# Data rate rate as a function of SNR and bandwidth

1. ## 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?

2. ## 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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3. ## 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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4. ## Re: Data rate rate as a function of SNR and bandwidth

Originally Posted by chessmath2009
Thanks. I have SNR =32 for BER=0.01. Therefore I cannot achieve this capacity is that correct? what modulation scheme do you suggest ?
That is good SNR. Show details of eye pattern and schematic. Does your filter have ripple or group delay distortion , excess ISI?
What is used for clock recovery? Comparator?

5. ## 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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6. ## Re: Data rate rate as a function of SNR and bandwidth

Originally Posted by chessmath2009
Thanks. I have SNR =32 for BER=0.01. Therefore I cannot achieve this capacity is that correct? what modulation scheme do you suggest ?
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.

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Originally Posted by chessmath2009
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.
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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Originally Posted by chessmath2009
Thanks. I have SNR =32 for BER=0.01. Therefore I cannot achieve this capacity is that correct? what modulation scheme do you suggest ?
Are you doing simulations over AWGN channel?

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7. ## Re: Data rate rate as a function of SNR and bandwidth

Yes. Simulation is done over AWGN channel.

8. ## 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.

9. ## Re: Data rate rate as a function of SNR and bandwidth

Originally Posted by chessmath2009
Yes. Simulation is done over AWGN channel.
Why then you have BER of 0.01 at SNR=32 (is this dB?). In AWGN with BPSK you will have BER much lower than that at SNR=10dB (I think in the order of 10^-5 or something). How do you compute the BER?

10. ## 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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11. ## 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