Now if I receive a HIGH bit, I know its supposed to be around 5v. So I can simply integrate 5*5 (squared) over the bit period (around 100ns if im receiving 10Mbps). This way I can know my Eb. I still need my No..

Any comments u say might probably help me figure this out..

 

[goonsvondoom]

goonsvondoom,

Thanks for the help.

Actually im simulating digital baseband signals for RF transmittion. You can read more about my system here. Also if u can make a suggestion there about what i need that would be amazing.

My digital levels are 5, -5. I added simple White Gaussian Noise before I generate my digital signal so im actually receiving values like 4.9, 4.8, 4.7, 5.1,5.2 ... etc when HIGH (3.5 ~ 6) and -4.9,-4.8, -5.2 .. etc when LOW. (-3.5 ~ -6).

Now u know that, my transmission medium is the wireless RF.

Now if I receive a HIGH bit, I know its supposed to be around 5v. So I can simply integrate 5*5 (squared) over the bit period (around 100ns if im receiving 10Mbps). This way I can know my Eb. I still need my No..

Any comments u say might probably help me figure this out..

Ok now I understand exactly, whats going on. This sounds like an interesting project. May I ask if this is related to work or school or is a hobby?

But I think I might have an answer for you. Oh and by the way in my last post where I was confused about squaring the digital signal over the period, I totally missed that that was your power formula (V^2)/(1/f)... got it...

Ok, my experience designing digital circuits is very limited (at best) but I think this may help you. Like I was saying in my last post, noise begins at any temp above absolute zero (and maybe at absolute zero too I'm not a physicist, but generally..). I found a formula that I think will be of great help. It's from wikipedia:

https://en.wikipedia.org/wiki/Noise_spectral_density

It said right on that link that that No = kT. where k is Boltzmann's Constant in joules per Kelvin and K is the systems noise temp in Kelvins. I'm afraid I may not be of any help as far as explaining how to use this, but it feels warm, if you know what I mean so check it out.

However you did give me some numbers above basically saying that the noise was +/- .1V for high and low. And the both high and low are ideally around 5V or -5V. You're basically saying that 5V is your signal and your noise is .1.

However the chart says the s/r is the energy of the bit divided by the spectral density of the noise. Unfortunately I've never dealt directly with such a problem, but now I'm interested so I'll keep you posted. I've been sitting here with my scientific calculator giving it a wing but I haven't come up with anything.

I think the key is going to involve you getting some temperature info about the circuit as I beleive the noise in question here is thermal noise. Check out that link and some of the others that link to it and let me know if that was useful at all...