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# How to measure the Eb/No of a digital BPSK signal ???

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#### cmosbjt

##### Full Member level 5
eb/n0

In order to measure the BER of my BPSK demodulator, I need to know what is the Eb/No of my input BPSK signal.

I use a function generator to generate the BPSK signal, which has a square waveform. Then I add white noise on top of the BPSK signal. By changing the white noise level, I can change the Carrier to Noise (C/N) ratio.

There is no band pass filter in front of the demodulator.

By definition:

Eb/No = C/N * Bw/fb (Bw is the bandwidth, fb is the bit rate)

Here are my questions:

1. The sqaure wave has a fundamental tone and many harmonics. How to determine the C/N? (using a spectrum analyzer (specifying the bandwidth) ? or a power meter (broad band) ? )

2. The BPSK signal I generate is a square wave, it has theoratically an infinate bandwidth as an ideal square wave has infinate harmonic components. So what is the bandwidth (Bw) in this case?

eb no measurement

You have to take a reasonable assumption for the bandwidth. I have read somewhere in most US standards, BW is defined as the spectrum that contains at least 90% of the energy of the signal. You could use that as a working defintion and find the bandwidth.

In principle the square wave has infinite amplitude, this is caused by the assumption of instantaneous transition from 0 to 1 and back. In reality the transition time is a small number and most of the energy is centered around the fundmental frequncy of the square wave itself.
-b

### cmosbjt

Points: 2
bpsk eb/no

I would suggest you to take a look at the spectrum. The answer should be obvious.

I would be more concerned about the measurement set up.

BRM

bpsk bw

Hi,

regards

bandwidth of bpsk signal

Every communication receiver has limitted bandwidth that determine the amount of noise get into the system. in theory the Receiver bandwidth is the minimum possible bandwidth of the transmitted signal. In practice transmiiter filter has special form that prevent aliasing the wellknow filter is rised cosine.

bpsk eb

I am using Spectrum analyzer to measure the in band noise density. The problem is, the input impedance of BPSK receiver is not 50Ohm, it is high impedance instead. The frequency is about 10Mhz. Therefore the signal source I am using is set to high impedance load. In this case, using the 50Ohm spectrum analyzer will have significant missmatch and will heavily load the signal gen. The singal it measure will not be the same as when my receiver is loaded. How to solve this problem?

I did a testing on a BPSK receiver. The measurement data is attached. Since the measurement is kind of tricky. I am not sure if the measurement is correct. So if you look at the measurement data, and if the data is correct, do you think the receiver is bad or average? Give me some comment please.

Thanks a lot.

eb n0 ber

Let's start from the beginning:
In the definition of Eb/N0 the BW is exactly the one occupied by the signal only (only first harmonic, in you case of square wave). When you will calculate the sensitivity of the overall receiver, then you should also consider the noise in the RX chain filter.

To go in the details of your measurement setup, most probably you are using an 33120A signal generator or a similar one. The only thing that the generator does when switching from 50 ohm load to high impedance load is to double the amplitude of the signal. Just take care of it in your calculation. Be aware of signal reflections when not matched (also if you have only 10 MHz, as you said, there are a lot of harmonics due to square wave shape, and a couple of meter cable can modify the shape of the signal. Check it at both end of cable.
there is a 3 dB difference between theory and meas for BER>1e-4. Check Signal level vs. noise level as I said before. Check also the bandwidth of bpsk filter in the receiver. It can add a significant noise if it's BW is larger than modulation BW.
There is a >3dB difference for BER=1e-5 and lower. Maybe you are not taking enough samples in these cases. Be aware that you need to take 10 times samples when going from BER=1e-n to BER=1e-(n+1) to keep the same accuracy.
I hope it can help.
Mazz

### cmosbjt

Points: 2
eb/no definition

Mazz said:
Let's start from the beginning:
In the definition of Eb/N0 the BW is exactly the one occupied by the signal only (only first harmonic, in you case of square wave). When you will calculate the sensitivity of the overall receiver, then you should also consider the noise in the RX chain filter.

To go in the details of your measurement setup, most probably you are using an 33120A signal generator or a similar one. The only thing that the generator does when switching from 50 ohm load to high impedance load is to double the amplitude of the signal. Just take care of it in your calculation. Be aware of signal reflections when not matched (also if you have only 10 MHz, as you said, there are a lot of harmonics due to square wave shape, and a couple of meter cable can modify the shape of the signal. Check it at both end of cable.
there is a 3 dB difference between theory and meas for BER>1e-4. Check Signal level vs. noise level as I said before. Check also the bandwidth of bpsk filter in the receiver. It can add a significant noise if it's BW is larger than modulation BW.
There is a >3dB difference for BER=1e-5 and lower. Maybe you are not taking enough samples in these cases. Be aware that you need to take 10 times samples when going from BER=1e-n to BER=1e-(n+1) to keep the same accuracy.
I hope it can help.
Mazz
The 1st harmonic of a sqare wave? Do you mean only the fundamental tone? The BPF filters out all the harmonic? Which means the signal is just a sinewave after the BPF, is that what you mean?
In reality, I don't have flexibility to change the BPF bandwidth. I have a BPF at about 10MHz, I have to live with whatever the bandwidth is.

measure eb/no

cmosbjt
yes I mean that you have to deal with only the fundamental tone. Let me try to explain better.
"1. The sqaure wave has a fundamental tone and many harmonics. How to determine the C/N? (using a spectrum analyzer (specifying the bandwidth) ? or a power meter (broad band) ? ) "
If I have understood your question, you are trying to relate the C/N of the measurement with the Eb/N0 in the simulation. The use of a spectrum analyzer is the correct option. The information is in the fundamental signal, not in its harmonics. The BW to use is the occupied signal BW to evaluate both signal and noise in order to have the same ratio as in Eb/N0.
Have you made progress to understand why there's a difference between simulations and meas?
Mazz

bandwidth of bpsk

using a specrum analyzer, measure the amplitude of the second haemonic and the next harmonics, if the ratio between the firs harmonic and second harmonic is very small, i think that the measured Eb/No is correspondig to the first harmonic

eb/n0 c/n

You can calculate the SNR as Ps/PN instead. Ps couls be measure easily in time domain (Ac^2/2) but how do you generate noise?[/quote]

eb measure meaning of

c/no eb/n0

there is a 3 dB difference between theory and meas for BER>1e-4. Check Signal level vs. noise level as I said before. Check also the bandwidth of bpsk filter in the receiver. It can add a significant noise if it's BW is larger than modulation BW.

oncerning receiver noise bandwidth. First, Eb/No is supposed to be a universal figure of merit for any kind of receiver, so it's measured at the receiver input terminals and is independent of anything inside that receiver. Different receiver designs for the same signal might use multiple filters with different shapes and bandwidths, but that would not affect the Eb/No of the signal at their inputs.

You cannot generate perfect square wave in real system. The spectrum will be filtered as sqrt(cos) and the like.

Add: if the the wave in basic band is square, then the bpsk wave will display sudden change.

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