fsk BER vs eb/no chart

[robismyname]

fsk ber

Has anyone seen a BER vs Eb/No chart for FSK that goes down to 10^-6? I see alot of BER vs. Eb/No charts for 802.11 modulation techniques but nothing for FSK. IF you know wher I can find it please provide link or post document.

 

[madengr]

eb/n0

Yes, in Sklar's "Digital Communications". For PB=10E-6 non-coherent FSK you need about Eb/N0=15 dB. For coherent FSK its Eb/No=14 dB. Here are the formulas:

Coherent:
PB=Q(sqrt(Eb/N0))

Non-coherent:
PB=1/2*e^(-1/2*Eb/N0)

For PE<10E-4 non-coherent requires only 1 dB more than coherent.

 

[robismyname]

fsk bit error rate

Yes, in Sklar's "Digital Communications". For PB=10E-6 non-coherent FSK you need about Eb/N0=15 dB. For coherent FSK its Eb/No=14 dB. Here are the formulas:

Coherent:
PB=Q(sqrt(Eb/N0))

Non-coherent:
PB=1/2*e^(-1/2*Eb/N0)

For PE<10E-4 non-coherent requires only 1 dB more than coherent.

Thanks!

I forgot that I have this book..Bernard Sklar, 1988 edition. I will check into it. BTW, what is the difference between coherent and noncoherent? Is it synonomous to NRZ (non return to zero) and RZ?

 

[biff44]

ber fsk

I second that question. Have never heard of "coherent fsk".

Usually "coherent" refers to a system that locks the local oscillator phase to the average phase of the received signal, in some sort of carrier tracking loop. Since there is no phase information in an FSK signal, just what does coherent detection mean?

 

[madengr]

ber eb/n0

Sklar says that in coherent FSK the two symbols are always orthogonal (zero correlation). I take it this means the beat frequency of the two tones is an integer multiple of the data rate; similar to OFDM. Since they are orthogonal you can use a true matched filter to get the maximum energy of each symbol. However coherent FSK requires 3 dB more Eb/N0 than BPSK for the same PE, and requires the same hardware, so it's pointless to use.

The non-coherent FSK demodulation from bit-banging a VCO only looks at the envelope; i.e. the tried and true discriminator and data-slicer.

Since there is no phase information in an FSK signal, just what does coherent detection mean?

If you wait until both tones cross zero at the same time before sending one or the other then the phase would be preserved. So if the transitions of your data bits occur at these crossings then the symbols would be orthogonal.

 

[robismyname]

coherent fsk ber

I found a QPSK BER vs eb/no chart in Dr. Kamilo Feher's book - Wireless Digital Communication. I was comparing the channel capacity for QPSK and FSK modulation using the equation:

channel capacity=[BW]log2(1+S/N) (from Daniel M Dobkins Book)

i used BW=1MHz; S/N came from the BER vs eb/no FSK and QPSK charts

From my analysis I found that FSK has better channel capacity than QPSK? Is this true? How can this be. Perhaps I am using the wrong QPSK BER vs eb/no chart?

I thougt QPSK would have better channel capacity than FSK because at the same bw of fsk, qpsk will have 2 times the data rate of fsk

FSK Channel Capacity
[BW]log2(1+S/N)
3.56 Mbps BER of 10^ - 3 (SN = 10.8)
3.71 Mbps BER of 10^ - 4 (S/N = 12.1)
3.82 Mbps BER of 10^ - 5 (S/N = 13.1)
3.89 Mbps BER of 10^ - 6 (S/N = 13.8)


QPSK Channel Capacity
[BW]log2(1+S/N)
2.87 Mbps BER of 10^ - 3 (S/N=6.3)
3.23 Mbps BER of 10^ - 4 (S/N = 8.4)
3.39 Mbps BER of 10^ - 5 (S/N =9.5)
3.50 Mbps BER of 10^ - 6 (S/N =10.3)

 

[madengr]

eb n0 ber

You need to double the S/N for QPSK in your capacity calculations. Think of it this way; you send the same bit stream to FSK and QPSK modulators, but the QPSK de-multiplexes the bit stream and modulates two orthogonal carriers, therefore the Eb/N0 is doubled, so is the S/N, so your channel capacity doubles.

That PSK error chart is misleading; instead of "Probability of Bit Error" and "Eb/N0" the axis should be re-labeled "Probability of Symbol Error" and "Es/N0". It's 1 bit/symbol for BPSK, 2 bits/symbol for QPSK. The RF channel contains symbols, not bits. The bits come out of a demodulator. If he is going to call it bits he needs to break out QPSK and BPSK on separate curves.

 

[robismyname]

fsk　ber

You need to double the S/N for QPSK in your capacity calculations. Think of it this way; you send the same bit stream to FSK and QPSK modulators, but the QPSK de-multiplexes the bit stream and modulates two orthogonal carriers, therefore the Eb/N0 is doubled, so is the S/N, so your channel capacity doubles.

When you say the EB/No is doubled, do you mean add 3dB to Eb/No or multiply the Eb/No by 2? For instance if I use the QPSK BER vs Eb/No chart and find that for BER of 10^-3 my Eb/No is 6.3. Do I add 3db to 6.3 to make 9.3 or do I multiple 6.3x2 to get 12.6? All the books add 3dB. Do you have a better QPSK chart than the one Feher has? I'm suspecting that Feher chart is not accurate. Because Sklar's FSK chart and Feher's QPSK chart has very similar Eb/No's across all the BER's (10^-1 - 10^-7) I was expecting QPSK to have higher Eb/No's than FSK.

That PSK error chart is misleading; instead of "Probability of Bit Error" and "Eb/N0" the axis should be re-labeled "Probability of Symbol Error" and "Es/N0". It's 1 bit/symbol for BPSK, 2 bits/symbol for QPSK. The RF channel contains symbols, not bits. The bits come out of a demodulator. If he is going to call it bits he needs to break out QPSK and BPSK on separate curves.

Good observation. Good point about seperating BPSK and QPSK.

I noticed in Sklar book his FSk chart is labeled "Bit Error Probability,PB" and Eb/No. In Feher book he labels PSK as "Probablity of Bit Error, PE" and Eb/No. Is PE and PB synonomous in this situation?

 

[madengr]

eb n0

Add 3dB. When talking about bits going in/out of a mod/de-mod then QPSK has 3dB higher Eb/N0 than BPSK.

Technically PE is probability of symbol error, and PB is bit error. I think Fehrs chart is just wrong; he should have called it symbol error and used Es/N0 for the X-axis. Sklar does the same thing. Really all you need to consider is that QPSK has 3dB higher Eb/N0 than BPSK for the same data rate, or can handle twice the data rate for the same PB as BPSK. Sklar says QPSK has two orthogonal channels of BPSK. I don't like that terminology. The channel is a physical path through space and circuitry in which symbols pass, not bits. See section 3.8.4 of Sklar and that will clear things up. What is really needed is chart comparing BPSK, QPSK, and m-ary PSK with EB/No and PB referenced to the modulator I/O, not some channel.

 

[bingdao89]

coherent fsk

Yes, in Sklar's "Digital Communications". For PB=10E-6 non-coherent FSK you need about Eb/N0=15 dB. For coherent FSK its Eb/No=14 dB. Here are the formulas:

Coherent:
PB=Q(sqrt(Eb/N0))

Non-coherent:
PB=1/2*e^(-1/2*Eb/N0)

For PE<10E-4 non-coherent requires only 1 dB more than coherent.

Thanks!

I forgot that I have this book..Bernard Sklar, 1988 edition. I will check into it. BTW, what is the difference between coherent and noncoherent? Is it synonomous to NRZ (non return to zero) and RZ?

i think this is really right!