I'm currently testing the performance of an energy detector using two tests. One test involves finding the optimal threshold to achieve a probability of detection(Pd) of 0.9 and a probability of false Alarm (Pfa) of 0.1.

Having completed the first test, the next test I want to do is to see how varying SNR affects both Pd and Pfa, given a constant threshold. If Pd is the probability of the detector detecting a signal given the signal of interest is being transmitted and pfa is the probability of the detector detecting a signal given the signal of interest is not being transmitted how exactly can I vary SNR to get Pfa. I'm sure its something that I'm not quite understanding but if the signal of interest is not being transmitted and all that the receiver is picking up is noise, how do I have a SNR?

I'm currently testing the performance of an energy detector using two tests. One test involves finding the optimal threshold to achieve a probability of detection(Pd) of 0.9 and a probability of false Alarm (Pfa) of 0.1.

Having completed the first test, the next test I want to do is to see how varying SNR affects both Pd and Pfa, given a constant threshold. If Pd is the probability of the detector detecting a signal given the signal of interest is being transmitted and pfa is the probability of the detector detecting a signal given the signal of interest is not being transmitted how exactly can I vary SNR to get Pfa. I'm sure its something that I'm not quite understanding but if the signal of interest is not being transmitted and all that the receiver is picking up is noise, how is there a SNR in the case of Pfa?