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# Help with Eb/No and BER relationship for QPSK-Viterbi(DVB-S)

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#### clein

##### Newbie level 3
dvb-s ber

Hello!

I need to simulate with Matlab a QPSK modulation using Viterbi Coding. I need to obtain the theoricals graphs of the Eb/No and BER relationship for differents code rates (in fact, I need to obtain the graphs for Eb/No and BER relationship for a DVB-S system).

From "Error Control Systems", Stephen B. Wicker I have that BER can be calculated for BPSK as follows:

Pbsk = (1/k)·Q(√2dfree Eb/No)

If for a QPSK we have that Pqpsk = (1-Pbsk)², I obtain that:

Pqpsk = (2/k)·Q(x)·( 1 - ½·(1/k)·Q(x) ) where x = √2·dfree·Eb/No

Well, if I try to calculate it with Matlab I don't obtain the values that are specified in ETSI EN 300 421, I obtain lesser values of BER.

I calulate it defining some values of Eb/No and using dfree values indicated in ETSI EN 300 41.

I would like to know what are the mistakes, if I'm in the correct way or if there is another way to solve it.

Thanks!

qpsk viterbi

If somebody is interested in this item, I've found the answer in 'DVB Document A014 Rev. 1 March 1998' Annex G.11

The BER after Viterbi in the DVB-S is less or equal than:

Pb(Eb/No) ≤ 1/k * 1/2 * Σ (d = dfree, ∞) w(d) · erfc(√Rc·d·Eb/No)

where:

Rc = k/n (code rate)
w(d)≡weigth of d (see document).

Re: dvb-s ber

Dear Clein,
Could you email me your m. file for the DVBS simultation. I have done the similar in .mdl but thought it is easier to simulate in m file. i can send you my model if you are interested.

thanks.

Hello!

I need to simulate with Matlab a QPSK modulation using Viterbi Coding. I need to obtain the theoricals graphs of the Eb/No and BER relationship for differents code rates (in fact, I need to obtain the graphs for Eb/No and BER relationship for a DVB-S system).

From "Error Control Systems", Stephen B. Wicker I have that BER can be calculated for BPSK as follows:

Pbsk = (1/k)·Q(√2dfree Eb/No)

If for a QPSK we have that Pqpsk = (1-Pbsk)², I obtain that:

Pqpsk = (2/k)·Q(x)·( 1 - ½·(1/k)·Q(x) ) where x = √2·dfree·Eb/No

Well, if I try to calculate it with Matlab I don't obtain the values that are specified in ETSI EN 300 421, I obtain lesser values of BER.

I calulate it defining some values of Eb/No and using dfree values indicated in ETSI EN 300 41.

I would like to know what are the mistakes, if I'm in the correct way or if there is another way to solve it.

Thanks!

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