A BPAM system is used to transmit information using the following pulse and signal constellation:

 

If the BPAM signal has a phase of φ and frequency fc, use the mean of the samples at the MF output as the likelihood function and derive a Maximum Likelihood method for estimating φ from the received signal.

 

Assuming φ is small, draw a block scheme implementing the estimator. 

g(t) AME fc [Hz] t [sec] '00' '01' '10' '11' 1 2 3 4 y(t)