In Slide 6 of this PDF, it says that the performance of binary signaling is as follows:

enter image description here

I can understand the approximation for high SNR in the incoherent FSK and DPSK case, but how do we get the approximation for the coherent BPSK and FSK case?


For coherent BPSK, Taylor series expansion for is as follow,

If X = SNR, then its expansion for [X/(1+X)]^1/2 is, = 1 - 1/2X + O(1/X^2), now put into your equation of P(e), You will get as you stated.


for all approximation you have to expand SNR equation through this formula, (aX + b)^n = a^n.X^n - n.a^(n-1).b.X^(n-1) ... n.a.b^(n-1).X + b^n

Using "a" "b" and "n" to stand for any coefficient or exponent we might have

  • \$\begingroup\$ Is there something missing after your first line? The Taylor series expansion? \$\endgroup\$ – Rayne Mar 27 '16 at 11:36
  • \$\begingroup\$ No, is start from so, I think I have to remove, let me edit. \$\endgroup\$ – Prakash Darji Mar 27 '16 at 11:44
  • \$\begingroup\$ I'm sorry, I still can't tell how you got [X/(1+X)]^1/2 = 1 - 1/2X + O(1/X^2)... \$\endgroup\$ – Rayne Mar 27 '16 at 11:57
  • \$\begingroup\$ It's ok now, I finally understand. Thanks for pointing me in the correct directions! \$\endgroup\$ – Rayne Mar 27 '16 at 12:09
  • \$\begingroup\$ you're welcome... \$\endgroup\$ – Prakash Darji Mar 27 '16 at 12:17

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