Hi
Let me confirm I understood your question properly. You want to estimate the shape of the transmitted signal. But you don't know what shape this signal has, is that true??
If it is true, you should consider other assumptions as well. For example, need to know the frequency band in which your signal is transmitted, if you receive a signal whose band is wider or narrower than your signal, then your signal will be totally distorted. You need to know the nature of the propagation channel, if it is nonlinear around your signal's bandwidth, then it definitely distort the shape of your signal.
well, good luck in your project
Sal