# Approximation for high SNR

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

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?

## 1 Answer

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

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