You are right. But I have one more question.
The response h(t) of the matched filter is the reversed, time delayed version of the signal being transmitted. But if h(t) is dependent on the signal to be transmitted, then it means we'll have to design a seperate matched filter for each signal that we want to transmit. Can't we design a general match filter whose impulse response is independent of one single signal, so that we don't have to design a seperate matched filter for every signal we want to transmit?