I have generated colored noise from the white gaussian noise using auto-regressive model (by solving Yule-walker equation). The covariance matrix that I used to generate the colored noise is [1 0.2;0.2 1].
It shows that variance(power) of white noise and colored noise are same. So if I don't whiten the colored noise, the BER performance of the white noise and colored noise should be same because power of both noise are same (1 in this case).
But the simulation shows that the BER performance of colored noise is nearly 1.4 dB degraded as compared to the white noise. It seems the covariance term (0.2) is causing this BER degradation.
Can anyone please explain why this happened? I used the matched filter as the original pulse shape in both cases. Does this affect the performance?
I am considering my threshold as: if the matched filter output at signal interval >0 then bit 1 is transmitted else bit 0 is transmitted.