A carrier component is transmitted on the quadrature carrier in a communication system t...

A carrier component is transmitted on the quadrature carrier in a communication system that transmits information via binary PSK. Hence, the received signal has the form

where φ is the carrier phase and n(t) is AWGN. The un modulated carrier component is used as a pilot signal at the receiver to estimate the carrier phase.

a. Sketch a block diagram of the receiver, including the carrier phase estimator.

b. Illustrate mathematically the operations involved in the estimation of the carrier phase φ.

c. Express the probability of error for the detection of the binary PSK signal as a function of the total transmitted power PT = Ps + Pc. What is the loss in performance due to the allocation of a portion of the transmitted power to the pilot signal? Evaluate the loss for Pc/PT = 0.1.