I think you probably refer to the case where you take the magnitude of the signal to do the detection and in that case I agree with you. However, in rocpfa, the coherent case means that you don't have to use the magnitude. Instead, you can do a perfect match and only deal with noise in the I channel. Hence the threshold will be different and therefore the Pd are a bit different too.
Different plots using rocpfa
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I got different plots using rocpfa for 1 pulse with Coherent and Non-Coherent integrations. However, it should give the same answer.
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