BPSK BW Requirement

Started by maxplus 9 months ago9 replieslatest reply 8 months ago340 views

I captured a BPSK waveform at RF on a spectrum analyser.  I need to determine the 99% bandwidth.  I have a CSV plot. Does anyone knows how to determine 99% BW from CSV plot?

Also, I need to determine the BW requirement for a given bit rate.  But it is confusing as some text books states that the BW is equal to the bit rate.  Others sources quote as twice the bit rate (maybe they referring to the complete main lobe with both sides).  If a filter is used then the roll off factor should be taken into consideration.  So what is the BW requirement for a BPSK waveform.  I thought it is twice the bit rate to take into negative and positive sides about Fc. Thank you

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Reply by SlartibartfastSeptember 1, 2023

For BPSK the symbol rate is equal to the 3dB bandwidth, which won't change for most pulse filter shapes.   The payload bit rate then depends on consideration for any Forward Error Correction (FEC) code rate, overhead for framing, etc.

The coded bit rate will double for QPSK compared to BPSK, but the symbol rate will still be equal to the 3dB bandwidth.  Basically, for any PSK, QAM, APSK, etc., single-carrier signal the symbol rate is usually equal to the 3dB bandwidth.

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Reply by kazSeptember 1, 2023

Well, back to basics. For plotting vector of N samples apply FFT and scale frequency axis as(0:1/N:1-1/N)*Fs Then measure bandwidth from 0 to 3db point(baseband)

For baseband, bandwidth needs to be restricted by shaping filter otherwise it will cause trouble to adjacent signals. The maximum frequency to be passed is half symbol rate (for BPSK symbol rate = bit rate). This frequency represents 10101010... so you can imagine that such pattern can be recovered by receiver from the peaks and troughs of this frequency. All other symbol patterns fall below 10101010... in terms of frequency. 

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Reply by maxplusSeptember 1, 2023

Many thanks for your explanation.

In the message,  it states that the 3dB of BPSK is the symbol rate.

I thought that the first null either side of Fc every 1/symbol rate. 

How would I determine the 99% bw? 

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Reply by ReinoTSeptember 1, 2023

I assume that the spectrum you got is a power spectrum. You need to integrate it as function of frequency using a suitable integration formula to prepare a cumulative power i.e. 100% power. Then starting from lowest frequency spot the frequency where the cumulative value is 0.5%. On the high side of the cumulative spectrum search 99.5% point and the corresponding frequency. The difference of those frequencies is you 99% bandwidth. you You may need to use an interpolation to get those frequencies depending on the frequency resolution of your csv file.

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Reply by ReinoTSeptember 1, 2023

I forgot to point you a reference to the issue. Rec. ITU-R SM.853-1.


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Reply by kazSeptember 1, 2023

The definition of bandwidth is based on 3dB point since the transition band is hard to follow through. For example in the case of root raised cosine filter with beta rolloff, the transition band starts rolling off at the frequency of (1 – Beta) x Rs/2 reaching the -3dB cut-off point at the frequency of Rs/2. Any frequency energy beyond Rs/2 is viewed as unavoidable excess band.

I guess your 99% means beta is 0.01 of Rs/2. 

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Reply by maxplusSeptember 4, 2023

Many thanks for the assistance. 

I read Proakis Digital Communications text book and a tutorial on Shannon in ComplextoReal, the bandwidth is equal to the symbol rate.


Where will be the first null be occurring?

Just checking, do you have an interpolation file to calculate OBW. Thank you.

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Reply by ReinoTSeptember 6, 2023

The requirement was to determine 99% bandwidth from a measurement. The 99% bandwidth is one of the definitions that is used to define how much a signal uses bandwidth without causing too much interference to other users. Another measure how much interference is generated is a neighbor channel attenuation. A typical requirement is 70 dB. The signal shaping has an important effect to the 99% and especially neighbor channel attenuation. 

The calculation is done using integration of the power spectrum of the signal. Note it is not the FFT amplitude spectrum that is usually given in linear scale.

There is another issue that effects to the calculation result. It is the bandwidth of the measurement equipment. I assume that for your purpose it was defined properly. Usually there is a certain difference between theoretical spectrum and measured one due to the measurement equipment bandwidth and modulation implement imperfections.

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Reply by kazSeptember 6, 2023

Thanks, hence for applying the 99% bandwidth definition to a single vector I will suggest the following:

Do N point FFT on vector, square each output to get power per bin (I^2+Q^2). Add up all to get total power. 

DC centre the bins and add up power from first negative bin until their sum becomes 0.5% of total power. determine frequency at the bin (F1).

Keep adding until your sum becomes 99.5% of total power. Determine frequency of the bin(F2).

99% bandwidth = F2-F1