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4th July 2015, 23:47 #1
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Data rate rate as a function of SNR and bandwidth
I plotted BER vs SNR for BPSK modulation in Matlab and I am given bandwidth of channel (bandlimited channel). lets say it is BW1. I would like to find the data rate based on this information. I am using Shannon capacity formula: Therefore
C=BW*log2(1+SNR).
However I wonder for this equation the bandwidth is actually bandwidth of my channel or not? also what is the SNR since in Matlab we usually loop through the eb/No and call that one SNR can I use that value for SNR or should I convert it to real SNR by multiplying by a constant?

5th July 2015, 02:25 #2
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Re: Data rate rate as a function of SNR and bandwidth
It is the bandwidth of the channel. However, you can plot the normalized capacity C/BW in bit/s/Hz. For each SNR there is a capacity, so you need to loop over the range of SNR of interest to plot the capacity curve. If you are using BPSK, you cannot achieve the capacity at high SNR.

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5th July 2015, 03:42 #3
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Re: Data rate rate as a function of SNR and bandwidth
Thanks. I have SNR =32 for BER=0.01. Therefore I cannot achieve this capacity is that correct? what modulation scheme do you suggest ?

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5th July 2015, 03:57 #4
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Re: Data rate rate as a function of SNR and bandwidth
A good design question lists your overall requirements™ The best question deserves a better answer. ™
... Tony Stewart EE since 1975

5th July 2015, 17:59 #5
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Re: Data rate rate as a function of SNR and bandwidth
Thanks I will post the detail of my system as well. Just one question that I still need to know. What is SNR in the above equation? Since in Matlab we loop through eb/No can I use those values for SNR ? should I convert it by multiplying by data rate and divide by bandwidth?
Thanks.

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6th July 2015, 01:33 #6
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Re: Data rate rate as a function of SNR and bandwidth
Capacity is only achieved when Gaussian symbols are transmitted, which is not realistic. If you are using BPSK the corresponding capacity is called the achievable rate, and it is 1 bit/channel use for uncoded symbols. You cannot exceed this. However, at low SNR, since the Gaussian noise is the dominant factor, the capacity and achievable rate are almost identical.
   Updated   
Not necessary. You just define SNRdB=0:20, and compute the capacity for each point in linear scale SNR=10.^(SNRdB./10), and then plot SNRdB vs. the capacity with semilogy command in MATLAB. That is it.
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Are you doing simulations over AWGN channel?
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6th July 2015, 01:37 #7
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Re: Data rate rate as a function of SNR and bandwidth
Yes. Simulation is done over AWGN channel.

6th July 2015, 01:48 #8
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Re: Data rate rate as a function of SNR and bandwidth
It also assumes only a matched receiver filter with zero ISI group delay is used so the gaussian channel only has gaussian noise and no unequal group delay, skew, asymmetry or added noise.
It also requires an ideal discriminator that integrates all the energy of the symbol with ideal clock synchronization for sampling the total energy at exact end of symbol Time to determine the symbol value .
... rather than weaker methods of centre sampling.
the BER curve of actual results vs ideal tells me where opportunities exist to improve a design using different data patterns. I used best case, worse case and random data to compare. Threshold of curve and slope of curve of actual vs ideal.
I also used this method for early magnetic RLL HDD's when soft and hard error rates were important to my evaluation. An error budget can be created for any design sections and thus compared.A good design question lists your overall requirements™ The best question deserves a better answer. ™
... Tony Stewart EE since 1975

6th July 2015, 01:57 #9
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6th July 2015, 03:35 #10
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Re: Data rate rate as a function of SNR and bandwidth
I have a band limited channel before AWGN channel I belie this is effect of ISI. What do you think about this?

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7th July 2015, 03:36 #11
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Re: Data rate rate as a function of SNR and bandwidth
ISI is caused by ripple in group delay (rate of change in phase) over spectrum
Choose Raised Cosine filter instead.
https://en.wikipedia.org/wiki/Raisedcosine_filterA good design question lists your overall requirements™ The best question deserves a better answer. ™
... Tony Stewart EE since 1975
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