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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?

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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.

Note:

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

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  • \$\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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