BPSK bit error probability help !!!

[anilresat]

Hi, i have a problem with calculating the bit error probability of BPSK modulation using the matched filter:

As it's known well the bit error probability of BPSK (with matched filter at the receiver) can be written as:

P(e) = ½*erfc(√SNR)

My problem is that from an article i've read that if the matched filter output is reduced by a factor for example A the bit error probability changes into this form:

P(e) = ½*erfc[(√SNR)*A]

What's the reason for that and what's the relationship between matched filter output and bit error probability for BPSK? Thanks in advance...

 

[Mityan]

From wiki: In telecommunications, a matched filter is obtained by correlating a known signal, or template, with an unknown signal to detect the presence of the template in the unknown signal.
So the output of matched filter is correlation between received signal and template. The less correlation - the more the BER.
Or in terms of SNR (the same wiki article): The matched filter is the linear filter, h, that maximizes the output signal-to-noise ratio.
The less the output - the less the SNR which leads to BER growth.